Abstract
Through a combination of overlap functions (which have symmetry and continuity) and a fuzzy β-covering fuzzy rough set (FCFRS), a new class of FCFRS models is established, and the basic properties of the new fuzzy β-neighborhood lower and upper approximate operators are analyzed and studied. Then the model is extended to the case of multi-granulation, and the properties of a multi-granulation optimistic fuzzy rough set are mainly investigated. By theoretical analysis for the fuzzy covering (multi-granulation) fuzzy rough sets, the solutions to problems in multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problem methods are built, respectively. To fully illustrate these methodologies, effective examples are developed. By comparing the method proposed in this paper with the existing methods, we find that the method proposed is more suitable for solving decision making problems than the traditional methods, while the results obtained are more helpful to decision makers.
Highlights
In order to fill this research gap, we propose two types of models, namely fuzzy β-covering fuzzy rough set model based on the overlap function, and this is extended to the multi-granulation case, i.e., the FCOMGFRS model based on the overlap function and the FCPMGFRS model based on the overlap function
Aiming at the combination of multi-criteria decision-making (MCDM) problems and the fuzzy β-covering fuzzy rough set model based on the overlap function models, we propose a new class of problem solving methods inspired by Zhang’s article [23]
In order to illustrate the results obtained in this paper more clearly, we show a short comparison of the fuzzy β-covering fuzzy rough set model based on the overlap function
Summary
Covering rough set theory is an important extension form of classical rough set theory and an important theoretical method for processing incomplete information system data [2]. It is of practical significance to study the rough set model based on covering. Fuzzy positive and negative ideal solutions A+ and A− based on the set of criteria C. The expert presents the assessments for the collection of alternatives concerning criteria. Based on the proposed covering methods, we prefer a decision-making algorithm to detect the best alternative in the following steps.
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