Determining Unfuzzy Nondominated Solutions in Combinatorial Optimization Problems with Fuzzy Costs

Abstract

This paper deals with a general combinatorial optimization problem with fuzzy costs. The set of nondominated solutions with respect to an assumed fuzzy preference relation, according to the Orlovski's concept, is supposed to be the solution of the problem. A special attention is paid to the unfuzzy nondominated solutions (the solutions which are nondominated to the degree one). The main results of the paper are several new, weakened conditions on a fuzzy preference relation that allow to reduce the problem of determining unfuzzy nondominated solutions to the underling problem with deterministic costs. These solutions can be obtained by means of classical algorithms for the underling crisp problem, avoiding a construction of the special ones for the fuzzy problem. Moreover, it is shown that several known from literature fuzzy preference relations fulfill the proposed conditions. The approach is illustrated by a computational example.