The aim of the present paper is to discuss methodological characteristics of fuzzy set theory. The following four characteristics are considered and simple examples are shown. (1)Fuzzy logic as a subject in mathematical logic: fuzzy prolog is an application of fuzzy logic. (2)A fuzzy set as a family of its α-cuts: several basic operations are denned to be commutative with α-cuts. Applications are found in fuzzy graphs and cluster analysis. (3) Interporative reasoning: fuzzy control is a typical example. A number of relations between measurement values and control values are interporated by fuzzy sets to cover the whole space. (4) Linguistic modeling: fuzzy sets directly realize correspondence between a linguistic expression and a combination of distributions in a metric space. This feature enables visual understanding of modeling processes in various applications.
