Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making

D Ajay; Ganeshsree Selvachandran; J Aldring; Pham Huy Thong; Le Hoang Son; Bui Cong Cuong

doi:10.1007/s11042-023-14532-9

Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making

Multimed Tools Appl. 2023 Apr 12:1-24. doi: 10.1007/s11042-023-14532-9. Online ahead of print.

Authors

D Ajay¹, Ganeshsree Selvachandran^{2

3}, J Aldring^{1

4}, Pham Huy Thong⁵, Le Hoang Son⁵, Bui Cong Cuong⁶

Affiliations

¹ Department of Mathematics, Sacred Heart College, Tamilnadu, India.
² Institute of Actuarial Science and Data Analytics, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur Malaysia.
³ Symbiosis Institute of Technology Symbiosis International University, Pune, 412115 India.
⁴ Panimalar Engineering College, Department of Mathematics, Chennai, 600 123 Tamil Nadu India.
⁵ VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam.
⁶ Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam.

Abstract

The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.

Keywords: Aggregate operator; Decision making; Einstein exponential operational laws; Exponential operational laws; Spherical fuzzy set.

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