IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

470 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

A COMPARATIVE STUDY OF AHP, ELECTRE III & ELECTRE IV 

BY EQUAL OBJECTIVE & SHANNON’S ENTROPY OBJECTIVE 

& SAATY’S SUBJECTIVE CRITERIA WEIGHTING IN A 

PRIVATE SMALL HYDROPOWER PLANTS INVESTMENTS 

SELECTION PROBLEM 

 
Burak Omer Saracoglu  

Orhantepe Mahallesi,  

Tekel Caddesi,  

Geziyolu Sokak,  

34865 Dragos, Kartal, Istanbul, Turkey 

E-mail: burakomersaracoglu@hotmail.com
1
 

 

 

ABSTRACT 

 

Private small hydropower plant investments are more challenging than medium and large 

private hydropower plant investments when considering engineering analysis. One of the 

necessary tasks is the selection of the most appropriate private small hydropower 

investment amongst several alternatives. Brokerage, consultancy and private investor 

activities are a few examples of these kinds of real world activities. There are many 

multi-criteria decision making (MCDM) or multiple-criteria decision analysis (MCDA) 

methods, and different researchers prefer different methods This research study 

investigates three methods at once for the same problem: Analytic Hierarchy Process 

(AHP), Elimination and Choice Translating Reality (ELECTRE) III and ELECTRE IV. 

A comparative investigation is conducted on one simple unique selection model for all 

three methods. This unified model has seven objective factors (catchment area, project 

runoff, net head, flow rate, firm energy, secondary energy, investment cost). An 

additional comparison is also made on the criteria weighting amongst equal objective, 

Shannon’s Entropy objective and Saaty’s subjective criteria weighting. The simplistic 

unified model is structured in three levels. There are seven alternatives in the pre-

development investment stage. The Super Decisions software and the ELECTRE III-IV 

software are implemented in this study. The pairwise comparisons of factors results in an 

inconsistency value of 0,09511 which is 7
th
 in the Saaty's AHP weighting. The Shannon’s 

Entropy objective weighting represents a difference in the rate of the expert decision 

maker’s evaluations ranging between -67% and 671%. The equal weighting represents a 

rate change between -64% and 626%. Both approaches can't represent human judgments 

(here only one expert decision maker) well in this model. Fortunately, the same 

                                                 
1
 Acknowledgements: The author would sincerely like to express his deepest thankfulness to Mrs. 

Rozann Whitaker Saaty for her guidance, help and pre-review, to Dr. David Weiss for his help on 

the Carrot
2
, also to the REN21 Secretariat, and to Mr. Steinar Hansen on behalf of the Smakraft 

for the digital graphics and photos. 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

471 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

alternative (Alternative 3) ranks first. These findings promise that further studies on this 

subject can give some clues for the development of an autonomous computer based 

intelligent decision support system. Some observed pros and cons of these methods are 

also presented in this study. The observations and critical issues are presented during 

modeling, application, evaluation and analysis to help researchers, consultants, and 

readers in the small hydropower investments research and practical fields.   

 

Keywords: AHP; Carrot
2
; ELECTRE III; ELECTRE IV; investment; Shannon’s Entropy; 

small hydropower plant 

 

 

1. Introduction 

The importance and effectiveness of renewable energy in solving climate change and 

economic growth problems have been accepted by governing bodies in many countries in 

the world today. The Renewable Energy Policy Network for the 21st Century (REN21), 

which is an international non-profit association at the United Nations Environment 

Programme (UNEP), has recorded that 145 countries in the world have renewable energy 

support policies and 164 countries have renewable energy targets set by early 2015 

(Figure 1). Accordingly, this research study aims to contribute to scientific studies and 

developments in this field.  

 

 
 

Figure 1. Countries with renewable energy policies and targets  

(Source: REN21, 2015) 

 

There are various renewable power generation types that produce clean energy, such as 

concentrating solar thermal, geothermal, hydro, photovoltaics, and wind (REN21, 2015). 

Today, hydropower is the most widely installed renewable energy type. 

 

The history of hydroelectric power plants started in the Cragside country house in 

Northumberland, England in 1878. In those days, this technology could only power a 

single lamp. The first hydropower plant, generating 12,5 kilowatts (kW) in a private and 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

472 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

commercial customer system (equivalent 250 lights), was commissioned on the Fox 

River in Wisconsin, USA in 1882 (IEA Hydropower, 2015; IHA, 2015; NHA, 2015; 

Schmidt & Denny, 2004). This long history has placed hydropower technology in an 

advantageous position amongst the other renewable energy technologies. Technical and 

technological maturity, very long lifespan and economic competitiveness are some of 

these advantages (Hall, 2003; IHAICLD, 2000; Lako et al., 2003). Thus, hydropower 

technology should always be on the radar of private investors (power plant portfolio) 

throughout the world. 

 

Hydropower plants are usually classified according to their installed capacities. One of 

the detailed classification approaches splits the installed capacities into the categories 

large, medium, small, mini, micro and pico. The upper limits and lower limits of these 

groups differ in several regions. For instance, the upper limit (25.000 kW) and the lower 

limit (1.000 kW) are common for the small hydropower plants in India. In the United 

States of America, these limits are presented as 1.000 kW and 30.000 kW (Bajaj et al., 

2007; Berakovic et al., 2009; Dragu et al., 2010; EREC, 2012; Kurien & Sinha, 2006; 

Moreire & Poole, 1993; Saxena, 2007). In this study, the small hydropower plants are 

accepted as 1 MW < P ≤ 10 MW. This range was chosen based on the installed capacities 

in the electricity generation licensing procedures in Turkey by the Electricity Market Law 

6446, the Regulation on the Unlicensed Electricity Generation in the Electricity Market, 

and the Communication Concerning the Application of Regulation on the Unlicensed 

Electricity Generation on the Electricity Market of the Republic of Turkey (Official 

Gazette 28603, 2015; Official Gazette 28783, 2015), and the definition of small 

hydropower plants supported by the European Commission (EC) and the European Small 

Hydropower Association (ESHA) (EC, 2014; ESHA et al., 2008).  

 

Small hydropower plants are more challenging than large and medium hydropower 

plants, because they have little or no storage reservoir. Their investment analysis and 

decisions regarding them are more difficult than others. Consequently, this study focuses 

on private small hydropower plant investment decisions. Two private small hydropower 

plants are presented in Figure 2.  

 

 
 

Figure 2. Two private small hydropower plants in Norway: Vassvik 3.100 kVA 

(left), Ytre Alsaker 5.490 kVA (right)  

(Source: Småkraft AS http://www.smaakraft.no/) 

 

This research study concentrates on Turkey and is conducted there for three main 

reasons. The first reason is that it is the homeland of the author. The second reason is the 

http://www.smaakraft.no/


IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

473 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

level of interest and the excitement of private investors (foreign and domestic) about 

small hydropower plants in Turkey demonstrated by the number of license applications. 

There are more than 200 private small hydropower plant license applications as of 

September 2013 according to the official website of the EMRA (Republic of Turkey 

Energy Market Regulatory Authority) (EMRA, 2013). The final reason is the 

characteristics of the private investors' in Turkey. Simple observations made before this 

study show that these investors have very different organizations, management 

approaches, and capabilities. However, similar research studies on this core subject can 

be organized and performed in different countries because of the existence of small 

hydropower plants in 148 countries or territories (total 75 GW in 2011/2012: Asia 65%, 

Europe 16%, Americas 13%, Africa 5%, Oceania 1%) worldwide (UNIDO and ICSHP, 

2013). In short, this research study isn't particular, specific and unique to Turkey, but the 

comparative case is performed in Turkey. 

 

Another important issue is the knowledge creation, the knowledge acquisition, and the 

problem statement and scope of this study. There is only one expert decision maker or 

"intellectual capital" in this application. The declarative, the procedural, the causal, the 

conditional, the relational, and the pragmatic knowledge types are based on the 

knowledge created by several resources and the ones acquired as shown in Figure 3. The 

research scope focuses on the second hand tasks such as the brokerage, the consultancy 

and the private investors' activities. 

 
 

Figure 3. Data, information, knowledge environment and model in this study (Icon: 

signore_green, 2015; see terms for knowledge: Alavi & Leidner, 1999)  

(GIS: geographic information system, EMRA: Republic of Turkey Energy Market 

Regulatory Authority, DSI: General Directorate of State Hydraulic Works) 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

474 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

Finally, this research study was inspired by previous research studies by Saracoglu 

(2015a,b,c) on decision making and small hydropower plant investments. In these 

studies, ELECTRE III (ELECTRE: Elimination and Choice Translating 

Reality/Elimination Et Choix Tradusiant la Realite), ELECTRE IV, Shannon’s Entropy, 

AHP (Analytic Hierarchy Process), and DEXi (Decision EXpert for Education) were 

implemented in the investment selection of small hydropower plants. Moreover, research 

by Saaty and Daji (2015), and  Zanakis et al., (1998) inspired the idea for this research.  

 

The main research aim of this study is very well described by a quote: “Good decisions 

come from experience, and experience comes from bad decisions” (possibly by Mark 

Twain, American novelist and journalist).  

 

According to the author's point of view, these kinds of studies are very important for 

understanding small hydropower plants, their investments and the decision making 

methods. Researchers and practitioners in this field can learn from this approach and take 

into account the critical success and failure issues based on the outcomes and findings of 

this study in the short and long term. 

