A fuzzy constraint satisfaction problem in the wine industry

The paper reports on a real case study coming from wine industry, which is an example of linear constraint satisfaction problem, where the constraints are flexible, may have different levels of priority or involve ill-known (imprecise or fuzzy) parameters. Fuzzy sets and possibility theory offer a unified framework that allows for the modelling of i) preferences between different ways of satisfying a flexible constraint, of ii) uncertainty pervading data, and of iii) priority among constraints. Indeed, actual constraints are often flexible and their satisfaction a matter of degree. That is why they are conveniently described by fuzzy sets. Uncertain pieces of data can be represented by means of possibility distributions, and the level of priority of a constraint can be viewed as the maximum degree of acceptability of a solution that violates this constraint. In the following the fuzzy set-based approach to the handling of soft and uncertain constraints is presented and its interest is illustrated on the case study.