Plane Thermoelastic Waves in Infinite Half-Space Caused


Decision Making: Applications in Management and Engineering  
ISSN: 2560-6018 
eISSN: 2620-0104  

 DOI: https://doi.org/10.31181/dmame0313052021b  

* Corresponding author. 
 E-mail address: bipradasbairagi79@gmail.com (B. Bairagi) 

A NEW FRAMEWORK FOR GREEN SELECTION OF 
MATERIAL HANDLING EQUIPMENT UNDER FUZZY 

ENVIRONMENT  

Bipradas Bairagi*1 

1 Department of Mechanical Engineering, Haldia Institute of Technology, India 
 

Received: 1 April 2022;  
Accepted: 13 May 2022;  
Available online: 13 May 2022. 

 
Original scientific paper 

Abstract. In the rapidly changing global circumstances, managements of 
industrial organizations are making decisions for their survival in business 
atmosphere in future. Decision makers in industries are steering their 
respective organizations towards for appropriate decision making satisfying 
the condition of ‘Go green’. Appropriate decision making in fuzzy environment 
is always a hard task. The current investigation explores a new multi criteria 
decision making approach for green selection of material handling equipment 
under fuzzy environment. The proposed technique has the capability of 
capturing effects of economical, environmental and social factors of benefit, 
non-benefit and target based criteria under uncertainty and vague 
information. The proposed method is illustrated with a suitable example on 
material handling equipment selection under fuzzy environment. The result 
clearly shows that the proposed technique is useful and effective in the 
decision making process regarding green material handling selection under 
fuzzy environment. 

Key words:  MCDM, Green material handling equipment selection, Decision
  making, Fuzzy sets. 

1.   Introduction  

In today’s highly competitive global market scenario industrial organizations 
worldwide are facing difficulty and their existence as well as survival is under 
uncertainty. In this circumstance the industrial organizations are persistently seeking 
means of resolving the difficulties and trying to attain satisfactory condition of going 
green. Selection of material handling equipment under multi criteria decision making 
environment plays a crucial role for the sustainable development especially for 
manufacturing organizations. Substantial development needs consideration of 
economical, environmental and social factors. Green material handling equipment 
selection procedure gives emphasis on meeting requirements of present without 
compromising the capability of future generations to meet their needs. Therefore for 



 Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)  

2 

gaining sustainable development the decision makers consciously incorporates social 
economical or environmental criteria in material handling selection. A wide range of 
literature on material handling equipment selection shows that the previous search 
works in this regard have not given enough attention. New research with proper 
decision making attitude is still essential to show top level management the ray of 
hope for their survival and existence in the tough competitive business world.  

Selection of material handling equipment for manufacturing application is 
essential. Previous researchers’ attention is inadequate to select material handling 
equipment considering green factors. A broad literature survey on material handling 
equipment selection explores this deficit of research work on the field.  

Goswami and Behera (2021) made an investigation for the capability and 
applicability of two well-known MCDM approaches ARAS and COPRAS for the 
evaluation and selection of conveyors, AGV and robots as material handling 
equipment.  Soufi et al. (2021) introduced an AHP based MCDM methodology for the 
evaluation and selection of material handling equipment to be utilized in 
manufacturing systems. Satyam et al. (2021) applied a multi attribute decision 
making approach for evaluation and selection of conveyors as material handling 
equipment. Nguyen et al. (2016) advocated a combined multi criteria decision 
making model for the evaluation and selection of conveyor as the material handling 
equipment based on fuzzy analytical hierarchy process and fuzzy ARAS with vague 
and imprecision information. Mathewa and Sahua (2018) made a comparison among 
the novel multi-criteria decision making approaches by solving a problem on material 
handling equipment selection. None of the above researchers considered green issues 
in their investigations.  