 

In this paper, a comparison is made on the findings of the combination of ELECTRE III, 

ELECTRE IV, and AHP methods with Shannon’s Entropy, Saaty’s AHP, and equal 

weighting approaches. The comparison is based on a unique model, and therefore no 

model differences exist to be investigated. Moreover, the alternatives are taken from real 

life applications and are the same for each combination of methods, and therefore no 

alternative differences exist to be investigated. Above all, this comparative study will 

hopefully contribute to the previous studies in the literature (Saracoglu, 2015a,b,c) in 

order to develop an autonomous computer based intelligent decision support system for 

the real world cases.  

 

2. Previous research in the literature 

Key terms were defined in order to get the best hit rates on online scientific databases and 

journal websites. Moreover, the search activity was performed only on titles, abstracts 

and keywords at first. This preference eliminates all of the inappropriate documents and 

will hopefully only show documents where both methods were discussed in the same 

document. The full text search option has produced widely dispersed articles in previous 

studies. The selected key terms with operators in this review were very close to the 

current subject (search queries in Table 1). The search terms and queries were defined 

according to the advanced search tips such as, "choose search terms that are specific or 

closely related to the topic of interest", "use the singular form of the word", "use 

connectors" and basic search strategies (ScienceDirect®, 2015a,Van Rijsbergen, 1979). 

  

  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

475 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

Table 1 

Search queries (until 25/07/2015) 

 

Search  Number(#)  

Search Queries 

#1 "AHP" AND "ELECTRE III" AND "hydro" 

#2 "AHP" AND "ELECTRE IV" AND "hydro" 

#3 "Analytic Hierarchy Process" AND "ELECTRE III" AND "hydro" 

#4 "Analytic Hierarchy Process" AND "ELECTRE IV" AND "hydro" 

#5 "AHP" AND "ELECTRE III" 

#6 "AHP" AND "ELECTRE IV" 

#7 "AHP" AND "ELECTRE" 

#8 "Analytic Hierarchy Process" AND "ELECTRE" 

#9 "Analytic Hierarchy Process" AND "Elimination and Choice 

Translating Reality" 

 

Books, chapters, journals, proceedings, transactions, magazines, and newsletters were all 

searched during this review until 25/07/2015. The titles and the abstracts were reviewed 

one by one and the full text of studies, the author viewed as important, were reviewed. 

Some of these documents (according to abstract and full text review) were presented in 

the following paragraphs in this section. The search results of this literature review were 

also summarized in Table 2 for other researchers and following studies. 

 

Table 2 

Summary of literature review (until 25/07/2015) 

 

Scientific publisher  

#1 

 

#2 

 

#3 

 

#4 

 

#5 

 

#6 

 

#7 

 

#8 

 

#9 

ACM Digital 0 0 0 0 2 0 5 2 0 

ASCE Online 0 0 0 0 0 0 1 1 0 

American Society 0 0 0 0 0 0 29 16 0 

Cambridge Journals 0 0 0 0 0 0 4 3 1 

Directory of Open 0 0 0 0 6 0 15 3 1 

Emerald Insight 0 0 0 0 0 0 3 1 0 

Google Scholar 95 16 87 11 1.030 201 3.940 3.490 220 

Hindawi Publishing 0 0 0 0 2 0 2 3 0 

Inderscience 0 0 0 0 0 0 3 0 0 

IJAHP 0 0 0 0 0 1 1 0 0 

Science Direct 0 0 0 0 4 0 22 9 0 

Science Publishing 0 0 0 0 0 0 0 0 0 

Springer 12 2 10 1 145 35 619 469 26 

Taylor & Francis 0 0 0 0 2 0 6 5 0 

Wiley-Blackwell 0 0 0 0 0 0 3 3 0 

World Scientific 0 0 0 0 0 0 2 2 0 

 

There were some papers that presented comparative studies in scientific journals until the 

date of 25/07/2015; however none of these studies were in real world investments within 

small hydropower plants. There were only 18 studies in the literature that were close to 

the current study. Lootsma & Schuijt (1998), Raju & Pillai (1999), Mahmoud & Garcia 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

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Analytic Hierarchy Process 

476 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

(2000), Akpinar et al. (2005), Gilliams et al. (2005), Grau et al. (2010), Sawicka et al. 

(2010), Geldermann & Schobel (2011), Ozcan et.al. (2011), Shaverdi et.al. (2011), 

Phogat & Singh (2013), Ur-Rehman & Al-Ahamri (2013), Janiak & Zak (2014), Massei 

et al. (2014), Samaras et al. (2014), Zak et.al. (2014), Sabzi & King (2015), and Sanchez-

Lozano et al. (2015) applied several MCDM methods. In short, there were 18 

comparative studies discussing AHP and ELECTRE methods in the literature. These 

studies were in varying fields such as solar power, transportation, hydropower, 

production and manufacturing, banking, logistics, painting, and agricultural. The 

hydropower (water, river, etc.) related studies were by Raju and Pillai (1999), Mahmoud 

and Garcia (2000), and Samaras et al. (2014), and none of these studies looked at private 

investments and small hydropower plants. Therefore, to our knowledge this paper is the 

first study in the private small hydropower plant investment selection problem of this 

scope (AHP, ELECTRE III, ELECTRE IV, and Shannon’s Entropy).  

 

The ELECTRE (ELimination Et Choix Traduisant la REalite: ELimination and Choice 

Expressing the REality) methods family was born with ELECTRE I (electre one) in the 

1960s. It was mentioned in many studies that Bernard Roy was the father of these 

methods. Govindan and Jepsen (2014) wrote: 

 
"The first ELECTRE method was presented by Benayoun et al. (1966) who reported on 

the works of the European consultancy company SEMA with respect to a specific real 

world problem. But the first journal article did not appear until 1968, when Roy (1968) 

described the method in detail. Later, it was renamed to ELECTRE I."  

 

The ELECTRE methods were grouped under the outranking approach (the European 

school of multicriteria decision analysis, the European school approach, the French 

school of multicriteria decision analysis) (Huang & Chen, 2005; Lootsma, 1990). 

Detailed information and studies on the ELECTRE methods can be found on the official 

websites of the LAMSADE (Laboratoire d'Analyse et Modélisation de Systèmes pour 

l'Aide à la DEcision: http://www.lamsade.dauphine.fr/) in France, the EURO Working 

Group Multicriteria Decision Aiding (http://www.cs.put.poznan.pl/ewgmcda/), and 

Professor Dr. Bernard Roy (http://www.lamsade.dauphine.fr/~roy/). The ELECTRE III 

(electre three) was developed for use with pseudo-criteria and the fuzzy binary 

outranking relations for ranking actions (Roy, 1991; Lair et al., 2004, Damaskos & 

Kalfakakou, 2005). The ELECTRE IV (electre four) was recommended for use when 

working without the relative criteria importance coefficients (Roy, 1991; Bashiri & 

Hejazi, 2009; Figueira et al., 2010). The “decision aiding” term was preferred to the term 

“decision support”, “decision making”, and “decision analysis” (Figueira et al., 2010). 

For more details about the principles and the equations of the ELECTRE III and the 

ELECTRE IV methods see Saracoglu (2015a), Ishizaka & Nemery (2013) and Figueira et 

al. (2005). 

 

Several weighting methods such as the rating method, the utility function method, the 

extreme weight approach and the entropy method have been presented in scientific 

studies (Tzeng et al., 1998). The weighting methods could be grouped by subjective and 

objective weight assessment methods (Lotfi & Fallahnejad, 2010). In the literature, the 

subjective weight assessment was typically based on the decision maker’s preferences; on 

the other hand the objective weight assessment was often based on hard data. However, 

there were some occasions when the objective factors were evaluated by the decision 

maker. Moreover, there were also some occasions where the subjective factors 

http://www.lamsade.dauphine.fr/
http://www.cs.put.poznan.pl/ewgmcda/
http://www.lamsade.dauphine.fr/~roy/


IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

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evaluations by the decision makers were treated with the objective weight assessment 

approaches (Akyene, 2012; Lotfi & Fallahnejad, 2010; Safari et al., 2012; Saracoglu, 

2015a; also OnlineStatBook, 2015 for the statistical basis on this respect). As a result, it 

was tricky to classify the subjective weight assessment and objective weight assessment 

methods for our study. In this study, the subjective weight assessment term was used 

when the decision maker had the discriminative power (e.g. Saaty’s AHP subjective 

criteria weighting) and the objective weight assessment was preferred when hard data had 

the discriminative power (e.g. Shannon’s Entropy objective criteria weighting). In other 

words, when the criteria weights were calculated based on the criteria values of the 

alternatives, the objective weight assessment term was used. Entropy methods are one of 

the applied objective weight assessment methods (Tzeng et al., 1998). Some studies 

support entropy methods, however others do not. (Lesne, 2011; Logan, 2012; Zhou et al., 

2013). There were several entropy methods developed in the information and decision 

analysis research field such as the Kullback-Leibler divergence (Kullback & Leibler, 

1951), the Renyi Entropy (Bromiley et al., 2004), the De Luca and Termini, Szmidt and 

