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On characterization of fuzzy soft rough sets based on a pair of border implicators. (English) Zbl 1357.68240
Summary: Fuzzy set theory, soft set theory and rough set theory are powerful mathematical tools for dealing with various types of uncertainty. This paper is devoted to define a broad family of soft fuzzy roughsets, each one of which, called an \((I, J)\)-soft fuzzy rough set, is determined by a pair of border implicators \((I, J)\). Alternatively, it shows that a fuzzy soft set can induce a \(T\)-equivalence fuzzy relation which is used to granulate the universe. In particular, we prove that \((I, J)\)-fuzzy soft rough sets in our work are equivalent to \((I, J)\)-fuzzy rough sets of Y. Ouyang et al. [Inf. Sci. 180, No. 4, 532–542 (2010; Zbl 1189.68131)] by using a \(T\)-equivalence fuzzy relation determined by a fuzzy soft set. Furthermore, basic properties of \((I, J)\)-fuzzy soft rough sets are investigated. Meanwhile, an operator-oriented characterization of \((I, J)\)-fuzzy soft rough sets is proposed. Finally, an example is given to illustrate the approach of present paper.

68T37 Reasoning under uncertainty in the context of artificial intelligence
03E72 Theory of fuzzy sets, etc.
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