A new perspective on reasoning with fuzzy rules

✍ Scribed by D. Dubois; H. Prade; L. Ughetto

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 255 KB
• Volume: 18
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.10103

✦ Synopsis

This article expresses the idea that information encoded on a computer may have a negative or positive emphasis. Negative information corresponds to the statement that some situations are impossible. Often, it is the case for pieces of background knowledge expressed in a logical format. Positive information corresponds to observed cases. It is encountered often in data-driven mathematical models, learning, etc. The notion of an "if . . . , then . . ." rule is examined in the context of positive and negative information. It is shown that it leads to the three-valued representation of a rule, after De Finetti, according to which a given state of the world is an example of the rule, a counterexample to the rule, or is irrelevant for the rule. This view also sheds light on the typology of fuzzy rules. It explains the difference between a fuzzy rule modeled by a many-valued implication and expressing negative information and a fuzzy rule modeled by a conjunction (a la Mamdani) and expressing positive information. A new compositional rule of inference adapted to conjunctive rules, specific to positive information, is proposed. Consequences of this framework on interpolation between sparse rules are also presented.