Kacprzyk (Hung & Chen, 2009) and the base method as the Shannon’s Entropy 

(Shannon, 1948; Crooks, 2015). There were several applications of the Shannon’s 

Entropy in many research fields in the literature (Akyene, 2012; Fu et al., 2015; Safari et 

al., 2012; Saracoglu, 2015a, Zou et al., 2006). Akyene (2012) presented a solution based 

on the Shannon’s Entropy and TOPSIS methods for the mobile phone selection problem 

where twelve factors (dimensions, weight, screen size, memory, RAM, speed, blue tooth, 

camera, operating system, CPU, battery, price) were taken into account. The weights of 

these factors were calculated by the Shannon’s Entropy method, and the selection process 

was performed by the TOPSIS method. Fu et al. (2015) recommended a new publishing 

index for the scientific institution rankings. The corrected count and number of articles 

criteria were used for the proposed method, and a comparison of the current and proposed 

approaches for the Asia-Pacific ranking of the Nature Publishing Index was given. Safari 

et al. (2012) used the Shannon’s Entropy and the PROMETHEE methods for the supplier 

selection based on 6 factors (capacity, delivery, quality, shipment accuracy, warranty 

policies, availability of raw materials). Saracoglu (2015a) conducted an experimental 

research study to understand how private small hydropower plant investments could be 

selected by two ELECTRE methods with different weighting approaches. The weighting 

approaches were the Shannon’s Entropy, the equal weighting and the Saaty's AHP 

criteria weight assignment. The ELECTRE III and the ELECTRE IV methods were used 

for the evaluations of the actions based on 17 factors. Some of these factors were first 

evaluated by the expert decision makers, according to the verbal statements (very good to 

very bad according to the Likert 5 type scale. Then the ordinal data were used as the 

interval data for the objective weight assignments. Zou et al. (2006) worked on the Three 

Gorges reservoir water quality assessment problem where water quality monitoring data 

for 4 indicators were used. They compared the results with the traditional method. The 

Shannon’s Entropy objective weighting method was presented according to the previous 

studies in the literature as below (Abdullah & Otheman, 2013; Akyene, 2012; Zou et al., 

2006; Shannon, 1948; Saracoglu, 2015a): 

 

 Initialized decision matrix: X=(xij)n×m  

 i represents the criteria (1 ≤ i ≤ n)  

 j represents the alternative (1 ≤ j ≤ m) 

 Normalized matrix: R=(rij)n×m 

 0 ≤ rij ≤ 1 (normalized matrix elements rij are between 0 and 1) 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

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http://dx.doi.org/10.13033/ijahp.v7i3.343 

 where  

 maximization criterion 

 𝑟𝑖𝑗 =
𝑥𝑖𝑗−min𝑖{𝑥𝑖𝑗}

max𝑖{𝑥𝑖𝑗}− min𝑖{𝑥𝑖𝑗}
        (1) 

 minimization criterion 

 𝑟𝑖𝑗 =
max𝑖{𝑥𝑖𝑗}−𝑥𝑖𝑗

max𝑖{𝑥𝑖𝑗}− min𝑖{𝑥𝑖𝑗}
        (2) 

 entropy: ei (other representations as H, H(p(x) or H(A))) of the i
th
 criterion 

 𝑒𝑖 = −𝑘 ∑ 𝑓𝑖𝑗 ln(𝑓𝑖𝑗 )
𝑚
𝑗=1 ,  

 where 𝑓𝑖𝑗 =
𝑟𝑖𝑗

∑ 𝑟𝑖𝑗
𝑚
𝑗=1

, k=1/ln(m), when fij=0 ⇒ fij ln(fij)=0.   (3) 

 weight of entropy of i
th
 criterion 

 𝑤𝑖 =
1−𝑒𝑖

𝑛−∑ 𝑒𝑖
𝑛
𝑖=1

  

 where 0 ≤ wi ≤ 1, ∑ 𝑤𝑖 = 1
𝑛
𝑖=1       (4) 

 

The AHP methodology was developed and first presented in the 1980s by Thomas L. 

Saaty (Saaty, 1980, 1987, 1990). The description and definition of this method are given 

as: 
"In its general form the AHP is a nonlinear framework for carrying out both deductive 

and inductive thinking without use of the syllogism by taking several factors into 

consideration simultaneously and allowing for dependence and for feedback, and making 

numerical tradeoffs to arrive at a synthesis or conclusion. " (Saaty, 1987).  

 

In this definition, some possible difficult and important terms were "deductive thinking", 

"inductive thinking", and "syllogism"; for definitions please visit IEP (2015) and 

Wikipedia (2015a) for deductive thinking, and inductive thinking, and Cambridge 

University Press (2015) and LDOCE (2015) for syllogism. 

 

The AHP method was grouped under the American school of multicriteria decision 

approach (Pomerol & Barba-Romero, 2012; Lootsma, 1990). This method has been 

applied in many different research fields such as health, transportation-railway project 

strategic investment decisions, and shipbuilding-new shipbuilding yards investment 

location selection in countries master plans (Andreichicova & Radyshevskaya, 2009; 

Macura and Selmic, 2015, Saracoglu, 2013). As usual for any scientific research subject 

some studies supported the AHP method in the literature while others were opposed 

(Barzilai, 1998; Saaty, 2004; Saaty et.al., 2009). For more details about the principles and 

the equations of the AHP method see Brunelli (2015), Saaty (2004) and Saaty & 

Sodenkamp, (2010). 

 

The scope of this work is to understand, analyze, investigate and compare the findings of 

one of the American school methods (AHP) and two of the European school methods 

(ELECTRE III and ELECTRE IV) with objective and subjective weighting methods 

(equal, Shannon's Entropy, Saaty's AHP, and no weighting approaches) on a simplistic 

unified small hydropower plant investment selection model in the pre-development 

investment stages. This research study will hopefully contribute to the main aim of 

building up an intelligent autonomous decision or executive support system (human like 

computer reasoning and modeling) in the renewable energy field. 

 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

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Analytic Hierarchy Process 

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ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

3. Comparative research model, case, results, and discussion 

The comparative research model and its case study were built on the pillars of the 

methods (ELECTRE III, ELECTRE IV, AHP, and Shannon’s Entropy) and the cognitive 

limitations of humans (long term and short term memory). The simplistic unified and 

unique research model and its case study have to satisfy all requirements of these 

methods; hence it must be developed very carefully under the restrictions of these 

methods.  

 

Modeling constraints and guidance in this research study (please read the original 

documents cited in this text to avoid any conceptual, pragmatic, and semantic change or 

shift). 

 

These pillars are found in this study as: 

 

1) Apply ELECTRE II, ELECTRE III, or ELECTRE IV for ranking problems (Figueira 

et al., 2010, Ishizaka & Nemery, 2013) 

2) Use ELECTRE III when expressing the relative importance of the pseudo-criteria are 

possible (Dias et al., 2006) 

3) Use ELECTRE IV under three conditions (not able, does not want, cannot express the 

relative importance). "Using ELECTRE IV is only valid if the following two conditions 

are satisfied: no criterion is either preponderant or negligible when compared to any 

subset of half of the criteria" (Dias et al., 2006) 

4) Use more than five criteria up to twelve or thirteen in ELECTRE methods (Figueira et 

al., 2005) 

5) Use a maximum of 9 factors in each level in the AHP method (Gawlik, 2008; Kruger 

& Hattingh, 2006; Saaty, 1980) 

6) Preferable to apply ELECTRE methods in problems with large number of alternatives 

(Pohekar & Ramachandran, 2004; Soncini-Sessa et al., 2007) 

7) Preferable to apply ELECTRE methods when at least one criterion can be evaluated by 

an ordinal scale or a weakly interval scale (Figueira et al., 2005) 

8) Preferable to apply ELECTRE methods when criteria have a strong heterogeneity 

(Figueira et al., 2005) 

9) Build AHP model that is complex enough for capturing the situation and nature of the 

problem, but small and easy enough for handling changes (Saaty, 1987) 

10) Take into account the principles of sensory information storage (SIS), short-term 

memory (STM) and long-term memory (LTM) in the decision analysis. "Sensory 

information storage holds sensory images for several tenths of a second after they are 

received by the sensory organs. The functioning of SIS may be observed if you close 

your eyes, then open and close them again as rapidly as possible. As your eyes close, 

notice how the visual image is maintained for a fraction of a second before fading" 

(Heuer, 1999). "Information passes from SIS into short-term memory, where again it is 

held for only a short period of time—a few seconds or minutes. Like SIS, short-term 

memory holds information temporarily, pending further processing. This processing 

includes judgments concerning meaning, relevance, and significance, as well as the 

mental actions necessary to integrate selected portions of the information into long-term 

memory" (Heuer, 1999). "Some information retained in STM is processed into long-term 

memory. This information on past experiences is filed away in the recesses of the mind 

and must be retrieved before it can be used. In contrast to the immediate recall of current 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

480 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

experience from STM, retrieval of information from LTM is indirect and sometimes 

laborious" (Heuer, 1999). 

11) Take into account the principles of working memory by obeying the magical number 

7, and the 7±2 rule to guarantee the trustworthiness (Miller, 1956; Shiffrin & Nosofsky, 

1994). 

