Multi‐adjoint intuitionistic fuzzy rough sets

Abstract

The combination of fuzzy information systems (ISs) and multi‐adjoint theory has become a hot issue in the study and applications of artificial intelligence. An intuitionistic fuzzy set has more flexible and practical ability to represent information and is better in dealing with ambiguity and uncertainty when compared with the fuzzy set. Multi‐ adjoint intuitionistic fuzzy rough sets are constructed by using adjoint triples under intuitionistic fuzzy IS. For this purpose, the authors propose intuitionistic fuzzy indiscernibility relation and multi‐adjoint approximation operators. The basic results in the multi‐adjoint fuzzy rough set model are generalised to multi‐adjoint intuitionistic fuzzy rough set model. The analogous results are also verified. After that, a novel approach of attribute reduction is proposed. First, a kind of approximate reduction to keep the dependence of the positive region to a degree is formulated. Second, they propose a heuristic algorithm to compute the attribute reduction. At last, they employ an example to describe the processing of the algorithm.