Fuzzy Combinatorial Optimization Problem

Modeling the weights by means of closed intervals is perhaps the simplest form of uncertainty representation. For every weight we must only specify a range of possible values. In this chapter we discuss a more sophisticated uncertainty evaluation. The key idea is to extend the notion of the classical closed interval to the fuzzy one. A fuzzy interval can be seen as a family of closed intervals parametrized by the value of λ ∈ [0,1]. It is reacher in information than a classical one and allows a representation that is at once both pessimistic and optimistic. A fuzzy interval has an interpretation in the setting of possibility theory, which is described for instance in a book by Dubois and Prade [44]. In Section 10.1 we describe the concept of a fuzzy interval and its possibilistic interpretation. We will consider then a combinatorial optimization problem in which the uncertain weights are modeled by means of fuzzy intervals.