Fonseca et al. (2004) developed a prototype expert system for the purpose 
industrial conveyor selection. Poon et al. (2011) addressed selection and allocation of 
MHE for stocha production material demand problems by using genetic algorithm. 
Lashkari et al. (2004) proposed an integrated model of operation allocation and 
material handling equipment selection in cellular manufacturing systems. Sujono and 
Lashkari (2007) presented a method for determining the operation allocation and 
material handling equipment. Chan et al. (2001) advocate an intelligent material 
handling equipment selection advisor (MHESA) composed of three modules. Kulak 
(2005) proposed a decision support system named fuzzy multi-attribute material 
handling equipment selection (FUMAHES).  

Tuzkaya et al. (2010) developed an integrated fuzzy multi-criteria decision 
making methodology combining fuzzy sets, Analytic Network Process and 
(PROMETHEE) for MHE selection. Chatterjee et al. (2010) gave solution the robot 
selection problem using two suitable multi-criteria decision-making methods and 
compared the relative performances. Shih (2008) presented a group TOPSIS to select 
robots by incremental benefit–cost ratio.  

The gap analysis of the above literature review exposes that, despite the fact that 
previous researchers have attempted to apply MCDM techniques for selection of 
material handling equipment, still, this effort is inadequate for exhaustive and 
extensive decision making regarding green selection of proper material handling 
devices (MHD) from several available alternatives under multiple criteria decision 
making. The literature survey clearly shows that the previous researchers did not 
address the problem of green selection of material handling at a satisfactory level. 

 
The objective of the present study is to develop a decision making framework that 

can be an essential tool in solving problem regarding green selection of material 
handling equipment for industrial organizations.  



A New Framework for Green Selection of Material Handling Equipment under Fuzzy…  

3 

The motivation of the research work is our environment. Our planet is changing 
constantly. Due to rapid global industrialization,   our surrounding environment is 
being constantly harmed from pollutant substance emitted from industries. And its 
adverse effect is falling on all living creature including human society. We the human 
being can steer the direction of change towards the welfare of the beautiful planet 
only by making careful and wise decision in every step of our practical life. We can 
reduce the harmful effect on the earth caused by the use of different material 
handling equipment in industry. The lack of suitable decision making frame work in 
the open literature has ignited the motivation to accomplish the current research 
work.   

The rest of the paper is organized as follows. Section 2 presents the proposed 
algorithm. Section 3 describes an empirical example on green material handling 
equipment selection. Section 4 is dedicated for essential concluding remarks.  

2. Proposed Algorithm 

This research work proposes a novel algorithm consists of 8-steps as follows.   
Step 1: Construction of performance rating matrix: A matrix consisting of 

performance rating of alternatives with respect to criteria is estimated by the experts 
or decision makers. Since the decision is to make under uncertainty, linguistic 
variables are recommended for estimation of performance of alternatives.  Seven 
degrees of linguistic variables with abbreviation and corresponding Triangular Fuzzy 
Number (TFN) are suggested for performance estimation as presented in Table 1.  

 
The performance rating matrix is denoted by   

 
nmijPR

LVM


                                                                                                                          (1) 

LVij denotes performance rating of alternative Ai with respect to criterion Cj in 
linguistic variable. Here, m and n represents number of alternatives and criteria 
respectively.  

Step 2: Construction of weight matrix: In a decision making process different 
criteria may have different importance. This importance weight is estimated by the 
decision makers on the basis of their unanimous decision making attitude through 
discussion. Seven degrees of linguistic variables with abbreviation and corresponding 
Triangular Fuzzy Number (TFN) suggested for weight estimation are presented in 
Table 2. The weight matrix for measuring criteria importance is formed as follows.   

 
njW

LWM



11

                                                                                                                             (2)                                         

LW1j denotes the linguistic weight for criterion Cj.  Here n is number of criteria. 

