Yemets' O. Solving the combinatorial optimization problems on fuzzy sets

The object of the research is combinatorial optimization problems and methods of their solving. The goal of the work is the research of the problems of combinatorial optimization on fuzzy sets, development and the investigation of methods of solving these problems, the development of the fuzzy set theory apparatus for applying for solving combinatorial optimization problems. The research was conducted with using the theory and algebra methods, fuzzy set theory, combinatorial analysis, mathematical modelling, geometrical designing, theory of algorithms and their analysis. The definitions of fuzzy combinatorial sets of permutation, partitions, allocations are introduced. Operations and ratio under fuzzy numbers are introduced. Their necessary properties are proved. Arrangement of rectangles with fuzzy sizes in the fuzzy size bread are defined. Application of the developed apparatus for the one problem of the Euclidean combinatorial optimization as problem on fuzzy permutations and as problem on fuzzy partitions is shown. The problem is solved by branches and measures. A heuristic method for solving the problem of packing rectangles with widths which are described by fuzzy numbers is proposed. The problem about pack under uncertainty which is set fuzzy numbers is formulated. Its mathematical model is constructed. A heuristic method for its approximate solving are proposed. Polynomial estimates of complexity heuristic methods are received. An area of implementation is economics (management, control)