On the Measurement of TL - Fuzzy Rough Sets

In fuzzy rough sets a fuzzy T-similarity relation is employed to describe the degree of similarity 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 reasonable selection of triangular norm is clearly meaningful to practical applications of fuzzy rough sets. In this paper we first discuss the selection of triangular norm and emphasize the well-known Lukasiewicz´s triangular norm T_L as a reasonable selection. We then propose a function for each approximation operator in T_L -fuzzy rough sets to measure its approximating ability. The measurement functions of lower and upper approximation operators are natural generalizations of belief and plausibility functions in the evidence theory respectively. By using these two functions, accuracy measure, roughness degree, entropy and conditional entropy are defined for T_L-fuzzy rough sets