Abstract
The existing concepts of picture fuzzy sets (PFS), spherical fuzzy sets (SFSs), T-spherical fuzzy sets (T-SFSs) and neutrosophic sets (NSs) have numerous applications in decision-making problems, but they have various strict limitations for their satisfaction, dissatisfaction, abstain or refusal grades. To relax these strict constraints, we introduce the concept of spherical linear Diophantine fuzzy sets (SLDFSs) with the inclusion of reference or control parameters. A SLDFS with parameterizations process is very helpful for modeling uncertainties in the multi-criteria decision making (MCDM) process. SLDFSs can classify a physical system with the help of reference parameters. We discuss various real-life applications of SLDFSs towards digital image processing, network systems, vote casting, electrical engineering, medication, and selection of optimal choice. We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators. Some new operations on picture fuzzy sets are also introduced. Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers (SLDFNs) are proposed. New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation (SLDFWGA) and spherical linear Diophantine fuzzy weighted average aggregation (SLDFWAA) operators are developed for a robust MCDM approach. An application of the proposed methodology with SLDF information is illustrated. The comparison analysis of the final ranking is also given to demonstrate the validity, feasibility, and efficiency of the proposed MCDM approach.
Highlights
Classical mathematics is not necessarily useful when solving real-world issues because of the complexities and vagueness inherent in such questions
We proposed a new extension of fuzzy sets named the spherical linear Diophantine Fuzzy set (SLDFS) which is more efficient to address various uncertainties in a parametric way
We described the graphical analysis of spherical linear Diophantine fuzzy sets (SLDFSs) to compare it with other fuzzy sets
Summary
Classical mathematics is not necessarily useful when solving real-world issues because of the complexities and vagueness inherent in such questions. A novel model of spherical linear Diophantine fuzzy set (SLDFS) is introduced with the constraints 0 ≤ α T + β U + η K ≤ 1 and 0 ≤ α + β + η ≤ 1, where α , βand ηare reference parameters corresponding to the satisfaction, abstinence, and dissatisfaction grades respectively, and taken from the interval [0, 1] The beauty of this new idea is that we can take all the grades independently from [0, 1] and reference parameters categorize the structure and handle uncertainties in a parametric manner. SLDFS is more efficient and effective as compared to picture fuzzy set, SFS, T-SFS, and neutrosophic set
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