TY  - EJOU
AU  - Riaz, Muhammad 
AU  - Hashmi, Masooma Raza 
AU  - Pamucar, Dragan 
AU  - Chu, Yuming 

TI  - Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2021
VL  - 126
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Spherical linear Diophantine fuzzy set; new operations of picture fuzzy sets; spherical linear Diophantine fuzzy weighted geometric aggregation operator; spherical linear Diophantine fuzzy weighted average aggregation operator; MCDM

DO  - 10.32604/cmes.2021.013699