Table1. Seven degrees of linguistic variables for assessing performance  

Description Abbreviation Triangular Fuzzy Numbers 

Extremely High   EH (1,1,1) 

Very High VH (0.8,0.9,1) 
High H (0.6,0.7,0.8) 
Medium M (0.4,0.5,0.6) 
Low L (0.2,0.3,0.4) 
Very Low VL (0,0.1,0.2) 
Extremely Low EL (0,0,0) 



 Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)  

4 

 
Step 3: Conversion of rating from linguistic terms to TFN: Linguistic rating is not 

suitable for decision making under multiple conflicting criteria. That is why they are 
required to be transformed into fuzzy numbers. The current approach suggests 
triangular fuzzy numbers for making calculation simple and straightforward. Table 1 
shows the rating and equivalent fuzzy numbers. Performance rating matrix in fuzzy 
numbers is presented as follows. 

   
nm

u
ij

m
ij

l
ijnmijPRF

rrrrM


 ,,~
                                                                                  

(3)  
 

,
l

ijr ,
m

ijr
u

ijr stand for lower , middle and upper value of respective TFN 

respectively. 
Step 4: Conversion of weight from linguistic terms to TFN: Linguistic weight is not 

suitable for decision making under multiple conflicting criteria. That is why these are 
required to be changed into fuzzy numbers. The present approach suggests triangular 
fuzzy numbers for making calculation simple and straightforward. Table 2 shows the 
rating and equivalent fuzzy numbers. weight matrix in fuzzy numbers is presented as 
follows. 

   
nm

u
j

m
j

l
jnmjWF

wwwwM


 1111 ,,
~

                                                                            
(4)

                     
 

,
l
ijw ,

m
ijw

u
ijw

 
stand for lower , middle and upper value of respective TFN 

respectively. 
Step 5: Normalization of fuzzy performance rating: Based on the desired value, 

criteria can be divided in 3 different categories, viz. benefit criteria (higher value is 
desired), non-benefit criteria (lower value is desired) and target based criteria 
(Neither higher nor lower value is desired instead a certain target value is desired). 
Normalization of fuzzy rating is implemented using appropriate formula depending 
on the nature of criteria. Following formulae are recommended for executing 
normalization process. 

For benefit criteria: 





















u
ij

ji

u
ij

u
ij

ji

m
ij

u
ij

ji

l
ij

ij
r

r

r

r

r

r
r

(max
,

)(max
,

)(max
,,,

           
                                                                                  (5) 

For non-benefit criteria           





















u
ij

ji

l
ij

u
ij

ji

m
ij

u
ij

ji

u
ij

ij
r

r

r

r

r

r
r

(max
1,

)(max
1,

)(max
1

,,,

                                                        (6) 

Table 2. Seven degrees of recommended linguistic weights of criteria  

Description Abbreviation Triangular Fuzzy Number 

Absolutely Important      AI (1,1,1) 

Extremely important      EI (0.8,0.9,1) 

Very important      VI (0.6,0.7,0.8) 

Medium  Important      MI (0.4,0.5,0.6) 

Ordinarily Important      OI (0.2,0.3,0.4) 

Slightly Unimportant      S  (0,0.1,0.2) 

Unimportant       UI (0,0,0) 



A New Framework for Green Selection of Material Handling Equipment under Fuzzy…  

5 

For target based criteria         




















)(max)(max

1,
)(max)(max

1,
)(max)(max

1

,,,,,,

u
ij

ji

l
ij

u
ij

ji

l
T

u
ij

ji

m
ij

u
ij

ji

m
T

u
ij

ji

u
ij

u
ij

ji

u
T

ij
r

r

r

r

r

r

r

r

r

r

r

r
r

                    (7) 

The normalization process is carried out in so as to convert all the fuzzy 
performance ratings in benefit sense irrespective of nature of criteria. 

Step 6: Weighted normalized rating: Weighted normalized rating is the rating 
modified by respective criteria weight. This paper recommends following nonlinear 
integration of an alternative rating with each criterion weight. 

For benefit criteria Eq. (8) is applied.
 

