Abstract
Abstract
Theories of the rough set (RS) and the fuzzy set (FS) are constructed to accommodate the uncertainty in the data analysis. Linear Diophantine FS (LD-FS) as a novel approach to decision-making (DM), broadening the predominating theories of intuitionistic FS (IFS), Pythagorean FS (PFS), q-rung orthopair FS (q-ROFS) deals with uncertain and vague information by considering the control or reference parameters. Exploring RSs in the framework of LD-FS is a propitious direction in RS theory, where LD-FSs are approximated by Linear Diophantine fuzzy relation (LD-FR). The primary aim of this article is to develop a new linear Diophantine fuzzy RS (LDF-RS) model based on an LD-FR over dual universes. The notions of lower and upper approximations of an LD-FS are introduced by using an LD-FR, and several fundamental structural properties are explored. Moreover, a connection between LDF-RSs and linear Diophantine fuzzy topology (LDF-topology) is established. In addition, some similarity relations among LD-FSs based on their lower and upper approximations are studied. Finally, a DM approach is crafted for the ranking of alternatives using the notions of LDF-RS. Moreover, a numerical example is designed and compared with some existing techniques.
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Reference48 articles.
1. Fuzzy sets;Zadeh;Inf. Control,1965
2. Intuintionistic fuzzy sets;Atanassov;Fuzzy Sets Syst.,1986
3. Pythagorean fuzzy subsets;Yager,2013
4. Generalized orthopair fuzzy sets;Yager;IEEE Transecrtions on Fuzzy Systems,2017
5. New Similarity measure and distance measure for Pythagorean fuzzy set;Peng;Complex & Intelligent Systems,2019
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献