Fermatean Fuzzy Schweizer–Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer–Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.

[1]  Hu-Chen Liu,et al.  New method for emergency decision making with an integrated regret theory-EDAS method in 2-tuple spherical linguistic environment , 2022, Applied Intelligence.

[2]  Xindong Peng,et al.  When CCN meets MCGDM: optimal cache replacement policy achieved by PRSRV with Pythagorean fuzzy set pair analysis , 2022, Artificial Intelligence Review.

[3]  Peide Liu,et al.  COPRAS method based on interval-valued hesitant Fermatean fuzzy sets and its application in selecting desalination technology , 2022, Appl. Soft Comput..

[4]  Rosa M. Rodríguez,et al.  A comprehensive minimum cost consensus model for large scale group decision making for circular economy measurement , 2022, Technological Forecasting and Social Change.

[5]  M. Goh,et al.  An extended picture fuzzy MULTIMOORA method based on Schweizer–Sklar aggregation operators , 2022, Soft Computing.

[6]  Hai Wang,et al.  An integrated qualitative group decision-making method for assessing health-care waste treatment technologies based on linguistic terms with weakened hedges , 2022, Appl. Soft Comput..

[7]  Yejun Xu,et al.  Social network clustering and consensus-based distrust behaviors management for large-scale group decision-making with incomplete hesitant fuzzy preference relations , 2021, Appl. Soft Comput..

[8]  S. Wan,et al.  Personalized individual semantics based consensus reaching process for large-scale group decision making with probabilistic linguistic preference relations and application to COVID-19 surveillance , 2021, Expert Syst. Appl..

[9]  Zeshui Xu,et al.  Green supplier selection based on probabilistic dual hesitant fuzzy sets: A process integrating best worst method and superiority and inferiority ranking , 2021, Appl. Intell..

[10]  Jun Liu,et al.  An innovative index system and HFFS-MULTIMOORA method based group decision-making framework for regional green development level evaluation , 2021, Expert Syst. Appl..

[11]  Sifeng Liu,et al.  A novel approach to three-way conflict analysis and resolution with Pythagorean fuzzy information , 2021, Information Sciences.

[12]  Mark Goh,et al.  Statistics-based approach for large-scale group decision-making under incomplete Pythagorean fuzzy information with risk attitude , 2021, Knowl. Based Syst..

[13]  A. Mishra,et al.  Fermatean fuzzy CRITIC-EDAS approach for the selection of sustainable third-party reverse logistics providers using improved generalized score function , 2021, J. Ambient Intell. Humaniz. Comput..

[14]  S. Jeevaraj,et al.  Ordering of interval-valued Fermatean fuzzy sets and its applications , 2021, Expert Syst. Appl..

[15]  Madjid Tavana,et al.  An integrated group fuzzy best-worst method and combined compromise solution with Bonferroni functions for supplier selection in reverse supply chains , 2021, Cleaner Logistics and Supply Chain.

[16]  Zeshui Xu,et al.  Green supplier selection based on probabilistic dual hesitant fuzzy sets: A process integrating best worst method and superiority and inferiority ranking , 2021, Applied Intelligence.

[17]  Ganesh Ghorai,et al.  Multiple attribute decision-making based on different types of Dombi aggregation operators under Fermatean fuzzy information , 2021, Soft Computing.

[18]  James J. H. Liou,et al.  Application of an MCDM model with data mining techniques for green supplier evaluation and selection , 2021, Appl. Soft Comput..

[19]  Grigorios L. Kyriakopoulos,et al.  Fermatean Fuzzy CRITIC-COPRAS Method for Evaluating the Challenges to Industry 4.0 Adoption for a Sustainable Digital Transformation , 2021, Sustainability.

[20]  Guiwu Wei,et al.  CPT-MABAC method for spherical fuzzy multiple attribute group decision making and its application to green supplier selection , 2021, J. Intell. Fuzzy Syst..

[21]  Harish Garg,et al.  An efficient intuitionistic fuzzy MULTIMOORA approach based on novel aggregation operators for the assessment of solid waste management techniques , 2021, Applied Intelligence.

[22]  Sait Gül.  Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID‐19 testing laboratory selection problem , 2021, Expert Syst. J. Knowl. Eng..

[23]  A. Mishra,et al.  Multi-criteria healthcare waste disposal location selection based on Fermatean fuzzy WASPAS method , 2021, Complex & Intelligent Systems.

[24]  Qaisar Khan,et al.  Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management , 2021 .

[25]  Arunodaya Raj Mishra,et al.  Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection , 2021, Expert Syst. Appl..

[26]  K. S. Ravichandran,et al.  Double-hierarchy hesitant fuzzy linguistic information-based framework for green supplier selection with partial weight information , 2021, Neural Computing and Applications.

[27]  Peide Liu,et al.  Complex q-rung orthopair fuzzy Schweizer-Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making , 2021, J. Intell. Fuzzy Syst..

[28]  Gulfam Shahzadi,et al.  Hamacher Interactive Hybrid Weighted Averaging Operators under Fermatean Fuzzy Numbers , 2021 .

[29]  Zheng Pei,et al.  A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment , 2021, International Journal of Machine Learning and Cybernetics.

[30]  M. Goh,et al.  A novel Kano-QFD-DEMATEL approach to optimise the risk resilience solution for sustainable supply chain , 2020, Int. J. Prod. Res..

[31]  H. Fazlollahtabar,et al.  GREEN SUPPLIER SELECTION BASED ON THE INFORMATION SYSTEM PERFORMANCE EVALUATION USING THE INTEGRATED BEST-WORST METHOD , 2021, Facta Universitatis, Series: Mechanical Engineering.