     

1 1

0 0 0
, , ,

, ,
max max max

l m u

j j ij
w w wl m u

ij ij ijwn
ij

l u u
ij ij ij

i j i j i j

r r r
r dx dx dx

r r r
  

 
 

  
  
 

                                       (8) 

For non-benefit criteria Eq. (9) is applied.
 

 

     

1 1

0 0 0, , ,

1 , 1 , 1
max max max

u m l
j j ijw w wu m l

ij ij ijwn
ij

u u u
ij ij ij

i j i j i j

r r r
r dx dx dx

r r r
  

      
      
         
      

      
      

                                                    (9) 

For target based criteria Eq. (10) is used. 
 

           

1 1

0 0 0
, , , , , ,

1 , 1 , 1
max max max max max max

u m l

j j ij
w w wu m lu m l

ij ij ijwn T T T
ij

u u u u u u
ij ij ij ij ij ij

i j i j i j i j i j i j

r r rr r r
r dx dx dx

r r r r r r
     

 
 

    
 
 
 

  
                                                                                                                                                              

                                                                                                                                                               (10)
                                                                           

 

Step 7: Defuzzification of performance rating is accomplished using the following 
Eq. (11)-Eq. (13) 
For benefit criteria used Eq. (11) is employed. 

 

                               (11)                                                                              

  

 
For non-benefit criteria

 

     

1 1

0 0 0
, , ,

1
1 4 1 1

6 max max max

u m l

j j ij
w w wu m l

ij ij ijnw
ij

l u u
ij ij ij

i j i j i j

r r r
r dx dx dx

r r r
  

      
      

           
            

      

         (12)                 
 

For target based criteria  

           

1 1

0 0 0
, , , , , ,

1
1 4 1 1

6 max max max max max max

u m l

j j ij
w w wu m lu m l

ij ij ijT T T

u u u u u u
ij ij ij ij ij ij

i j i j i j i j i j i j

r r rr r r
dx dx dx

r r r r r r
     

 
 

        
 
 
 

  

             
 

                                                                                                                                                    
(13) 

     

1 1

0 0 0
, , ,

1
4

6 max max max

l m u

j j ij
w w wl m u

ij ij ijwn
ij

u u u
ij ij ij

i j i j i j

r r r
r dx dx dx

r r r
  

 
 

   
  
 

  



 Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)  

6 

Step 8: Performance Index: Performance index indicates responsible for measuring 
performance, ranking and selection. The current investigation advocates the 
following technique in calculation performance indicator (PI) by integrating 
individual contribution of each criterion towards the evaluation of alternatives. 

 
 

      
 






































































NBCj

l
ij

w

u
ij

ji

l
ij

m
j

w

u
ij

ji

m
ij

u
j

w

l
ij

ji

u
ij

dx
r

r
dx

r

r
dx

r

r

0
,

1

0
,

1

0
,

max
1

max
14

max
1

6

1 , 

            
 




















TBCj

l
ij

w

u
ij

ji

l
ij

u
ij

ji

l
T

m
j

w

u
ij

ji

m
ij

u
ij

ji

m
T

u
j

w

u
ij

ji

u
ij

u
ij

ji

u
T

dx
r

r

r

r
dx

r

r

r

r
dx

r

r

r

r

0
,,

1

0
,,

1

0
,,

maxmax
1

maxmax
14

maxmax
1

6

1                                     

      (14) 

Hence PIi denotes performance index of ith alternative. Performance index has its 
beneficial sense, that is higher value is desirable. Thus alternatives are arranged in 
the descending order of their respective PI value. The alternative with the highest 
value of performance index is considered the best alternative. The alternative with 
least value of performance index is considered as the worst alternative and so on. 