12) Choose realistic threshold values in the ELECTRE methods (Rogers & Bruen, 1998; 

Saracoglu, 2015a). 

 the indifference threshold of a criterion (q) has to be the highest value which beyond 
it the difference is perceptible 

 the preference threshold of a criterion (p) may be easily selected as at least twice as 
the indifference threshold (p) where symmetrical about the mean value 

 the veto threshold of a criterion (v) may be easily defined as at least three times as the 
preference threshold 

 for maximization criteria v ≥ p ≥ q, for minimization criteria additive inverse  
(Rogers & Bruen, 1998; Saracoglu, 2015a) 

 

Under these rules and guidelines, a simple and unified model is built in this study, 

because it makes it easier to do the following: 

 

1) Understand AHP, ELECTRE III, ELECTRE IV, Shannon’s Entropy weighting, equal 

weighting, Saaty's AHP weighting methods and approaches 

2) Compare the findings 

3) Find, collect, and process data and information 

4) Evaluate factors (e.g. avoid difficulty and too much complexity of evaluating or 

pairwise comprising of some subjective and objective factors as such Ganser, 2001; 

Ganser, 2005; McDaniel et al., 2015; Zukauskas & Vveinhardt, 2015) 

5) Take small steps and open new doors for the development of a human like intelligent 

autonomous support system 

 

Based on this, the model criteria were first studied based on three research studies in this 

specific field (Saracoglu, 2015a, b, c). Only seven factors were selected and used. During 

this selection process, the electrical installed capacity (in Watts) of a small hydropower 

plant is intentionally taken into consideration (Equation 5) because the plan is to use this 

equation as an objective function or a constraint in the future combined multi objective 

optimization and multi criteria decision making research studies. 

 

P = ηtr × ηg × ηt × ρw× g × Q × Hnet       (5) 

 

(ηtr: efficiency of transformer, ηg: efficiency of generator, ηt: efficiency of turbine, ρw: 

density of water (kg/m
3
), g: gravity (m/s

2
), Q: rated discharge (m

3
/s), Hnet: net head (m)) 

(for extraction of this formula/equation see Eliasson and Ludvigsson, 2000; ESHA, 2004; 

ESHA, 2005)  

 

The wisdom, "let first the data speak", is followed in this study, therefore the objective 

factors are first selected for this simplistic unified comparative model (Jorba et al., 2008). 

These attributes are also investigated using the help of Carrot
2
. "Carrot

2
 is an open source 

software project that includes several text clustering algorithms which include bisecting 

K-means, Suffix Tree Clustering and Lingo algorithm" (Carrot
2
, 2015; Zamir & Etzioni, 

1999; Osinski & Weiss, 2005). The documents are clustered for each factor on the 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

481 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

Carrot
2
 desktop and studied one by one on some preferred clusters. The basic private 

small hydropower plant investment selection factors (criteria/attributes) in this study are 

as follows: 

 

 C1: Catchment Area (drainage basin, catchment, catchment basin, drainage 

area, river basin, water basin) (objective criteria, km
2
) (more is better ↑ ↑). The catchment 

area is defined as, "The land area where precipitation falls off into creeks, streams, rivers, 

lakes, and reservoirs. It is a land feature that can be identified by tracing a line along the 

highest elevation between two areas on a map" (USGS, 2015). Georges River (2015) 

defines it as, "An area of land where water collects when it rains, often bounded by hills. 

As the water flows over the landscape it finds its way into streams and down into the soil, 

eventually feeding the river. Some of this water stays underground and continues to 

slowly feed the river in times of low rainfall. Every inch of land on the Earth forms part 

of a catchment". Langbein & Iseri (1995) define the drainage area as, "A stream at a 

specified location is that area, measured in a horizontal plane, which is enclosed by a 

drainage divide", and drainage basin as, "A part of the surface of the earth that is 

occupied by a drainage system, which consists of a surface stream or a body of 

impounded surface water together with all tributary surface streams and bodies of 

impounded surface water". The European Small Hydropower Association or ESHA 

(2004) defines it as, "The whole of the land and water surface area contributing to the 

discharge at a particular point on a watercourse". When the catchment area of a small 

hydropower plant is calculated by any means, the location of weirs (diversion dam, 

diversion weir) is taken into account. If there is more than one weir in the project, the 

total catchment area as an equivalent catchment area is calculated by the sum of all 

catchment area values in the evaluation of this study. When two catchment areas of small 

hydropower plants are compared or evaluated, the large one is preferred to the smaller 

one in this study. The properties of catchments are not used and considered in this 

simplistic unified decision aiding (decision making) model. The data of the small 

hydropower plant investments are directly taken and tabulated in this study. This criterion 

is a site and design specific factor. The Carrot
2
 is used for gathering additional 

information for better perception in an easy and fast way as shown in Figure 4. Further 

details of this criterion are discussed in Saracoglu (2015a, b, c). 

 

 
 

Figure 4. Carrot
2
 workbench clustering results for "drainage basin" on 29/07/2015, 

Source: Wiki, Algorithm: Lingo, Visualization: FoamTree (generated by the 

Carrot
2
 http://carrot2.org & the Paint.NET) 

 

http://carrot2.org/


IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

482 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 C2: Project Runoff (objective criteria, hm
3
) (more is better ↑ ↑) The project 

runoff is the mean annual total runoff of the catchment area in this study. This term can 

also be used as only runoff. Langbein & Iseri (1995) define it as, "part of the precipitation 

that appears in surface streams". There are also a few important terms that help to 

understand the meaning of project runoff for mall hydropower plants. Langbein & Iseri 

(1995) define streamflow as, "The discharge that occurs in a natural channel. Although 

the term discharge can be applied to the flow of a canal, the word streamflow uniquely 

describes the discharge in a surface stream course. The term "streamflow" is more 

general than runoff, as streamflow may be applied to discharge whether or not it is 

affected by diversion or regulation". Langbein & Iseri (1995) define overland flow as 

"the flow of rainwater or snowmelt over the land surface toward stream channels. After it 

enters a stream, it becomes runoff". USGS Water Science School (2015a) discusses 

surface runoff as, "Many people probably have an overly-simplified idea that 

precipitation falls on the land, flows overland (runoff), and runs into rivers, which then 

empty into the oceans. That is "overly simplified" because rivers also gain and lose water 

to the ground. Still, it is true that much of the water in rivers comes directly from runoff 

from the land surface, which is defined as surface runoff. When rain hits saturated or 

impervious ground, it begins to flow overland downhill. It is easy to see if it flows down 

your driveway to the curb and into a storm sewer, but it is harder to notice it flowing 

overland in a natural setting".  The ESHA (2004) defines it as, "The rainfall, which 

actually does enter the stream as either surface or subsurface flow". When the project 

runoff of a small hydropower plant is calculated by any means, the location of weirs 

(diversion dam, diversion weir) is taken into account. If there is more than one weir in the 

project, the total project runoff as equivalent total project runoff is calculated by the sum 

of all total project runoff values in the evaluation of this study. Moreover, the 

environmental flow runoff (for ecosystems and human livelihoods) isn't included in this 

total. When two project runoff values of small hydropower plants are compared or 

evaluated, the larger one is preferred to the smaller one in this study. The data on the 

small hydropower plant investments are directly taken and tabulated in this study. This 

criterion is a site and design specific factor. The Carrot
2
 is used for gathering additional 

information for better perception in an easy and fast way as shown in Figure 5. Further 

details of this criterion are discussed in Saracoglu (2015a, b, c). 

  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

483 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 

 
 

Figure 5. Carrot
2
 workbench clustering results for "runoff" on 29/07/2015  

Source: Wiki, Algorithm: Lingo, Visualization: Circles (generated by the Carrot
2
 & 

the Paint.NET) 

 

 C3: Net Head (objective criteria, m) (more is better ↑ ↑) The net head is defined 

as, "The gross head minus all hydraulic losses except those chargeable to the turbine" 

(EIA, 2015). The head is sometimes called the water pressure.  The ESHA (2004) defines 

it as, "The gross head minus the sum of all the losses equals the net head, which is 

available to drive the turbine". The losses are generally caused by trash racks, pipe 

friction, bends and valves. The gross head is defined as, "A dam's maximum allowed 

vertical distance between the upstream's surface water (headwater) forebay elevation and 

the downstream's surface water (tailwater) elevation at the tail-race for reaction wheel 

dams or the elevation of the jet at impulse wheel dams during specified operation and 

water conditions" (EIA, 2015). ESHA (2004) defines the gross head as, "The vertical 

distance that the water falls through in giving up its potential energy (i.e. between the 

upper and lower water surface levels)". Here, the turbine type is important because some 

types of turbines discharge the water to the atmosphere. If there are multiple net heads in 

the project (cascade group projects or other clustered projects), the equivalence of these 

net heads according to the electrical installed power equation is calculated and used in the 

evaluation. This equivalent net head is an approximation and assumption of this study. 

Some detailed technical conditions such as total efficiencies of turbines, generators and 

transformers are assumed to be the same for all alternatives and actions. When two 

project net head values of small hydropower plants are compared or evaluated, the larger 

one is preferred to the smaller one in this study. The data on the small hydropower plant 

investments are directly taken and tabulated in this study. This criterion is a site and 

design specific factor. The Carrot
2
 is used for gathering additional information for better 

perception in an easy and fast way as shown in Figure 6. Further details of this criterion 

are discussed in Saracoglu (2015a, b, c). 

