Kondruk N. Methods of criterion space clustering in the vector exercises of linear programming and their application in diet therapy

The decision support systems of doctor-dietitian for individualized diet making in diet therapy and nutrition was created. A general mathematical model of the procedures of individualized diets using the apparatus VELP with large criteria dimension and indistinct parameters of limitation was developed. The methods of clustering of local criteria VELP on the set of contradictory, strongly bound and strongly bound consistent criteria that allow the controversy were proposed. A general method for solving VELP with criteria space of large dimension based on clustering of criterion space, the definition of cluster representatives and their weight coefficients with convolution into a single integral criterion was worked out. The method of additive convolution solution of VELP based on clustering of criterion space was improved. Herewith the possibility of compensation problem solving of one local criteria group by others, as well as the possibility of building such VELP Pareto-optimal solution, which is locally optimal for the maximum number of criteria was shown. The approach to find VELP effective solutions with criteria space of large dimension and indistinct parameters was developed. Thesis focused on the efficiency increase solution of vector exercises of linear programming (VELP) with large dimensional criteria space based on criterion space clustering on the set of strongly related and conflicting criteria.