A new method for feature selection based on fuzzy similarity measures using multi objective genetic algorithm

Abstract

38 triangular norms, t-norm and t-conorm only differ on their boundary conditions. Some additional properties of t-norm and t-conorm are presented in the following definitions [11]. A function is dual t-conorm of t-norm such that for all x both the following equivalent equalities hold, and , where (1 – x) and (1 – y) are respectively complements of x and y. Next we present a list of the main well know and most frequently used t – norms [11], [12]: By using the duality we can easily establish the Yu's t-conorm, which is: B. Similarity measures for Fuzzy sets In this section we present a brief review of similarity measures for fuzzy sets and their axiomatic basis. Since the concept of similarity has a wide range of applications, there are different approaches present in literature as axioms for degree or measure of similarity. These axioms have differences and similarities depending upon the contexts in which they are constructed. At first hand, a similarity measure for fuzzy sets is expected to be a T-equivalence on which is later realized to be a very unrealistic requirement. Some other lists of properties are also found in literature that a reasonable similarity measure must satisfy. We shall suffice to present a set of axioms formulated by Bustince [13] for an interval valued similarity measure. A function is called a normal interval valued similarity measure, if satisfies following properties for all A, B, C : I. , II. , III. ,