 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

484 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 
 

Figure 6. Carrot
2
 workbench clustering results for "net head" on 31/07/2015 

Source: Wiki, Algorithm: Lingo, Visualization: Aduna Cluster Map (generated by 

the Carrot
2
 & the Paint.NET) 

 

 C4: Project Design Discharge (capacity, discharge, flow, flow rate, rate of flow) 

(objective criteria, m
3
/s) (more is better ↑ ↑) USGS Water Science School (2015b) 

defines discharge as, "The volume of water moving down a stream or river per unit of 

time, commonly expressed in cubic feet per second or gallons per day. In general, river 

discharge is computed by multiplying the area of water in a channel cross section by the 

average velocity of the water in that cross section". Here, the maximum project design 

discharge of the turbined water is taken into account. If there are more than one project 

design discharges in the project (several weirs, several turbines, cascade group projects or 

other clustered projects), the equivalence of these discharges according to the electrical 

installed power equation is calculated and used in the evaluation of this study. This 

equivalent discharge is an approximation and assumption of this study. Some detailed 

technical conditions such as total efficiencies of turbines, generators and transformers are 

assumed to be same for all alternatives and actions. When two project discharge values of 

small hydropower plants are compared or evaluated, the large one is preferred to the 

smaller one in this study. The data on the small hydropower plant investments are 

directly taken and tabulated in this study. This criterion is a site and design specific 

factor. Further details of this criterion are discussed in Saracoglu (2015a, b, c). 

 C5: Firm Energy (objective criteria, GWh) (more is better ↑ ↑) ESHA (2004) 

defines this as, “The power delivered during a certain period of the day with at least 90 – 

95% certainty”. When two project firm energy values of small hydropower plants are 

compared or evaluated, the larger one is preferred to the smaller one in this study. The 

data on the small hydropower plant investments are directly taken and tabulated in this 

study. This criterion is a site and design specific factor. Further details of this criterion 

are discussed in Saracoglu (2015a, b, c). 

 C6: Secondary Energy (objective criteria, GWh) (more is better ↑ ↑) The 

secondary energy is the remaining part of the total energy generated after the deduction 

of the firm energy of a small hydropower plant (Equation 6). Further details of this 

criterion are discussed in Saracoglu (2015a, b, c). 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

485 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

Etotal = Efirm + Esecondary        (6) 

 

(Etotal: total electricity generation (kWh), Efirm: firm energy (kWh), Esecondary: secondary 

energy (kWh), kilowatt hour unit is for this study, the unit can be megawatt hour, 

gigawatt hour, etc.) 

 C7: Investment Cost (objective criteria, USD) (less is better ↓ ↑) This includes 

the total estimated investment cost of the private small hydropower plants. The 

construction cost of the small hydropower plant structures such as the diversion weir, the 

de-silting tank, the channel, the tunnel, the headpond, or in other words the forebay, the 

penstock, the powerhouse, the tailrace, and the substation are also taken into account. 

Moreover, all related costs for the electromechanical equipment such the turbines, the 

generators, the transformers, the control systems, the diesel generators, the cooling 

systems, and the dewatering systems are all taken into account. Transmission lines and 

their related costs, all of the engineering studies and their related costs, supervision tasks 

and related costs are all taken into account. Moreover, the contingency, the financial 

costs, the expropriation costs, the insurance costs are all taken into account in this item. 

In addition to these cost items, the operational costs of the private small hydropower 

plants are also calculated. The data of small hydropower plant investments are directly 

taken and tabulated in this study. Henceforth, there isn't any design study and cost 

estimation performed in the current study. It is assumed that the investment costs of 

private small hydropower plants are the same items for all small hydropower plants. 

Moreover, it is assumed that the investment cost of private small hydropower plants 

contains all of the cost items of a small hydropower plant. Here, the only calculation 

made is for the currency exchange and time value of money change (Investopedia, 

2015a). We attempt to find the investment cost calculation date, then the foreign-

exchange rate data (USD: United States Dollar to TL: Turkish Lira or TL to USD) is 

taken from the official webpage of the Central Bank of the Republic of Turkey and used 

for the currency exchange (TCMB, 2015) of the investment cost (Equation 7).  

 

ICUSD date = ICTL date × CRTL to USD date      (7) 

 

(ICUSD date: investment cost of private small hydropower plant on the investment cost 

calculation date in USD, ICTL date: investment cost of private small hydropower plant on 

the investment cost calculation date in TL, CRTL to USD date: official currency rate of TCMB 

from TL to USD on the investment cost calculation date) 

 

The time value of money change is calculated by the future worth or the future value 

equation based on the compounded annual interest rate in this study (Investopedia, 

2015b) (Equation 8). The present value and the future value equations, and the detailed 

information about these terms can be found in Gitman et al. (2014), Known et al. (2004), 

Panneerselvam (2012), and several other engineering economics, financial management 

and financial accounting books. 

 

ICsmall hydropower plant investment today  = ICsmall hydropower plant investment initial value  × (1+i)
n
 (8) 

 

(ICsmall hydropower plant investment today: investment cost of private small hydropower plant today 

for this study in USD, ICsmall hydropower plant investment initial value: investment cost of private small 

hydropower plant on the investment cost calculation date in USD, i: interest rate, 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

486 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

approximation as the arithmetic mean of USD annual LIBOR rates in this study, n: years 

counted from the initial value of year to today as year 2015). 

 

The London Interbank Offered Rate (LIBOR) data are taken directly as 1 year/ 12 month 

rates from moneycafe.com (2015) and globalrates.com (2015). The arithmetic mean of 

the values from these two different web pages is calculated for each year (Equation 9). 

When only one data point exists, then this data is taken as the LIBOR value in its year. 

Next, the interest rate for a period is calculated by the arithmetic mean of LIBOR values 

in this period. This interest rate is a good approximation for the calculation of the time 

value of money change in the investment cost (Equation 10). By this approach, the 

complexity of the inflation in Turkey, the redenomination (removal of six zeros in 

Turkish Lira) in Turkey, and the exchange rates in Turkey are eliminated. The LIBOR 

data and the interest rates are presented in Figure 7.    

 

LIBORyear i  = (LIBORyear i moneycafe + LIBORyear i globalrate) / 2    (9) 

 

𝑖𝑦𝑒𝑎𝑟 𝑗 𝑡𝑜 𝑦𝑒𝑎𝑟 𝑘 =
1

(𝑦𝑒𝑎𝑟 𝑘 −𝑦𝑒𝑎𝑟 𝑗)
× ∑ 𝐿𝐼𝐵𝑂𝑅𝑦𝑒𝑎𝑟 𝑖

𝑦𝑒𝑎𝑟 𝑗
𝑦𝑒𝑎𝑟 𝑘     (10) 

 

When two investment costs of small hydropower plants are compared or evaluated, the 

smaller one is preferred to the larger one in this study. This criterion is a site and design 

specific factor. 

 

 
Years i Years i Years i 

2004-2015 2,18% 2005-2015 2,24% 2006-2015 2,15% 

2007-2015 1,84% 2008-2015 1,40% 2009-2015 1,00% 

2010-2015 0,83% 2011-2015 0,79% 2012-2015 0,80% 

2013-2015 0,69% 2014-2015 0,61% 2015-2015 - 

 

Figure 7. LIBOR 1 year or 12 month LIBOR (January) (Data: moneycafe.com, 

2015; globalrates.com, 2015) (Calculation: arithmetic mean) (generated by the 

Apache OpenOffice 4.1.1 Calc http://www.openoffice.org/ & the Paint.NET) 

 

http://www.openoffice.org/


IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

487 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

The current simplistic unified model structure for AHP, ELECTRE III and ELECTRE IV 

has three levels (Figure 8). There are seven private small hydropower plant investment 

alternatives or actions (Alternative1 to 7/Action1 to 7) (Table 4). There is only one expert 

decision maker who builds the model and presents his thoughts on the factors and 

alternatives. The objective factors aren't evaluated due to the alternatives because their 

approximate values are directly taken in several ways (Figure 3). The threshold values 

(indifference, preference, veto) in the ELECTRE methods are chosen based on the 

opinion of the expert decision maker. The criteria weights are calculated by the equal 

weighting, the Shannon's Entropy, and the Saaty's AHP approaches. While assigning the 

criteria weights by the pairwise comparisons of the expert decision maker, the linguistic, 

or verbal evaluation labels are used based on the Fundamental Scale of the AHP  (Saaty, 

1980; Saaty, 2008) and the Likert type scale (Likert, 1932: extension 1 to 9 of original 

work 5 point scale) (Saracoglu, 2015b). The expert decision maker judgments are made 

with the help of the Super Decisions version 2.2 software 

(http://www.superdecisions.com/) for the Saaty's AHP weighting. The inconsistency of 

the matrix is directly calculated by the Super Decisions software and recorded. The equal 

weighting and the Shannon's Entropy weighting calculations are made directly in a 

Microsoft Excel spreadsheet. 

