By V. V. Kolbin

The fields which are nearly completely thinking about conflicts, the place utilized arithmetic is effectively used, are legislation, army technological know-how, many branches of economics, sociology, political technological know-how, and psychology. There are reliable grounds to think that medication and a few branches of biology and ethics is usually integrated during this record. sleek utilized arithmetic can produce options to many tens of sessions of conflicts differing via the composition and constitution of the contributors, particular positive factors of the set in their pursuits or pursuits, and numerous features of the set in their activities, techniques, behaviors, controls, and judgements as utilized to numerous ideas of choice or notions of selection optimization.

The present problems with social and fiscal structures contain the need to coordinate and together optimize a number of strains of improvement and actions of contemporary society. therefore, the choice difficulties bobbing up in research of such structures are flexible, which indicates up not just within the multiplicity of members, their pursuits and complexity of reciprocal results, but additionally within the exhausting improvement of social software standards for various indices and flexible goals. The effective choice equipment for such advanced structures could be built in basic terms the root of especially built mathematical instruments.

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13) uses the coefficients Xj having different values. , the membership function of the fuzzy preference relation. 17) where fiQd(x) = lsup[fiQl (y,x) — fiQ2(x,y)] is the fuzzy subset of nondominated alternatives on the set (X,HQ2). X^'d' is the subset of nondominated alternatives on the set (X, p,Q2). The rational choice is the choice of the alternative having the highest degree of nondominance, i. , the largest value of function / u nd -. Chapter III discusses two examples and provides an algorithm to construct a rational choice of alternative in terms of a given class of problems.

X,y) G R and (y,x) £ R. The set of such pairs (x,y) is called the strict preference relation Rs on the set X. The relevant indifference relation R' in X is defined as follows [15]. 4. The pair (x,y) G R' if, and only if, neither x ^ y, nor y ^ x, or both preferences are simultaneously satisfied. In other words, (x,y) G R' when the available information in the form of the preference relation is insufficient for making a choice between alternatives x and y. 5 [15]. If(x,y) G Rs, we say that alternative x dominates alternative y(x >- y).

5). We show that the Condorcet paradox may not arise in this region or, more specifically, the majority rule generates the collective welfare order. 12 [26]. For a specified profile u and for the community N, let M(u) denote the majority relation: aM(u)b if, and only if, \N(u, a,b)\ > \N(u, b, a)\; and let M*{u) denote its asymmetric component: aM*(u)b if, and only if, \N(u, a, b)\ > \N(u,b,a)\. We say that the outcome is the Condorcet (weak) winner for the profile u given on A if it is a maximal element in M(u).