Some of the Properties of Fuzzy Discretisation

Abstract

The representation of subjective informations with fuzzy sets or distributions of possibility brings up the problem of numerizing these data for processing it by a computer. Two types of representation may be used for this : the first type consists in assigning to the value of the membership function of a fuzzy set, an explicit equation ; the second type requires the discretisation of the referential into a certain number of segments, and labeled by a point. A fuzzy set may be defined by assigning a value to the membership function to each segment. This latter technique has the disavantage of requiring, in order to get acceptable accuracy, the memorization of a large number of values for each fuzzy set or fuzzy relation. In order to partially overcome these disavantages, we proposed a method called “Fuzzy discretisation” which consists in cutting up a real space, not into disconnected segments, but rather into a series of nondisconnected fuzzy sets. This article's object is to extend the definition of this method to n-ary fuzzy relations and to demonstrate that using it alters only slightly the data treated.