Fermatean fuzzy framework based on preference selection index and combined compromise solution methods for green supplier selection in textile industry

Abstract

This work aims to enhance the efficiency and dependability of the green supplier selection process by developing a decision support tool. Thereby, a novel fuzzy group multi-criteria decision-making approach based on the Preference Selection Index (PSI) and Combined Compromise Solution (CoCoSo) methods under the Fermatean Fuzzy (FF) environment for green supplier selection is proposed. The primary novelties and contributions are: (i) for the first time, the FF-PSI model is developed to extract the priority weight values of criteria, (ii) an improved FF-CoCoSo methodology is proposed, and (ii) the FF-PSI-CoCoSo framework is offered for resolving challenging real-life problems. To present the framework’s practicality, a real-case study evaluating six suppliers concerning nine drives under economics, environmental, and technological aspects in a textile company in Turkey is conducted. The results indicate that “green warehousing” is the most essential driver for green suppliers, followed by “recycling” and “damaged product ratio.” A detailed sensitivity and comparison check is further conducted to display the solidity and effectiveness of the proposed framework. The suggested framework offers a reliable solution for green supplier selection and a precise sustainable rating of suppliers. Moreover, it can be addressed to solve various challenging real-world problems.

KEYWORDS:

• Green supplier selection
• sustainability
• Fermatean fuzzy sets
• MCDM
• PSI
• supply chain management

Disclosure statement

No potential conflict of interest was reported by the author(s).

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Data availability statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

List of abbreviations

AHP	=	Analytic Hierarchy Process
BWM	=	Best Worst Method
C	=	Cost
CoCoSo	=	Combined Compromise Solution
CODAS	=	Combinative Distance-based Assessment
COPRAS	=	Complex Proportional Assessment
DEA	=	Data Envelopment Analysis
DEMATEL	=	Decision-Making Trial and Evaluation Laboratory
DPR	=	Damaged Product Ratio
EI	=	Environmental Image
FF	=	Fermatean Fuzzy
FFS	=	Fermatean Fuzzy Sets
GW	=	Green Warehousing
IFS	=	Intuitionistic Fuzzy Sets
JIT	=	Just-In-Time
LDR	=	Late Delivery Ratio
MCDM	=	Multi Criteria Decision Making
MCGDM	=	Fuzzy group multi-criteria decision-making
MOORA	=	Multi-Objective Optimization on the basis of Ratio Analysis
QFD	=	Quality Function Deployment
OH&S	=	Occupational Health and Safety
PC	=	Pollution Control
PFS	=	Pythagorean Fuzzy Sets
PIPRECIA	=	Pivot Pairwise Relative Criteria Relevance Assessment
PROMETHEE	=	Preference Ranking Organization Method for Enrichment Evaluation
PSI	=	Preference Selection Index
R	=	Recycle
R&D	=	Research and Development
SAW	=	Simple Additive Weighting
SCE	=	Scenario
SL	=	Supplier
TA	=	Technical Assistance
TC	=	Technological Competence
TOPSIS	=	Technique for Order of Preference by Similarity to Ideal Solution
VIKOR	=	Multi-Criteria Optimization and Compromise Solution
WASPAS	=	Weighted Aggregated Sum Product Assessment

Notations

α	=	The membership degree
β	=	Non-membership degree
π	=	Indeterminacy degree
$X$	=	Discourse universe
$\tilde{K}$ and $\tilde{P}$	=	Fermatean Fuzzy Sets
$\lambda$	=	Positive real number
$d(\tilde{K},\tilde{P})$	=	The distance functions
$T$	=	The score functions of $\tilde{K}$
$A$	=	The accuracy functions of $\tilde{K}$
$\mathrm{Com}(\tilde{K})$	=	The complement of $\tilde{K}$
$T^p(\tilde{K})$	=	The defuzzified value of $\tilde{K}$
$\tilde{Z}$	=	Aggregated Fermatean Fuzzy
$p$	=	Total numbers of decision makers.
$\tilde{E}$	=	The Fermatean fuzzy decision matrix
${\tilde{e}}_{\mathrm{ij}}$	=	The Fermatean fuzzy value of ith alternative on jth criterion.
${\tilde{N}}_{\mathrm{ij}}$	=	The normalized Fermatean fuzzy value
${\tilde{U}}_j$	=	The average normalized value
${\mathrm{PV}}_j$	=	Preference value
$w_j$	=	Criteria weights
${\tilde{F}}_i$	=	The Fermatean sum of the weighted comparability
${\tilde{G}}_i$	=	The Fermatean power weight of comparability
$F_i$	=	The crisp sum of the weighted comparability
$G_i$	=	The crisp power weight of comparability
$a_{\mathrm{i\alpha }}$, $a_{\mathrm{i\beta }}$, $a_{\mathrm{i\gamma }}$	=	Aggregated appraisal scores
$a_i$	=	Final score