Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM
- Muhammad Riaz1, Masooma Raza Hashmi1, Dragan Pamucar2, Yuming Chu3,4,*
1 Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan
2 Department of Logistics, Military academy, University of Defence, Belgrade, 11000, Serbia
3 Department of Mathematics, Huzhou University, Huzhou, 313000, China
4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, China
* Corresponding Author: Yuming Chu. Email:
(This article belongs to this Special Issue: Intelligent Computing for Engineering Applications)
2 Department of Logistics, Military academy, University of Defence, Belgrade, 11000, Serbia
3 Department of Mathematics, Huzhou University, Huzhou, 313000, China
4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, China
* Corresponding Author: Yuming Chu. Email:
(This article belongs to this Special Issue: Intelligent Computing for Engineering Applications)
Received 17 August 2020; Accepted 30 September 2020; Issue published 19 February 2021
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.
Keywords
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
Cite This Article
Riaz, M., Hashmi, M. R., Pamucar, D., Chu, Y. (2021). Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM. CMES-Computer Modeling in Engineering & Sciences, 126(3), 1125–1164.
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