Multi-criteria optimization in terms of fuzzy criteria definitions

L. Raskin, National Technical University ", O. Sira, D. Sagaydachny, Kharkiv Polytechnic Institute", National Technical University "Kharkiv Polytechnic Institute", National Technical University "Kharkiv Polytechnic Institute"
2018 Mathematical Modeling and Computing  
The problems of multi-criteria optimization are considered. Known methods for solving these problems are generalized to the case when weights that take into account the relative importance of particular criteria are not clearly defined. The procedure for constructing membership functions of fuzzy numbers, given by sets of intervals of possible values, using a linearized computation of least squares methods is substantiated. In this case, for the description of fuzzy numbers, the membership
more » ... the membership functions of (L-R)-type were chosen. A method for solving a fuzzy multi-criteria optimization problem for a scalarized criterion is proposed. The technology of solving the problem reduces it to a linear fractional problem of mathematical programming. A converging iterative procedure for finding the optimal plan is described. An alternative method for solving the original fuzzy problem based on the formation of a Pareto-set of non-dominated options is considered. To solve this problem, a procedure has been proposed for comparing fuzzy numbers using a probability-theoretic approximation of their membership functions.
doi:10.23939/mmc2018.02.207 fatcat:2kkpu7xwlbbpjbwnfq6azgx4bi