Fermatean fuzzy copula aggregation operators and similarity measures-based complex proportional assessment approach for renewable energy source selection

Abstract

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method.

A Novel SIR Approach to Closeness Coefficient‐Based MAGDM Problems Using Pythagorean Fuzzy Aczel–Alsina Aggregation Operators for Investment Policy

“…Furthermore, we can spread them to other aggregation operators, such as power mean AOs, Bonferroni mean AOs, Hamacher AOs, Hamy mean AOs, and Dombi AOs with SIR techniques. In the future, there is a lot of potential in machine learning, information retrieval, data mining, artifcial intelligence, social network analysis, and many other areas in uncertain scenarios [38][39][40][41][42][43][44][45][46][47][48]. Tese are all fascinating topics for future studies.…”

The differential measure for Pythagorean fuzzy multiple criteria group decision-making

“…Two PFSs B 1 and B 2 are compared to the PFSs A using ( 17), ( 18), ( 20), ( 21), ( 22), (23), and (24). The PFSs are given as follows [48]: It is clear by intuition that A is better than B 1 , since the degrees of membership are higher and the degrees of nonmembership are lower.…”

“…Each of these sets has its characteristics, and the employment of these sets in diverse applications depends mainly on the application and the uncertainty and ambiguity of the information. Various MCDM and MCGDM methods that utilize diverse fuzzy sets have been utilized in solving various applications, e.g., economy [22,23], risk assessment [23,24], renewable energy [25,26], green supplier selection [27][28][29], and health care [30][31][32]. Even during the COVID-19 pandemic, MCDM methods played a role [33][34][35][36][37].…”

Fermatean Fuzzy IWP-TOPSIS-GRA Multi-Criteria Group Analysis and Its Application to Healthcare Waste Treatment Technology Evaluation

“…The research related to FFSs is gradually enriched in a great many areas. To assemble Fermatean fuzzy (FF) numbers, the FF Archimedean copula-based symmetric Maclaurin mean, soft aggregation, and Archimedean copula operators were proposed one after another [14][15][16]. Decision tools including TOPSIS, Measurement Alternatives and Ranking Based on Compromise Solution (MARCOS), and Elimination and Choice Transiting Reality (ELECTRE) in the FF environment were successfully extended to solve supplier selection [17], HCW treatment site selection [18], and biomedical material selection problems [19].…”