Abstract
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.
Highlights
Introduction an Literature ReviewConventional Mathematics is not always helpful to tackle real world problems due to hesitations and ambiguities present in their nature
In order to deal with such problems, we introduced a robust hybrid model named as spherical linear diophantine fuzzy set which fusion of spherical linear Diophantine fuzzy set (SLDFS), soft set, and rough set
We presented the graphical representation of SLDFS to compare it with some existing extensions of fuzzy sets
Summary
Conventional Mathematics is not always helpful to tackle real world problems due to hesitations and ambiguities present in their nature. In 2019, Riaz and Hashmi [69] established the idea of linear Diophantine fuzzy sets (LDFSs) with the accumulation of reference or control parameters This structure enlarge the valuation space of existing models and categorize the problem with the help of control parameters. To deal with real-life problems having uncertainties, vagueness, abstinence of the input, lack of information, we introduce novel concept of spherical linear Diophantine fuzzy soft rough set (SLDFSRS). It is fascinating to record that both algorithms generate the identical optimal alternative The organization of this manuscript is ordered as follows: Section 2 implements some elementary ideas of fuzzy sets, IFSs, neutrosophic sets, PFSs, SFSs, T-SFSs, soft sets, and rough sets.
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