 

 
 

Figure 8. Simplistic unified model structure for AHP, ELECTRE III and 

ELECTRE IV 

  

http://www.superdecisions.com/


IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

488 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

Table 4 

Private small hydropower plant investment actions/alternatives 

 

Actions/ 

Alternatives 

 

P 

 

C1 

 

C2 

 

C3 

 

C4 

 

C5 

 

C6 

 

C7 

Alternative1 6,56 470,00 302,90 31,54 24,00 0,85 18,45 10.069.000 

Alternative2 1,91 36,00 26,79 76,36 2,80 0,00 5,12 4.534.000 

Alternative3 8,55 4.550,00 589,22 19,58 50,00 4,58 24,49 22.054.000 

Alternative4 5,43 1.243,31 193,71 54,03 12,64 0,00 18,62 17.757.000 

Alternative5 3,91 352,00 103,20 60,28 7,50 1,25 10,56 3.948.000 

Alternative6 6,52 1.763,50 274,76 36,00 20,82 0,00 8,83 12.653.000 

Alternative7 9,23 1.945,00 301,62 59,14 18,00 0,00 30,01 26.654.000 

P: Installed Power (MW: megawatt), C1: Catchment Area (km
2
), C2: Project Runoff 

(hm
3
), C3: Net Head (m), C4: Discharge (m

3
/s), C5: Firm Energy (GWh/year), C6: 

Secondary Energy (GWh/year), C7: Investment Cost (USD) 

 

The equal weighting, the Shannon's Entropy weighting, and the Saaty's AHP weighting 

approaches for voting power or weight of the criteria on this simplistic unified small 

hydropower plant investment selection model in the pre-development investment stages 

are evaluated, calculated and compared. The equal weighting is 0,1429 per criteria, that 

sums to a total of 1,000 for seven factors. The Shannon's Entropy weighting is calculated 

according to its equations and the criteria weights are: catchment area 0,1517, project 

runoff 0,0979, net head 0,0858, discharge 0,1207, firm energy 0,3573, secondary energy 

0,1019, investment cost 0,0847. The Saaty's AHP weighting, that is the pairwise 

comparisons of the expert decision maker, starts with an inconsistency of 0,22171. The 

inconsistency reaches 0,09511 at the 7
th
 evaluation. At this level, there aren't any 

additional pairwise evaluations made because the desired inconsistency level in the AHP 

method is less than 0,10 (Saaty, 1990). The inconsistency value per evaluation in the 

Saaty's AHP weighting is presented in Figure 9. The recommendations of the Super 

Decisions software aren't taken into account when the evaluations are performed again. 

The number of pairwise comparisons is 21 for 7 factors with respect to the goal. There 

are 7 evaluations, making the total number of pairwise comparisons 147 in this study. It 

is observed that the evaluations of the expert decision maker fit a logarithmic trendline 

with a good R squared (coefficient of determination) value (Figure 9). This observation is 

recorded for future studies. The Shannon’s Entropy objective weighting representation 

difference rate (performance) of the evaluations of the expert decision makers ranges 

between -67% and 671% (Figure 10). The equal weighting representation difference rate 

ranges between -64% and 626% (Figure 10). These criteria weight findings show that 

neither of these objective weighting (equal and Shannon's Entropy) approaches are 

helpful in predicting the expert decision maker judgments and behavior on the criteria 

weights. The criteria weights and their representational capabilities of the Saaty's AHP 

weighting are shown in Figure 10. The equal weighting approach doesn't have the 

capability of discriminating the differences between the factors (Figure 10). Henceforth, 

this objective weighting approach can only predict the human judgments on the criteria 

weights well when the decision maker doesn't know anything about the factors and their 

details or when the factors being investigated don't have any major differences between 

themselves. For instance, an ordinary person can't decide or make any judgments on the 

weights of the factors of the firm energy and the secondary energy  because he or she 

doesn't know what these factors mean and which one is more important and so on (Figure 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

489 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

10). Although the Shannon's Information Theory (Shannon's Entropy) strictly depends on 

the probability of events (probability theory), its representation capability is still 

questionable and needs very detailed and long term research studies for the criteria 

weight assignments in the human decision making research field (Carter, 2014; Shannon, 

1948; Shannon, 1951). One of the important aspects of the Shannon's Entropy is that it is 

based on large quantities of information. Further research studies need to  investigate this 

issue with more hard data. The Shannon's Entropy objective weighting approach predicts 

fairly well the firm energy criteria weight (Figure 10). The performance of the Shannon's 

Entropy weighting in predicting the Saaty's AHP weighting for other factors is poor in 

this study. In short, the firm energy, the secondary energy and the investment cost factor 

weights are all predicted less than the Saaty's AHP weighting (Figure 10). The discharge, 

the net head, the project runoff and the catchment area criteria weights are all predicted 

more than the Saaty's AHP weighting (Figure 10). It is important to remember what 

William Bruce Cameron said, "Not everything that can be counted counts, and not 

everything that counts can be counted". Also, Edward Gibbon was wise when he stated, 

"The laws of probability, so true in general, so fallacious in particular". These two 

weighting approaches can't represent the expert decision maker judgments in this study 

because both the Shannon’s Entropy and the equal objective weighting approaches are 

based only on the hard data of the alternatives. However, Saaty's AHP subjective 

weighting assessment is based only on the expert knowledge. This observation is also 

recorded for future studies. 

 

 
 

Figure 9. Inconsistency values of pairwise comparisons in this study 

 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

490 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 
Code Criterion equal Shannon's Saaty's AHP 

C1 Catchment Area 0,1429 0,1517 0,0197 

C2 Project Runoff 0,1429 0,0979 0,0242 

C3 Net Head 0,1429 0,0858 0,0426 

C4 Discharge 0,1429 0,1207 0,0401 

C5 Firm Energy 0,1429 0,3573 0,3982 

C6 Secondary Energy 0,1429 0,1019 0,2163 

C7 Investment Cost 0,1429 0,0847 0,2590 

 Sum Of Weights 1,0000 1,0000 1,0000 

 

Figure 10. Criteria weights comparison (on top), objective weighting representation 

rate of Saaty's AHP weighting (on bottom) in this study 

 

The indifference threshold (q), the preference threshold (p), and the veto threshold (v) of 

criteria for the ELECTRE methods are chosen by the expert decision maker according to 

item 10 of the modeling constraints and guidance in Section 3 (Rogers & Bruen, 1998; 

Saracoglu, 2015a) (Table 5). All of these evaluations are totally subjective judgments. 

The ELECTRE III-IV software version 3.x is used in this study, so that the parameters 

and inputs are organized according to the software standards. This software defines the 

thresholds by two coefficients α and β as such: 

 

(𝑞 𝑜𝑟 𝑝 𝑜𝑟 𝑣)𝑗 = 𝛼𝑗 × 𝑔𝑗 + 𝛽𝑗       (11) 
 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

491 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

(q: indifference threshold, p: preference threshold, v: veto threshold, j: criteria number or 

criteria, gj: value or evaluation of the action or the alternative on the j
th
 criterion, αj and βj: 

coefficients of q, p, or v) 

 

In this study, the threshold values are decided as the constant values by the expert 

decision maker, so that the values in Table 5 are entered as β values on the ELECTRE 

III-IV software. This evaluation approach is simpler for the expert decision maker than 

defining two coefficients α and β. Instead of deciding these two coefficients, the expert 

decision maker directly decides the threshold values. The direct threshold preference is 

selected on the software. (Dias et al., 2006) 

 

Table 5 

Threshold values
*
 

 

Criterion  

Direction Of  

Preferences 

 

Indifference 

(qj) 

 

Preference 

(pj) 

 

Veto (vj) 

Catchment Area Max 500 1.000 3.000 

Project Runoff Max 200 400 1.200 

Net Head Max 40 80 240 

Discharge Max 10 20 60 

Firm Energy Max 0,9 1,8 5,4 

Secondary Energy Max 15 30 90 

Investment Cost Min 5.000.000 10.000.000 30.000.000 
*
 α values are taken as zero and β values are taken as threshold values 

 

The AHP model calculations are performed in the Super Decisions version 2.2 (see 

Figure 11 for the AHP model screen view) for the equal weighting, the Shannon's 

Entropy weighting, and the Saaty's AHP weighting approaches. The direct data input 

table is used for entering the data from Table 4 into Super Decisions. The zero values 

aren't accepted by the software, hence instead of zero values, values very close to zero are 

entered (0,00 ≈ 0,00001). Moreover, the values on the table are automatically changed to 

approximate values by the software (e.g. 1.243,31 ≈ 1243.3093; 4.534.000 ≈ 

4534000.09397). These values are checked one by one and it is assumed that there will 

not be any major effect on the results of the calculations in this subject. The matrices for 

the alternatives with respect to the objective factors aren't studied for their inconsistency 

because they are the objective factors. In this study, the priorities of the factors and the 

alternatives are taken by their normalized cluster values in Super Decisions. The 

preference orders of the alternatives by the equal weighting approach are Alternative 1 

(0,1247) (3
rd

 rank), Alternative 2  (0,0509) (7
th
 rank), Alternative 3  (0,3314) (1

st
 rank), 

Alternative 4 (0,1177) (4
th
 rank), Alternative 5  (0,0918) (6

th
 rank), Alternative 6 (0,1128) 

(5
th
 rank), and Alternative 7 (0,1708) (2

nd
 rank). The preference orders of the alternatives 

by the Shannon's Entropy weighting approach are Alternative 1 (0,1228) (3
rd

 rank), 

Alternative 2  (0,0324) (7
th
 rank), Alternative 3  (0,4348) (1

st
 rank), Alternative 4 

(0,0855) (6
th
 rank), Alternative 5  (0,1118) (4

th
 rank), Alternative 6 (0,0872) (5

th
 rank), 

and Alternative 7 (0,1255) (2
nd

 rank). The preference orders of the alternatives by the 

Saaty's AHP weighting approach are Alternative 1  (0,1274) (3
rd

 rank), Alternative 2 

(0,0325) (7
th
 rank), Alternative 3 (0,4120) (1

st
 rank), Alternative 4  (0,0973) (5

th
 rank), 

Alternative 5 (0,1159) (4
th
 rank), Alternative 6 (0,0678) (6

th
 rank) and Alternative 7  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

492 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

(0,1472) (2
nd

 rank). The findings show that Alternative 3 is ranked first for all methods, 

Alternative 7 is ranked second for all methods, and Alternative 1 is ranked third for all 

methods. These findings represent that the first three ranks match for each weighting 

approach on the AHP method even though their criteria weights aren't the same. The 4
th
 

rank is occupied by Alternative 4 in the equal weighting, Alternative 5 in the Shannon's 

Entropy weighting, and Alternative 5 in the Saaty's AHP weighting approaches. The 5
th
 

rank is occupied by Alternative 6 for equal weighting, Alternative 6 in the Shannon's 

Entropy weighting, and Alternative 4 in the Saaty's AHP weighting approaches. The 6
th
 

rank is occupied by Alternative 5 in the equal weighting, Alternative 4 in the Shannon's 

Entropy weighting, and Alternative 6 in the Saaty's AHP weighting approaches. 

