Abstract
Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued overlap function and lattice valued overlap function, but intuitionistic fuzzy overlap function (IF-overlap function) has not been studied. In this paper, the concept of IF-overlap function is proposed for the first time, then the generating method of IF-overlap function is given. The representable IF-overlap function is defined, and the concrete examples of representable and unrepresentable IF-overlap functions are given. Moreover, a new class of intuitionistic fuzzy rough set (IF-roght set) model is proposed by using IF-overlap function and its residual implication, which extends the IF-rough set model based on intuitionistic fuzzy triangular norm, and the basic properties of the new intuitionistic fuzzy upper and lower approximate operators are analyzed and studied. At the same time, the established IF-rough set based on IF-overlap function is applied to MCDM (multi-criteria decision-making) problems, the intuitionistic fuzzy TOPSIS method is improved. Through the comparative analysis of some cases, the new method is proved to be flexible and effective.
Highlights
Accepted: 12 August 2021Fuzzy set theory is a very effective mathematical tool to analyze and deal with inaccurate and incomplete information [1]
Because fuzzy rough sets are a special case of intuitionistic fuzzy rough sets (IF-rough sets), this paper focuses on intuitionistic fuzzy rough sets
IF-overlap function, as a non-associative binary function, can be widely used in decision making problems based on fuzzy preference relation, which can overcome the defect of associative property of continuous IF triangular norm in practical problems, and has a better effect in dealing with uncertain multi-attribute decision making problems
Summary
Fuzzy set theory is a very effective mathematical tool to analyze and deal with inaccurate and incomplete information [1]. The existing definitions have limitations in solving practical problems with intuitionistic fuzzy information In view of this limitation, this paper puts forward the definition of IF-overlap function, and studies some of its properties and representations. IF-overlap function, as a non-associative binary function, can be widely used in decision making problems based on fuzzy preference relation, which can overcome the defect of associative property of continuous IF triangular norm in practical problems, and has a better effect in dealing with uncertain multi-attribute decision making problems. There are two main reasons for this study: One is the rough set theory is an important tool to deal with uncertain information, the classical rough set is restricted because of its strict conditions, in order to expand the application scope of rough set theory, we found that IF the introduction of the theory makes a lot of problems to solve, through different logical operator combining the IF theory and rough set theory, such as IF-overlap function, enriched the theory of rough set. We conclude our work with a summary of the paper in Section 6, and outline future research
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