3. Illustrative Example  

A South-East Asian manufacturing organization plans to select material handling 
equipment including the factors related to green. A selection committee comprising of 
manager, experts and decision makers is formed. The committee chooses seven 
selection criteria keeping green selection in view under fuzzy environment. Safety 
(C1), operating friendliness (C2), environment friendliness (C3), robustness (C4), 
cost (C5), repeatability (C6), and human-interaction (C7) are the six selection criteria 
for material handling equipment. Safety, operating friendliness are social factors, cost 
is economical and environment friendliness is environmental factors. These factors 
are selected keeping green factors in view. Safety, operating friendliness, 
environment friendliness, and robustness are benefit criteria; cost and repeatability 
are non-benefit or cost criteria; whereas human-interaction is target based criteria. 
Four alternative material handling equipment designated by A1, A2, A3 and A4 are 
preliminarily selected after initial screening for further evaluation.   

3.1 Estimation of linguistic rating 

A detailed question-answer interview is conducted for the decision making 
committee to construct a performance rating matrix in terms of linguistic variable as 
furnished in Table 3. It is observed that Criteria C1, C2, C3 and C4 are benefit criteria, 
C5 and C6 are non-benefit criteria and C7 is target based criteria (TBC). Table 4 
represents performance rating matrix in terms of linguistic variable. The alternative 
material handling equipment A1 is awarded linguistic performance rating viz. EH, VH, 
M, EH, M, VH, and L with respect to criteria C1, C2, C3, C4, C5, C6 and C7. EH 
(extremely high rating is better and desirable) under benefit criteria. M and VH are 
provided under non-benefit or cost criteria. Comparatively, M (medium) is better 
than VH (very high). For C7, L (low) is expected value.   

      
 




















BCj

u
ij

w

u
ij

ji

u
ij

m
j

w

u
ij

ji

m
ij

l
j

w

l
ij

ji

l
ij

i dx
r

r
dx

r

r
dx

r

r
PI

0
,

1

0
,

1

0
,

maxmax
4

max6

1



A New Framework for Green Selection of Material Handling Equipment under Fuzzy…  

7 

Table 3. Performance rating matrix in terms of linguistic variables 

Estimated by 
Decision making 
committee 

Criteria 

 
Benefit Criteria 

Non-benefit 
Criteria 

 
TBC* 

A
lt

e
rn

a
ti

v
e

 Ai C1 C2 C3 C4 C5 C6 C7 
A1 EH VH M EH M VH L 
A2 VH H EH M VH M EH 
A3 M VL EH VH H L VH 
A4 EH M VH MI VL EH M 

*TBC stands for Target Based Criteria; Target value for TBC is set to M (medium). 
 

The importance weights of Criteria, C1, C2, C3, C4, C5, C6 and C7 are estimated as 
AI, EI, MI, OI, MI, EI, and AI in linguistic abbreviation. It implies that criteria C2 and 
criteria C6 are jointly given the highest importance. Criterion robustness (C4) is 
assumed relatively less important.   

 
Table 4. Weight matrix in terms of linguistic variables 

Estimated by 
Decision making 
committee 

Criteria 

 
Benefit Criteria 

Non-benefit 
Criteria 

 
TBC* 

C1 C2 C3 C4 C5 C6 C7 
Weight  AI EI MI OI MI EI AI 

*TBC stands for Target Based Criteria; Target value for TBC is set to M (medium). 

3.2 Calculation and Illustration  

Since the decision is to make in fuzzy environment, therefore performance rating 
of alternative and the importance weights of selection criteria have been extracted in 
the form of linguistic variables. These linguistic variables are not directly suitable for 
decision making. So conversion of linguistic variables into corresponding fuzzy 
number is an essential step. The conversion scale for the performance rating are as 
follows: Extremely High (1,1,1), Very High (0.8,0.9,1), High (0.6,0.7,0.8), Medium 
(0.4,0.5,0.6), Low (0.2,0.3,0.4), Very Low(0,0.1,0.2) and  Extremely Low (0,0,0). 
Conversion of linguistic terms to TFN is performed and shown in Table 5. 

