Problem of resource distribution at the fuzzy set of basic data

Abstract

The problem of rational distribution of a homogeneous resource was set on the assumption that the parameters of the objective function are fuzzy numbers with known membership functions. Standard technology of solving this problem is analyzed, its shortcomings are identified. Two approaches, in which these disadvantages are eliminated, are suggested. The first is based on the following. Membership function of the fuzzy value of the objective function of the problem is found. The position of this function depends on optimized choice, which is chosen in such a way as to move the body of the uncertainty of the objective function in the area of its extreme value. Another approach uses the following two-step procedure. In the first phase the original problem is solved, in condition that all of its fuzzy parameters are set at the level of modal values. Further composite criterion is constructed, one component of which determines the density of the body of uncertainty of the objective function, and the second describes the degree of deviation from the desired modal solutions. Thus, the original fuzzy problem is reduced to precise mathematical programming. The example is given.