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.
A New Framework for Green Selection of Material Handling Equipment under Fuzzy…
9
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.
Bairagi/Decis. Mak. Appl. Manag. Eng. (2022)
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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