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A new perspective on reasoning with fuzzy rules
Author(s) -
Dubois D.,
Prade H.,
Ughetto L.
Publication year - 2003
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.10103
Subject(s) - counterexample , modus ponens , fuzzy rule , computer science , artificial intelligence , rule of inference , fuzzy logic , inference , type 2 fuzzy sets and systems , perspective (graphical) , context (archaeology) , statement (logic) , fuzzy set , mathematics , theoretical computer science , fuzzy set operations , discrete mathematics , linguistics , philosophy , biology , paleontology
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. © 2003 Wiley Periodicals, Inc.