Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Axioms

Dragan Pamucar¹  Masooma Raza Hashmi²  Syeda Tayyba Tehrim²  Muhammad Riaz²  Goran Cirovic³ 

[1] Department of Logistics, Military Academy, University of Defence in Belgarde, 11000 Belgarde, Serbia;Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan;Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia;

关键词: spherical linear diophantine fuzzy set (SLDFS);    spherical linear diophantine fuzzy soft rough set (SLDFSRS);    score function;    core;    reduct;    MCDM;   

DOI  :  10.3390/axioms10030185

来源: DOAJ

【 摘 要 】

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in $[0,1]$. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

【 授权许可】

Unknown