Attributes reduction based on intuitionistic fuzzy rough sets

Intuitionistic fuzzy rough sets are the generalization of traditional rough sets by combining intuitionistic fuzzy set theory and rough set theory. The existing researches on intuitionistic fuzzy rough sets mainly concentrate on the establishment of lower and upper approximation operators by using constructive and axiomatic approaches. Less effort has been put on the attributes reduction of databases based on intuitionistic fuzzy rough sets. The aim of this paper is to focus on attributes reduction based on intuitionistic fuzzy rough sets. After reviewing attributes reduction with traditional rough sets, some equivalent conditions to describe the relative reduction with intuitionistic fuzzy rough sets are proposed, and the structure of reduction is completely examined. Based on discernibility matrix, an algorithm to compute all the attributes reductions is also developed. At last we employ an example to illustrate the concepts of attributes reduction.