Abstract
The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.
Highlights
We come across various problems in our surroundings that involve some uncertainties.For example, the notion of beautiful guys is imprecise, because we cannot uniquely classify all beautiful guys into two classes: beautiful guys and not beautiful guys. the beauty is not exact but rather an uncertain concept
We generalize the concept of the pessimistic multigranulation roughness (PMGR) of an FS based on two soft binary relation (SBr) to pessimistic multigranulation roughness (PMGR) of an FS based on multi SBrs
This article studies the pessimistic multigranulation roughness of a fuzzy set based on SBrs over two universes
Summary
We come across various problems in our surroundings that involve some uncertainties. For example, the notion of beautiful guys is imprecise (uncertain), because we cannot uniquely classify all beautiful guys into two classes: beautiful guys and not beautiful guys. They discussed the adjustable approaches to multi-criteria group decision making based on inverse fuzzy soft matrices in [12] Another mathematical method for dealing with problem containing imprecision is the rough set theory (RST), which was presented by Pawlak in 1982 [13]. To measure the uncertainty of knowledge, Ma and Sun [44] proposed probabilistic RS over dual universes, the graded RS model based on dual universes and its features were addressed by Liu et al [45], Shabir et al [46] discussed approximation of a set based on SBr over dual universes and their application in the reduction of an information system, Zhang et al [47] generalized FRS to dual universes with interval valued data, Wu et al [48].
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