Possibilistic Minmax Regret Sequencing Problems With Fuzzy Parameters

Abstract

In this paper, a class of sequencing problems with uncertain parameters is discussed. The uncertainty is modeled by the usage of fuzzy intervals, whose membership functions are regarded as possibility distributions for the values of unknown parameters. It is shown how to use possibility theory to find robust solutions under fuzzy parameters; this paper presents a general framework, together with applications, to some classical sequencing problems. First, the interval sequencing problems with the minmax regret criterion are discussed. The state of the art in this area is recalled. Next, the fuzzy sequencing problems, in which the classical intervals are replaced with fuzzy ones, are investigated. A possibilistic interpretation of such problems, solution concepts, and algorithms for the computation of a solution are described. In particular, it is shown that every fuzzy problem can be efficiently solved if a polynomial algorithm for the corresponding interval problem with the minmax regret criterion is known. Some methods to deal with NP-hard problems are also proposed, and the efficiency of these methods is explored.