APPLICATION OF FUZZY VECTOR OPTIMIZATION METHODS FOR DIET COMPILATION

Abstract

The purpose of this work is to study an approach to solving the problem of fuzzy vector optimization for compiling a diet. It is necessary to develop a daily ration that provides human needs in nutrients and energy and is the best in terms of costs and weight. For this purpose the problem of choosing the best alternative from a given fuzzy set of alternatives is solved, while the quality of the alternative is evaluated using several partial efficiency cri- teria. The goal in the task is fuzzily defined. According to the Zadeh – Bellman idea, a fuzzy solution to a problem is the intersection of a fuzzy goal and a fuzzy set of alternatives. The paper considers the problem of fuzzy two-criteria optimization. Partial criteria that are minimized are the weight and cost of the daily ration. Fuzzy needs for nutrients and kilocalories are determined by fuzzy triangular numbers. For an approximate solution of the problem, an algorithm is proposed according to which a sequence of linear programming problems is solved. The computer program was created that implements the solution of this problem in the Wolfram Matematica package. The following results were obtained: a set of products, their weight and cost were determined for the daily diet. The degree of confidence that the found plan is optimal is determined. On the basis of the proposed mathe- matical model and the method of its solution, a software application allowing to choose food products, enter the necessary restrictions in a user- friendly form, and receive one or more options for the daily ration at the output was created. Such an application will be useful for nutritionists, ath- letes, doctors and other people who are concerned with the problems of healthy eating.