Fuzzy constraint satisfaction

In this paper the issue of soft constraint satisfaction is discussed from a fuzzy set theoretical point of view. A fuzzy constraint is considered as a fuzzy relation. Different possible definitions for the degree of joint satisfaction of a set of fuzzy constraints are given, covering other specific soft constraint satisfaction problem (CSP) types such as partial and hierarchical CSP. It is shown that the classical CSP solving heuristics based on variable and value evaluations can be generalised and used to guide the solution construction process for solving fuzzy CSPs, and that the heuristic search can be replaced by branch-and-bound search. The solution process is illustrated with an example from the CSP literature. Finally, research issues are discussed