An approach of attributes reduction based on fuzzy TL rough sets

In fuzzy rough sets a fuzzy T-similarity relation is employed to describe the similarity degree between two objects and to construct lower and upper approximations for arbitrary fuzzy sets. Different triangular norm T identifies different point of view of similarity. Thus a reasonable selection of triangular norm is meaningful to practical applications of fuzzy rough sets. In this paper we discuss the selection of triangular norm and emphasize the well-known Lukasiewicz´s triangular norm T_L as a reasonable selection. And then we focus on attributes reduction with T_L-fuzzy rough sets. First we define attributes reduction with T_L-fuzzy rough sets and characterize it by dependency function. Second, the structure of proposed attributes reduction is investigated in detail by the approach of discernibility matrix. Third, an algorithm of computing attributes reduction is designed and finally a comparison with other methods of attributes reduction with fuzzy rough sets is performed using several experiments. The experimental results show that the method of attributes reduction with T_L-fuzzy rough sets is feasible and valid.