Constructive fuzzy sets with similarity semantics

Semantic interpretation of membership functions is still one of the unsettled issues of fuzzy set theory, although some proposals have been made and studied. In this paper, we present an alternative formulation called the constructive model of fuzzy sets, motivated by the concept of constructive mathematics. The model makes explicit use of knowledge regarding relationships between elements of a universal set, and a constructive method. As an example, we show that s-fuzzy sets can be constructed based on similarity and elementary fuzzy sets. Properties of the constructed fuzzy set system are examined in qualitative and quantitative terms.