An Interval-Valued Intuitionistic Fuzzy Rough Set Model

Article type: Research Article

Authors: Zhang, Zhiming

Affiliations: College of Mathematics and Computer Sciences Hebei University Baoding 071002 Hebei, China. E-mail: [email protected]

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.

Keywords: Rough sets, interval-valued intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy relations, interval-valued intuitionistic fuzzy rough sets, knowledge reduction

DOI: 10.3233/FI-2009-211

Journal: Fundamenta Informaticae, vol. 97, no. 4, pp. 471-498, 2009