On Fuzzy Similarity Relations for Heterogeneous Fuzzy Sets

The fundamental problem of development of formal models and methods of ill-structured problems of combinatorial optimization under uncertainty requires utilizing of fuzzy concepts of informal models and different types of scales for measurement of quality and quantity characteristics. In the paper, we introduce a concept of a fuzzy similarity scale. An inadequacy of traditional building a fuzzy similarity scale based on operators of fuzzy logic is shown. A concept of a linguistic correlation coefficient is offered, and conditions of its adequacy in scales of measurement of empirical objects properties on Stevens' classification are derived. For determining fuzzy similarity relations on heterogeneous fuzzy sets, we use the concept of the linguistic correlation coefficient.