[32]  Abbas Mardani,et al.  A new Pythagorean fuzzy-based decision-making method through entropy measure for fuel cell and hydrogen components supplier selection , 2021 .

[33]  Harish Garg,et al.  Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty , 2021, Int. J. Comput. Intell. Syst..

[34]  Yuan Rong,et al.  Complex q‐rung orthopair fuzzy 2‐tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection , 2020, Int. J. Intell. Syst..

[35]  Fatih Ecer,et al.  Sustainable supplier selection: A novel integrated fuzzy best worst method (F-BWM) and fuzzy CoCoSo with Bonferroni (CoCoSo’B) multi-criteria model , 2020 .

[36]  Harish Garg,et al.  Decision-Making Analysis Based on Fermatean Fuzzy Yager Aggregation Operators with Application in COVID-19 Testing Facility , 2020 .

[37]  Harish Garg,et al.  Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight , 2020, Soft Computing.

[38]  Hu-Chen Liu,et al.  Green Supplier Evaluation and Selections: A State-of-the-Art Literature Review of Models, Methods, and Applications , 2020, Mathematical Problems in Engineering.

[39]  Prasenjit Chatterjee,et al.  Development of an integrated decision making model for location selection of logistics centers in the Spanish autonomous communities , 2020, Expert Syst. Appl..

[40]  Divya Zindani,et al.  Interval-valued intuitionistic fuzzy TODIM method based on Schweizer–Sklar power aggregation operators and their applications to group decision making , 2020, Soft Computing.

[41]  Ronald R. Yager,et al.  Fermatean fuzzy sets , 2019, Journal of Ambient Intelligence and Humanized Computing.

[42]  Wenkai Zhang,et al.  Green supplier selection in electronics manufacturing: An approach based on consensus decision making , 2020 .

[43]  Weimin Ma,et al.  Three-way group decisions under hesitant fuzzy linguistic environment for green supplier selection , 2020, Kybernetes.

[44]  Na Li,et al.  Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making , 2020, Int. J. Intell. Syst..

[45]  Arunodaya Raj Mishra,et al.  Novel Single-Valued Neutrosophic Combined Compromise Solution Approach for Sustainable Waste Electrical and Electronics Equipment Recycling Partner Selection , 2020, IEEE Transactions on Engineering Management.

[46]  Salih Berkan Aydemir,et al.  Fermatean fuzzy TOPSIS method with Dombi aggregation operators and its application in multi-criteria decision making , 2020, J. Intell. Fuzzy Syst..

[47]  Ning Li,et al.  A Novel Multi-Attribute Group Decision-Making Method and Its Application in Solving the Downward Referral Problem in the Hierarchical Medical Treatment System in China , 2019, IEEE Access.

[48]  Huchang Liao,et al.  Cold Chain Logistics Management of Medicine with an Integrated Multi-Criteria Decision-Making Method , 2019, International journal of environmental research and public health.

[49]  Huchang Liao,et al.  A GREY COMBINED COMPROMISE SOLUTION (COCOSO-G) METHOD FOR SUPPLIER SELECTION IN CONSTRUCTION MANAGEMENT , 2019 .

[50]  E. Zavadskas,et al.  A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems , 2019, Management Decision.

[51]  Ronald R. Yager,et al.  Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods , 2019, Eng. Appl. Artif. Intell..

[52]  Umang Soni,et al.  Green supplier selection using multi-criterion decision making under fuzzy environment: A case study in automotive industry , 2019, Comput. Ind. Eng..

[53]  Huayou Chen,et al.  An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods , 2019, Inf. Sci..

[54]  Peide Liu,et al.  Multiple-attribute decision making based on single-valued neutrosophic Schweizer-Sklar prioritized aggregation operator , 2019, Cognitive Systems Research.

[55]  Hu-Chen Liu,et al.  An Extended Alternative Queuing Method with Linguistic Z-numbers and Its Application for Green Supplier Selection and Order Allocation , 2019, International Journal of Fuzzy Systems.

[56]  Jiahang Yuan,et al.  Approach for multi-attribute decision making based on novel intuitionistic fuzzy entropy and evidential reasoning , 2019, Comput. Ind. Eng..

[57]  Donghai Liu,et al.  Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods , 2019, Int. J. Intell. Syst..

[58]  Jianhua Ma,et al.  Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment , 2019, Inf. Sci..

[59]  R. Rakkiyappan,et al.  Interval-valued intuitionistic hesitant fuzzy entropy based VIKOR method for industrial robots selection , 2019, Expert Syst. Appl..

[60]  Ronald R. Yager,et al.  Some New Operations Over Fermatean Fuzzy Numbers and Application of Fermatean Fuzzy WPM in Multiple Criteria Decision Making , 2019, Informatica.

[61]  Yuanyuan Liu,et al.  Fermatean fuzzy linguistic set and its application in multicriteria decision making , 2018, Int. J. Intell. Syst..

[62]  Peng Wang,et al.  Some interval-valued intuitionistic fuzzy Schweizer–Sklar power aggregation operators and their application to supplier selection , 2018, Int. J. Syst. Sci..

[63]  Narges Banaeian,et al.  Green supplier selection using fuzzy group decision making methods: A case study from the agri-food industry , 2018, Comput. Oper. Res..

[64]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[65]  J. Rezaei.  Best-worst multi-criteria decision-making method: Some properties and a linear model , 2016 .

[66]  Ronald R. Yager,et al.  Pythagorean Membership Grades in Multicriteria Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[67]  Huayou Chen,et al.  Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making , 2014, Knowl. Based Syst..

[68]  Ronald R. Yager,et al.  Pythagorean Membership Grades, Complex Numbers, and Decision Making , 2013, Int. J. Intell. Syst..

[69]  Etienne Kerre,et al.  A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms , 2002 .

[70]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .