J4 ›› 2013, Vol. 48 ›› Issue (09): 56-63.

• Articles • Previous Articles     Next Articles

Generalized interval-valued fuzzy rough sets and axiomatic characterizations

ZHANG Hai-dong1, HE Yan-ping 2   

  1. 1. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, China;
    2. School of Electrical Engineering, Northwest University for Nationalities, Lanzhou 730030, Gansu, China
  • Received:2012-10-22 Online:2013-09-20 Published:2013-09-25

Abstract:

A general framework is presented for the study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by using constructive approach. Firstly, through employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Based on properties of interval-valued fuzzy residual implicator on LI,  some interesting properties of interval-valued fuzzy rough approximation operators are then examined. In the axiomatic approach, interval-valued fuzzy rough approximation operators are further defined by axioms. And different axiom sets can characterize the essential properties of interval-valued fuzzy rough approximation operators.

Key words:  interval-valued fuzzy sets; interval-valued fuzzy relation; interval-valued fuzzy rough approximation operators; axiomatic approach

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