A multicriteria system using gradual fuzzy rules and fuzzy arithmetic

We present a multicriteria fuzzy system that uses fuzzy gradual rules bases to model the user's preferences and fuzzy arithmetic to aggregate the results issued by the bases. We first present a multicriteria problem and its solution for the case of precise information. Then we extend the model to treat pieces of information that may involve imprecision/vagueness. We show that the use of residuated implication operators (employed by gradual rules), coupled with similarity relations (to guarantee consistency), offer a better treatment of the problem than a Mamdani-like approach. We illustrate the various features of the system by means of a simple example and describe an application of the formalism to social games.