Artificial intelligence

Diophantine equation

Mathematics

Multiple-criteria decision analysis

Mathematical optimization

Computer science

Discrete mathematics

Applied mathematics

Fuzzy logic

Computer Modeling in Engineering & Sciences

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.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM