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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.

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