Antosiak P. Analysis and optimization of fuzzy models of the collective ordinal expert assessment

The thesis deals with making optimal decisions at group expert estimation. The studies done are connected with the problem of choice at a group ordinal expert estimation. The thesis develops the rule of determination of strict collective ranking of alternatives in the shape of "median" in case of various types of fuzzy preferences. The results of theoretical studies have proved justifiability of such an approach following the fuzzy analogues of rational collective choice. When it comes to fuzzy ordinal expert judgment of the alternatives as well as judgments of alternatives in the shape of fuzzy tournaments, there have been developed indirect methods of strict collective ranking of alternatives. Two new principles of rational collective choice have been proposed for the problem of collective choice in Arrow setting and there have been thoroughly studied the problem of justifiability following these principles of some known rules of collective choice. The thesis shows the equivalence of the problem of determination of fuzzy preferences' "median" of alternatives' linear ordering problem for which procedures of sequential analysis of variants were developed and proved. Experimental studies have justified the effectiveness and expediency of their use, first of all, in terms of reduction of dimension of initial problem.