An Interval-Valued Intuitionistic Fuzzy Rough Set Model

  • Authors:

  • Zhiming Zhang

  • Affiliations:

  • College of Mathematics and Computer Sciences Hebei University Baoding 071002 Hebei, China. E-mail: zhimingzhang@ymail.com

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2009

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Abstract

Given a widespread interest in rough sets as being applied to various tasks of data analysis it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. This paper proposes an interval-valued intuitionistic fuzzy rough model by means of integrating the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory. Firstly, some concepts and properties of interval-valued intuitionistic fuzzy set and interval-valued intuitionistic fuzzy relation are introduced. Secondly, a pair of lower and upper interval-valued intuitionistic fuzzy rough approximation operators induced from an interval-valued intuitionistic fuzzy relation is defined, and some properties of approximation operators are investigated in detail. Furthermore, by introducing cut sets of interval-valued intuitionistic fuzzy sets, classical representations of interval-valued intuitionistic fuzzy rough approximation operators are presented. Finally, the connections between special interval-valued intuitionistic fuzzy relations and interval-valued intuitionistic fuzzy rough approximation operators are constructed, and the relationships of this model and the others rough set models are also examined.