Alternative 2 is ranked seventh for all methods. These findings show that the rankings of 

alternatives promise to be the same or very similar without any major disturbance with 

these weighting approaches. Hence, it is possible to represent human subjective 

evaluations by some objective weighting approaches when only considering the final 

ranks of the AHP method (only considering these factors in private small hydropower 

plant investments). Under these conditions, it is recommended that an investigation be 

started (review data, feasibility studies, etc.) into Alternatives 3, 7, and 1 for private small 

hydropower plant investment options.  

 

 
 

Figure 11. The AHP model on the Super Decisions software (open the electronic 

supplementary material: IJAHP2015SaatyAHPweighting.sdmod) 

 

The ELECTRE III and ELECTRE IV model calculations are performed on the 

ELECTRE III-IV version 3.x for the equal weighting, the Shannon's Entropy weighting, 

and the Saaty's AHP weighting approaches. The direct data input tables are used for 

entering the data from Table 4 into the ELECTRE III-IV. The descending and ascending 

distillations for both ELECTRE III & IV models are taken from the menu 

Results/Distillations on the software. The ranks of the actions in the final pre-order for 

both ELECTRE III & IV models are taken from the menu Results/Ranks in Final 

Preorder on the software. The complete results for both ELECTRE III & IV models are 

taken from the menu Results/Final Graph on the software. The descending and ascending 

distillations (left), the final pre-orders (middle), and the final graph (right) are presented 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

493 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

in Figures 12 to 17. Other important results (Concordance Matrix, Credibility Matrix, 

Ranking Matrix) are also taken from the menus and presented in the electronic 

supplementary material (IJAHP2015 Electronic Supplementary.pdf). It is helpful to be 

reminded that "descending distillation selects at first the best actions to end the process 

with the worst ones", oppositely "the ascending distillation selects first the worst actions 

to end the process with the best ones" (Dias et al., 2006). Moreover, "an action which is 

incomparable to a group of others will be ranked at the end of this group in the 

descending distillation and at the top in the ascending distillation. The actions which are 

considered equal (equivalence classes) in a distillation are displayed in the same box" 

(Dias et al., 2006). The final pre-orders should be understood as "any action which has no 

better action will have rank 1 (even if it is incomparable to many others), the actions of 

ranks 2 are those whose better actions are only of rank 1...." (Dias et al., 2006). The final 

graph is a good representation of the final rankings. In Figure 12 (left), Alternative 5 is 

the best action in the ELECTRE III with the Saaty's AHP weighting. It is at the first (top 

of the figure) of the selection process in the descending distillation. Alternative 3 follows 

Alternative 5 in the ELECTRE III with the Saaty's AHP weighting in the descending 

distillation. Alternative 7 is the worst action in the descending distillation. It is the last 

(bottom of the figure) of the selection process in the descending distillation (left in Figure 

12). Alternative 3 is the worst action in the ELECTRE III with the Saaty's AHP 

weighting in the ascending distillation (top of the figure). Alternative 1 and Alternative 5 

(in the same box) follow Alternative 3 (bottom of the figure). Alternative 7 is the best 

action in the ascending distillation. It is at the last (bottom of the figure) of the selection 

process in the descending distillation (left in Figure 12). Alternative 3 and Alternative 5 

are ranked first in ELECTRE III with the Saaty's AHP weighting (middle and right in 

Figure 12). Alternative 1 follows these two alternatives, and Alternative 7 is the worst 

preferred action (middle and right in Figure 12). Under these conditions, it is 

recommended that an investigation be started (review data, feasibility studies etc.) on 

Alternative 3 and Alternative 5 first, and then Alternative 1 for private small hydropower 

plant investment options. 

 

 
 

Figure 12. The ELECTRE III model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpsa.elp) by the Saaty's 

AHP weighting, distillations (on left), ranks in final preorder (on middle/center), 

final graph (on right) 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

494 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

In Figure 13 (left), Alternative 3 is the best action in the ELECTRE IV with the Saaty's 

AHP weighting. It is first (top of the figure) in the selection process in the descending 

distillation. Alternative 6 follows Alternative 3 in the descending distillation. Alternative 

2, Alternative 4, and Alternative 7 are the worst actions in the descending distillation. 

They are last (bottom of the figure) in the selection process in the descending distillation. 

Alternative 1 and Alternative 3 are the least actions in the ascending distillation (top of 

the figure). Alternative 4 is the best action in the ascending distillation. Alternative 3 is 

ranked first in ELECTRE IV with the Saaty's AHP weighting (middle and right in Figure 

13). Alternative 1, Alternative 5, and Alternative 6 follow this alternative, and Alternative 

4 is the least preferred action. Under these conditions, it is recommended that an 

investigation be started (review data, feasibility studies, etc.) into Alternative 3 first, then 

Alternative 1, Alternative 5, and Alternative 6 for private small hydropower plant 

investment options. 

 

 

 
 

Figure 13. The ELECTRE IV model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpsa.elp) by the Saaty's 

AHP weighting, distillations (on left), ranks in final preorder (on middle), final 

graph (on right) 

 

In Figure 14 (left), Alternative 3 is the best action in the ELECTRE III with the equal 

weighting. It is first (top of the figure) in the selection process in the descending 

distillation. Alternative 1, Alternative 6, and Alternative 7 follow Alternative 3 in the 

descending distillation, and Alternative 2, Alternative 4, and Alternative 5 are the worst 

actions in the descending distillation. They are last (bottom of the figure) in the selection 

process in the descending distillation. Alternative 3 is the worst action in the ascending 

distillation (top of the figure). Alternative 2 is the best action in the ascending distillation. 

Alternative 3 is ranked first in ELECTRE III with the equal weighting (on middle and 

right in Figure 14). Alternative 1, Alternative 6, and Alternative 7 follow this alternative, 

and Alternative 2 is the least preferred action. Under these conditions, it is recommended 

that an investigation be started (review data, feasibility studies, etc.) of the Alternative 3 

first, then Alternative 1, Alternative 6, and Alternative 7 for private small hydropower 

plant investment options. 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

495 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 
 

Figure 14. The ELECTRE III model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpew.elp) by the equal 

weighting, distillations (on left), ranks in final preorder (on middle), final graph (on 

right) 

 

In Figure 15 (left), Alternative 3 is the best action in the ELECTRE IV with the equal 

weighting. Alternative 6 follows Alternative 3 in the descending distillation. Alternative 

2, Alternative 4, and Alternative 7 are the worst actions in the descending distillation. 

Alternative 1 and Alternative 3 are the worst actions in the ascending distillation. 

Alternative 4 is the best action in the ascending distillation. Alternative 3 is ranked first in 

ELECTRE IV with the equal weighting (middle and right in Figure 15). Alternative 1, 

Alternative 5, and Alternative 6 follow this alternative. Alternative 4 is the least preferred 

action. Under these conditions, it is recommended that an investigation be started (review 

data, feasibility studies, etc.) of Alternative 3 first, then Alternative 1, Alternative 5, and 

Alternative 6 for private small hydropower plant investment options. 

 

 
 

Figure 15. The ELECTRE IV model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpew.elp) by the equal 

weighting, distillations (on left), ranks in final preorder (on middle), final graph (on 

right) 

 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

496 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

In Figure 16 (left), Alternative 3 is the best action in the ELECTRE III with the 

Shannon's Entropy weighting. Alternative 5 follows Alternative 3 in the descending 

distillation. The others are the worst actions in the descending distillation. Alternative 3 is 

the worst action in the ascending distillation. Alternative 4 is the best action in the 

ascending distillation. Alternative 3 is ranked first in ELECTRE III with the Shannon's 

Entropy weighting (on middle and right in Figure 16). Alternative 5 follows this 

alternative. Alternative 4 is the least preferred action. Under these conditions, it is 

recommended that an investigation be started (review data, feasibility studies, etc.) for 

Alternative 3 first, then Alternative 5 for private small hydropower plant investment 

options. 

 

 
 

Figure 16. The ELECTRE III model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpse.elp) by the Shannon's 

Entropy weighting, distillations (on left), ranks in final preorder (on middle), final 

graph (on right) 

 

In Figure 17 (left), Alternative 3 is the best action in the ELECTRE IV with the 

Shannon's Entropy weighting. Alternative 6 follows Alternative 3 in the descending 

distillation. Alternative 2, Alternative 4, and Alternative 7 are the worst actions in the 

descending distillation. Alternative 1 and Alternative 3 are the worst actions in the 

ascending distillation. Alternative 4 is the best action in the ascending distillation. 

Alternative 3 is ranked first in ELECTRE IV with the Shannon's Entropy weighting (on 

middle and right in Figure 16). Alternative 1, Alternative 5, and Alternative 6 follow this 

alternative. Alternative 4 is the least preferred action. Under these conditions, it is 

recommended that an investigation be started (review data, feasibility studies, etc.) for 

Alternative 3 first, then Alternative 1, Alternative 5, and Alternative 6 for private small 

hydropower plant investment options. 

