Abstract
Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators. The concept of reduct of a fuzzy soft set is introduced and the procedure to find a reduct for a fuzzy soft set is given. Furthermore, the concept of exclusion of a fuzzy soft set is introduced and the procedure to find an exclusion for a fuzzy soft set is given.
Highlights
Soft set theory [1], firstly proposed by Molodtsov, is a general mathematical tool for dealing with uncertainty
Soft set theory has been successfully applied in many fields such as functions smoothness, game theory, riemann integration, and theory of measurement [1]
It is worth noting that all of above works are based on the classical soft set theory
Summary
Soft set theory [1], firstly proposed by Molodtsov, is a general mathematical tool for dealing with uncertainty. Our work mainly studies the parameter reduction of fuzzy soft sets based on soft fuzzy rough sets, while Sun and Ma’s work [35] focused on the application of soft fuzzy rough sets in decision making. We extend Zhu and Wang’s work [36] and propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators.
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