 
Table 5. Fuzzy performance rating in terms of TFN 
 Benefit Criteria Non-benefit Criteria TBC* 

Ai C1 C2 C3 C4 C5 C6 C7 
A1 (1,1,1) (0.8,0.9,1) (0.4,0.5,0.6) (0.2,0.3,0.4) (0.4,0.5,0.6) (0.8,0.9,1) (0.2,0.3,0.4) 

A2 (0.8,0.9,1) (0.6,0.7,0.8) (0.2,0.3,0.4) (0.4,0.5,0.6) (0.8,0.9,1) (0.4,0.5,0.6) (1,1,1) 

A3 (0.4,0.5,0.6) (0,0.1,0.2) (1,1,1) (0.8,0.9,1) (0.6,0.7,0.8) (0.2,0.3,0.4) (0.8,0.9,1) 

A4 (0.2,0.3,0.4) (0.4,0.5,0.6) (0.8,0.9,1) 0.4,0.5,0.6) (0,0.1,0.2) (1,1,1) (0.4,0.5,0.6) 

*TBC stands for Target Based Criteria 

 
The conversion scale for the linguistic weight of criteria into triangular fuzzy 

number are as follows: Absolutely Important (1,1,1), Extremely important(0.8,0.9,1),  
Very important(0.6,0.7,0.8), Medium  Important (0.4,0.5,0.6), Ordinarily Important 
(0.2,0.3,0.4), Slightly Unimportant, (0,0.1,0.2) and Unimportant (0,0,0). Conversion of 
weight from linguistic terms to triangular fuzzy number is presented in Table 6.  
 



 Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)  

8 

Table 6. Weight matrix in terms of linguistic variables 
 Criteria 

Benefit Criteria Non-benefit Criteria TBC* 
 C1    C2 C3 C4 C5 C6 C7 
Weight  (1,1,1) (.8,0.9,1) (.4,0.5,0.6) (.2,0.3,0.4) (.4,0.5,0.6) (.8,0.9,1) (1,1,1) 
*TBC stands for Target Based Criteria 

Normalization of fuzzy performance rating is accomplished and the normalized 
performance fuzzy ratings are calculated by using respective Eq.( 5)- Eq.(7). For 
example, normalized fuzzy performance rating for the alternative A1, with respect to 
criteria C1 is carried out as follows. The criterion Safety (C1) is benefit criterion. 
Therefore, Eq. (5) has been used. The highest grade under the criterion C1 is (1,1,1). 
The upper point of the TFN is 1. Then the normalized performance rating for this case 
is obtained by dividing the each of the point, lower, middle, upper with 1(maximum 
upper point under the criterion).   The computed normalized performance rating is 
(1,1,1). Similarly the rest of the normalized performance ratings are calculated.  To 
take the account of the variation, different importance weights have been integrated 
with the already calculated normalized performance ratings. For the purpose, a new 
equation is introduced in the current proposed algorithm. Weighted normalized 
rating is computed by using Eq. (8) -Eq. (10) and shown in Table 7. 
 

Table 7. Weighted normalized fuzzy performance ratings 
 Benefit Criteria Non-benefit Criteria TBC* 
Ai C1 C2 C3 C4 C5 C6 C7 
A1 (1,1,1) (.64,0.81, 1) (0.16,0.25,.36) (0.04,.09,0.16) (0.16,0.25,0.36) (0,0.09,0.2) (0.6,0.8, 1) 

A2 (0.8,0.9,1) (.48,0.63,.8) (0.08, .15,.24) (0.08,0.15,.24) (0.0,0.05,0.12) (0.32,0.45,0.6) (0.4,0.5,0.6) 

A3 (0.4,0.5,0.6) (0,0.09,0.2) (0.16, 0.5 ,0.6) (0.16,0.27,0.4) (0.08,0.15,0.24) (0.48,0.63,0.8) (0.6,0.6,0.6) 

A4 (0.2,0.3,0.4) (.32,0.45,.6) (0.32,.45, 0.6) (0.08,.15,0.24) (0.16,0.45,0.6) (0,0,0) (1,1,1) 

