Fuzzy sets are fuzzy-continous

Abstract

In a classical arrangement we have on the one hand discrete symbolic and on the other hand continous numerical data attributes. The following evident questions arise: How can fuzzy sets be integrated in this classical schema? Are fuzzy sets discrete and/or continous? Can we measure how discrete, or continous, respectively, an attribute is? We will present the idea that fuzzy sets are continous and discrete sets with a certain degree by using a visualization technique. We measure continuity of a fuzzy set M by an area q(M)/spl isin/[0,1], that will be defined. If q(M)=0, then M is discrete. If q(M)=1, then it is continous. If q(M) is in (0,1), then M is defined as fuzzy-continous. Thus, a non-degenerated fuzzy set is a fuzzy-continous set. The value q(M) is a natural measure for fuzzy-continuity and 1-q(M) for fuzzy discreteness. Additionally to our theoretical consideration we will give some visualized examples.