Riasna I. Fuzzy combinatorial optimization models and their applications

Dissertation work is devoted to construction of fuzzy models of combinatorial optimization in the presence of qualitative and quantitative information taking into account the provisions of representative theory of measurement. Based on the analysis of modern approaches to the construction of formal models on fuzzy sets, problems of representation, uniqueness and adequacy have been identified. The concept of not predetermined fuzzy set is introduced, the essence of which is related to consideration of permissible transformations of measurement results. The classification of ill-structured problems with quantitative and qualitative information is proposed. Original approach to determination of the concept «fuzzy combinatorial object» is offered, which allows to strictly formalizing both the known and new classes of problems of combinatorial optimization.