V.M. Bilchuk, D.A. Grib, I.G. Dzeverin, O.V. Vorobyev, I.A. Nos

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A complex system is considered, purposeful functioning of which is determined by the factors, which by nature can have political, economic, social, ethical, ethnic, subjective and other orientations and together form a 1 iD d , i ,m set of a comparatively large size (a few tens or hundreds). Subjective content of the factors and the dimension of the D set are determined by the purposeful interest of a person making decision (PMD). Brought into correspondence to each factor of one or another nature mentioned above, the variables are in general random and of non-mass character. This determines that factors brought into consideration by PMD form non-stochastic, uncertain environment in which a complex system operates. Description of the process development behavior of complex system functioning of time is presented taking into account the significance levels of set D factors. For any subset of iÐ , i , jÐ , 1i, j ,kÐ , i ,n; 1 ij ,n ; 1 jk ,n factors that form the decomposition hierarchy of the structure D set factors, the significance levels of the factors meet the levels of non-dominated elements of fuzzy subset of fuzzy binary relation core of strict preference factors as the elements of the above-mentioned iÐ , i, jÐ , i , j ,kÐ subsets. A methodical approach is proposed to overcome the difficulties that are associated with practical impossibility of the experts to account the influence of all the factors of 1 iD d , i ,m number set, which make the residue in the process of determining the function values of fuzzy binary relation membership of couple of factors preference-indifference ( r , g ) r ,s D .