Raptean Fuzzy Set: A Fuzzy Extension and Its Application in Sustainable Evaluation of Clean Energy Barriers

Rajdip Mahajan; Abhijit Baidya; Pinki Majumder; Uttam Kumar Bera

doi:10.65069/jessd21202617

Authors

Rajdip Mahajan Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India Author https://orcid.org/0009-0008-0195-3053
Abhijit Baidya Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India Author https://orcid.org/0000-0003-0023-5099
Pinki Majumder Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India Author https://orcid.org/0000-0003-0061-9025
Uttam Kumar Bera Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India Author https://orcid.org/0000-0001-5426-7614

DOI:

https://doi.org/10.65069/jessd21202617

Keywords:

Raptean fuzzy set, Score function, Aggregation operators, Distance measure, Multi-criteria group decision-making, Clean energy barriers evaluation

Abstract

This study introduces the concept of the Raptean fuzzy set (RFS), characterized by a three-dimensional (3-D) fuzzy membership grade, representing a sophisticated expansion of the picture fuzzy set (PiFS), spherical fuzzy set (SFS), and Fermatean fuzzy set (FFS). Subsequently, algebraic operations on RFS, incorporating fundamental properties, are considered for better handling of uncertainty, inspired by the preliminary concept of fuzzy sets. Additionally, the score and accuracy functions have been proposed to defuzzify Raptean fuzzy numbers (RFNs) for the objective of ranking. Moreover, this study presents aggregation operators (AOs) for RFS, utilized for the aggregation of RF information, and provides rigorous theorems along with their corresponding proofs. Furthermore, the Euclidean distance and the Zhang and Xu distance have been introduced for two RFSs. Subsequently, we develop a Raptean fuzzy Weighted Aggregated Sum Product Assessment (WASPAS) method and an innovative ranking technique utilizing the Raptean fuzzy distance measure to tackle the complexities associated with multi-criteria group decision-making (MCGDM). Additionally, this study presents an application of MCGDM and addresses the sustainable evaluation of clean energy barriers, thereby demonstrating the practicability of the introduced models. Finally, the examined comparative and sensitivity analyses validate the stability and efficiency of the suggested MCGDM models and verify the greater decision space for RFS in decision-making problems.

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Raptean Fuzzy Set: A Fuzzy Extension and Its Application in Sustainable Evaluation of Clean Energy Barriers

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