*TBC stands for Target Based Criteria 

Weighted normalized performance ratings have been expressed in terms of 
triangular fuzzy number. TFN is not suitable for making final decision regarding the 
performance evaluation of the alternative material handling equipment. Therefore, it 
is essential to convert the fuzzy number into quantified corresponding crisp number. 
The process of converting the fuzzy number into crisp number is termed as 
defuzzification.  Conversely, the conversion process of crisp number into 
corresponding fuzzy number is termed as fuzzification. In the current study the 
defuzzification process is completed through the application of three different newly 
introduced appropriate equations. Eq. (11) has been implemented for benefit criteria, 
Eq. (12) has been used for cost or non-benefit criteria,  Eq. (13) has been applied for 
target oriented criterion C7. Table 8 shows defuzzified weighted normalized ratings 
as calculated by using Eq. (11)- Eq.(13). Performance index is the index of an 
alternative material handling equipment that express extent of benefit over the cost 
as well as non beneficial performance. For the purpose of estimation of performance 
index of each of the alternative material handling equipment a new, integration 
oriented technique has been proposed in the investigation as presented in Eq.(14). 
The performance index for each individual alternative has been shown in Table 8.  
 



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Table 8. Defuzzified weighted normalized rating, performance index and rank  
 Defuzzified Weighted Normalized Rating Performance 

Index 

 

 
Benefit Criteria 

Non-Benefit 
Criteria 

TBC* Rank 

Ai C1 C2 C3 C4 C5 C6 C7 PI  
A1 1 0.816 0.256 0.096 0.256 0.096 0.8 3.32 1 

A2 0.9, 0.636 0.156 0.156 0.056 0.456 0.5 1.96 4 

A3 0.5 0.096 0.560 0.276 0.156 0.636 0.6 2.28 3 

A4 0.3 0.456 0.456 0.156 0.456 0 1 2.82 2 

*TBC stands for Target Based Criteria 

Theoretically, the lower limit and the upper limit of performance index associated 
with any alternative can be 0 (zero) and n (where n is the number of criteria) 
respectively. In other words, the range of the performance index may vary from 0 to 
n, that is   zero is the lower limit and n (number of criteria) is the upper limit of the 
result (performance index).  
 

 
 

Figure 1. Performance indices of alternatives 
The performance indices of the alternative material handling equipment are 

diagrammatically represented in Figure1, for improved visualization, enhanced 
clarification and better comparison. Different alternatives are plotted along the 
horizontal axis, and the respective performance indices are depicted along the 
vertical axis. It is clearly observed from the Figure1 that alternative material handling 
equipment A1 attains the highest performance index.  A4 has the second highest 
performance index, A3 posses the next higher performance index, lastly A2 has the 
lowest performance index. The alternatives of material handling equipment are 
ranked accordingly.  

The performance indices of the alternatives Al, A2, A3 and A4 are 3.32, 1.96, 2.28, 
and 2.82 respectively. The alternatives are arranged as per the descending order of 
their performance indices. Therefore the ranking order of the alternatives are 
arranged as A1>A4>A3>A2.  It is seen that the alternative A1 has the highest 
performance index. Hence A1 is considered the best alternative and A2 is the worst 
one and so on. The ranking order is depicted in Figure 2.    

 



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10 

 
 