  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

497 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 
 

Figure 17. The ELECTRE IV model results on the ELECTRE III-IV Version 3 

software (open the electronic supplementary material: ijahpse.elp) by the Shannon's 

Entropy weighting, distillations (on left), ranks in final preorder (on middle), final 

graph (on right) 

 

The findings show that Alternative 3 is ranked first for all ELECTRE III approaches. 

These findings represent that the first rank matches for each weighting approach on the 

ELECTRE III method even though their criteria weights aren't the same. Alternative 1 

ranks second for the equal weighting and Saaty's AHP weighting. Alternative 1, 

Alternative 6 and Alternative 7 rank second in the equal weighting. This study shows that 

ELECTRE III can't discriminate much between the alternatives based on the similar 

findings. Even in the Saaty's AHP weighting, Alternative 3 and Alternative 5 rank first. 

However, these findings show that the rankings of alternatives still promise to be similar 

with minor disturbance with these weighting approaches in ELECTRE III. Hence, there is 

hope that it is possible to represent human subjective evaluations by some objective 

weighting approaches when only considering the final ranks on ELECTRE III method 

(only considering these factors in private small hydropower plant investments) (Figure 

18). In contrast and more importantly, similar results in the rankings don't necessarily 

mean that the way of thinking is similar. Therefore, future research should focus not only 

on just the ordinal rankings, but also its degree of dominance (Garuti, 2012). 

 

The findings show that Alternative 3 is ranked first, Alternative 1, Alternative 5, and 

Alternative 6 are ranked second, Alternative 2 and Alternative 7 are ranked third, and 

Alternative 4 is ranked fourth for all ELECTRE IV approaches. These findings show that 

all ranks match for each weighting approach on the ELECTRE IV method even though 

their criteria weights aren't the same. Alternative 1, Alternative 5, and Alternative 6 

occupy the same rank, while Alternative 2 and Alternative 7 also occupy the same rank. 

This study shows that ELECTRE IV can't discriminate the alternatives as ELECTRE III 

and AHP can. Even in the Saaty's AHP weighting Alternative 1, Alternative 5 and 

Alternative 6 rank second. However, these findings show that the rankings of alternatives 

promise to be the similar with no disturbance with these weighting approaches in 

ELECTRE IV. Hence, it is possible to represent human subjective evaluations by some 

objective weighting approaches with only considering the final ranks on ELECTRE IV 

method (only considering these factors in private small hydropower plant investments) 

(Figure 18). In contrast and more importantly, similar results in the rankings don't 

necessarily mean that the way of thinking is similar. Therefore, future research should 



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

498 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

focus not only on just the ordinal rankings, but also its degree of dominance (Garuti, 

2012). 

 

It is observed that Alternative 3 ranks first for all of the approaches while other 

alternatives have several ranks. Hence, it is believed that it is possible to represent the 

human subjective evaluations by some objective weighting approaches by only 

considering the final ranks on some multi criteria decision making methods (only 

considering these factors in private small hydropower plant investments) (Figure 18). If 

these kinds of findings are found in several studies, some computer based systems which 

work with very little human efforts can be modeled, designed and developed in the 

future. 

 

 
  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

499 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 
Output Methods Alternative Rank Priority Normal Weight 

1 Equal Weight AHP (AEW) Alternative 1 3 0,1247 

  Alternative 2 7 0,0509 

  Alternative 3 1 0,3314 
  Alternative 4 4 0,1177 

  Alternative 5 6 0,0918 

  Alternative 6 5 0,1128 
  Alternative 7 2 0,1708 

2 Shannon's Weight AHP (ASH) Alternative 1 3 0,1228 

  Alternative 2 7 0,0324 
  Alternative 3 1 0,4348 

  Alternative 4 6 0,0855 

  Alternative 5 4 0,1118 
  Alternative 6 5 0,0872 

  Alternative 7 2 0,1255 

3 Saaty's Weight AHP (ASA) Alternative 1 3 0,1274 
  Alternative 2 7 0,0325 

  Alternative 3 1 0,4120 

  Alternative 4 5 0,0973 
  Alternative 5 4 0,1159 

  Alternative 6 6 0,0678 

  Alternative 7 2 0,1472 
4 

Equal Weight ELECTRE III 
(EIIIEW) 

Alternative 1 2 - 

 Alternative 2 4 - 

 Alternative 3 1 - 
  Alternative 4 3 - 

  Alternative 5 3 - 

  Alternative 6 2 - 

  Alternative 7 2 - 

5 Shannon's Weight ELECTRE III 
(EIIISH) 

Alternative 1 3 - 
 Alternative 2 3 - 

  Alternative 3 1 - 

  Alternative 4 5 - 
  Alternative 5 2 - 

  Alternative 6 3 - 

  Alternative 7 4 - 
6 Saaty's Weight ELECTRE III 

(EIIISA) 

Alternative 1 2 - 

 Alternative 2 3 - 

  Alternative 3 1 - 
  Alternative 4 4 - 

  Alternative 5 1 - 

  Alternative 6 3 - 
  Alternative 7 5 - 

7 Equal Weight ELECTRE IV 

(EIVEW) 

Alternative 1 2 - 

 Alternative 2 3 - 
  Alternative 3 1 - 

  Alternative 4 4 - 

  Alternative 5 2 - 
  Alternative 6 2 - 

  Alternative 7 3 - 

8 Shannon's Weight ELECTRE IV 
(EIVSH) 

Alternative 1 2 - 
 Alternative 2 3 - 

  Alternative 3 1 - 

  Alternative 4 4 - 
  Alternative 5 2 - 

  Alternative 6 2 - 

  Alternative 7 3 - 
9 Saaty's Weight ELECTRE IV Alternative 1 2 - 

Equal Shannon's Saaty's Equal Shannon's Saaty's Equal Shannon's Saaty's 

Alternative 1 3 3 3 2 3 2 2 2 2

Alternative 2 7 7 7 4 3 3 3 3 3

Alternative 3 1 1 1 1 1 1 1 1 1

Alternative 4 4 6 5 3 5 4 4 4 4

Alternative 5 6 4 4 3 2 1 2 2 2

Alternative 6 5 5 6 2 3 3 2 2 2

Alternative 7 2 2 2 2 4 5 3 3 3

ELECTRE IIIAHP ELECTRE IV



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

500 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

 (EIVSA) Alternative 2 3 - 

  Alternative 3 1 - 
  Alternative 4 4 - 

  Alternative 5 2 - 

  Alternative 6 2 - 
  Alternative 7 3 - 

 

Figure 18. Comparative model in this study 

 

4. Conclusions, future applications and research 

In this paper, a comparative study was conducted for three weighting approaches (equal 

weighting, Shannon's Entropy, Saaty's AHP) with three multi criteria decision aiding 

methods (AHP, ELECTRE III, ELECTRE IV) on a simplistic unified private small 

hydropower plant investment selection problem in the renewable energy industry. 

 

One important observation made during this research study concerns the representation 

capability of the equal and the Shannon's Entropy objective weighting methods. 

Unfortunately, these methods can't represent the opinions, and the preferences of the 

expert decision maker on the factors taken by the pairwise comparisons of the Saaty's 

AHP method. Another important observation is related to the MCDM methods. The 

preferences of the expert decision maker can be considered very easily by the AHP 

method however, it is not easy to reach the desired level of consistency. Often, several 

attempts must be made to reduce the level of inconsistency, and this process is very time 

consuming. The ELECTRE methods do not have any special way to obtain criteria 

weights. One of the major disadvantages is perceived while deciding the threshold values 

which are very subjective for the decision makers. The investigations should be 

performed well whether or not the thresholds are convincing or unconvincing, however 

this is very difficult. Moreover, the ELECTRE III and the ELECTRE IV aren't capable of 

discriminating the actions when compared to the AHP in this study. One of the main 

advantages of these methods is their capability to split a big problem into smaller pieces 

and investigate these pieces in detail to solve the larger problem. They are very helpful in 

understanding real world problems and their possible solutions. Hence, future studies will 

always recommend to designers and engineers that they gather help and work with these 

methods in their professional lives. The authors think it is important that lectures on this 

subject be given at universities in the engineering disciplines. Finally, another surprising 

observation is made concerning the final ranks. Even though the weights aren't the same, 

the same alternative was ranked first. This finding gives support for continuing to work 

on this subject via an autonomous computer based intelligent decision support system. 

 

In the future, we aim to build and investigate data powered decision aiding models. When 

some statistical methods and approaches are integrated with these weighting methods and 

multi criteria decision making (AHP, ELECTRE III and ELECTRE IV) methods, the 

solutions of the small hydropower plant investment selection problem will become easier 

and more collective. In fact, there are already plans to use these methods in several 

hydropower plant categories and classes. In addition, plans for the application of these 

methods in solar power plants and the 100% renewable power grid are already being 

made by the researcher. We hope that this study and following ones will contribute to the 

practical research of these methods and to the renewable energy. 

  



IJAHP Article: Saracoglu, Mahallesi, Caddesi, Sokak/A comparative study of AHP, ELECTRE III 

& ELECTRE IV by equal objective & Shannon’s Entropy objective & Saaty’s subjective criteria 

weighting on the private small hydropower plants investment selection problem in Turkey 

 

 International Journal of the 
Analytic Hierarchy Process 

501 Vol. 7 Issue 3 2015 

ISSN 1936-6744 

http://dx.doi.org/10.13033/ijahp.v7i3.343 

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