A proposal of fuzzy thesaurus generated by fuzzy covering

Abstract

This paper discusses preciseness of data in terms of obtaining degree of similarity in which a fuzzy set can be used as an alternative to represent imprecise data. Degree of similarity between two imprecise data represented in two fuzzy sets is approximately determined by using a fuzzy conditional probability relation. More-over, the degree of similarity relationship between fuzzy sets corresponding to fuzzy classes as results of a fuzzy partition on a given finite set of data is examined. Related to a well known fuzzy partition, called fuzzy pseudopartition or fuzzy c-partition where c designates the number of fuzzy classes in the partition, we introduced fuzzy symmetric c-partition regarded as a special case of the fuzzy c-partition. In addition, we also introduced fuzzy covering as a generalization of fuzzy partition. Similarly, two fuzzy coverings, namely fuzzy c-covering and fuzzy symmetric c-covering are proposed corresponding to the fuzzy c-partition and the fuzzy symmetric c-partition, respectively. In this paper, special attention will be given to apply the concept of fuzzy c-covering in generating a fuzzy thesaurus.