Figure 2. Ranking order of the alternatives 

3.2 Comparison of the Results  

The results obtained by the proposed method have been compared with and 
validated by two well-known tools viz. Technique of Order Preference by Similarity to 
Ideal Solutions (TOPSIS) and Multi Objective Optimization on the basis of Ratio 
Analysis (MOORA). For the purpose of making comparison and validation, the same 
ranking problem on material handling equipment selection is once again solved by 
the methods separately.  In TOPSIS method, the closeness coefficient (CC) for each of 
the alternative is calculated. In MOORA method, net score is computed for each 
alternative material handling equipment.  The relevant information is furnished in 
the Table 9. It is observed that the closeness coefficient or relative closeness of the 
alternative A1, A2, A3 and A4 are 0.60, 0.42, 0.41 and 0.45 respectively. Therefore the 
ranking orders of the alternatives are A1>A4>A2>A3. It is obvious that TOPSIS 
method selects alternative A1 as the best alternative, A4 as the second best 
alternatives as the proposed methods. Though, the ranking orders of the A2 and A3 
do not match.   In MOORA method, alternative A1 is ranked 1 and regarded as the 
best method. The graphical representation of the ranking orders obtained by the 
proposed method and the two well-known existing methods TOPSIS and MOORA is 
portrayed in Figure 3. The alternatives are plotted along horizontal axis and the 
ranking orders are plotted along vertical axis. It is found that alternative A1 has been 
selected as the best alternative by all the three multi-criteria decision making 
techniques. These results verify and validate the novel framework in decision making 
under fuzzy environment.    
 

Table 9: Comparison and validation of the results  

 

Proposed Method TOPSIS MOORA 

Ai Performance Index Rank CC Rank Net  Score Rank 

A1 3.32 1 0.60 1 0.79 1 

A2 1.96 4 0.42 3 -0.07 2 

A3 2.28 3 0.41 4 -0.16 4 

A4 2.82 2 0.45 2 -0.1 3 
 
 



A New Framework for Green Selection of Material Handling Equipment under Fuzzy…  

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Figure 3. Comparision of ranking orders  

4. Conclusions 

The current investigation explores a new fuzzy MCDM framework in green 
selection of material handling equipment for industrial purpose considering multiple 
conflicting criteria. The novel framework is able to integrate economical, 
environment and social factors with vague information to meet the necessary 
requirements for green selection. The application of the proposed framework in 
solving the material handling evaluation problem clearly shows the way of 
implementation and the ability of the framework to make proper decision 
considering multiple criteria under fuzzy environment. The framework clearly selects 
the alternative material handling equipment A1 as the best one with the highest 
performance index 3.32.   Therefore it can be concluded that the proposed technique 
introduced in the current research work might be a useful and essential aid to 
managerial decision makers of manufacturing industry in solving problem on green 
selection of material handling equipment. The result of the proposed method is 
supported and validated by two exiting well-known multi-criteria methods. The 
novelty of the current study can be highlighted as follows:  

 Introduction of a novel mathematical model for fuzzy decision making. 
 Incorporation of green factors in evaluation of material handling equipment. 
 Consideration of benefit, non-benefit and target value based criteria.  
 Application of integration in fuzzy decision making environment.  
There are some limitations of the present approach though it has many 

advantages. This method cannot be used for objective factors or a mixture of 
objective and subjective factors. It has not addressed the consideration of 
heterogeneous group decision making. The current investigation is limited to 
independent criteria and decision making under fuzzy environment.  

An insight of the research exposes that a new paradigm has been explored in the 
current investigation. In this research work, performance rating and weights of 
criteria are estimated in the prescribed degrees of linguistic form. These are 
efficiently integrated for calculating the performance indices for proper decision 
making in the specific domain.  

The proposed model can be used for solving similar multi criteria decision 
making problems where decision is to make under fuzzy environment. The 



 Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)  

12 

appropriate implementation of the technique can be a useful managerial tool in 
solving industrial decision making problem.  

Consideration of interdependent factors, incorporation of heterogeneous group 
decision making process and decision making with both subjective and objective 
factors, in green selection of material handling equipment for industrial purpose 
might be some important directions of future research.  

Author Contributions: Conceptualization, B.B.; methodology, B.B.; validation, B.B.; 
formal analysis, B.B.; investigation, B.B.; resources, B.B.; writing—original draft 
preparation, B.B.; writing—review and editing, B.B.; visualization, B.B.; supervision, 
B.B.; The author has read and agreed to the published version of the manuscript. 
 
Funding: This research received no external funding. 
 
Conflicts of Interest: The author declares that he has no known competing financial 
interests or personal relationships that could have appeared to influence the work 
reported in this paper. 

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