Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems

✍ Scribed by P. Magrez; P. Smets

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 977 KB
• Volume: 4
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.4550040205

✦ Synopsis

Models for fuzzy deductive reasoning are becoming important in the field of knowledgebased systems. Zadeh suggested a compositional rule of inference, also called Generalized Modus Ponens. In order to study the fine structure of this model, we test seven rules of implication, usually found in the fuzzy literature, and two kinds of compositional rule with several properties which seems to be required by commonsense reasoning. But, as no rule is shown to satisfy these properties, we propose a new model for fuzzy Modus Ponens. The main idea of this model is to find a fuzzy extension of the meta-level rule of inference, in comparison with the object-level extension of the disjunctive syllogism such as the Zadeh's model. It is shown that our model satisfies all the intuitively required properties, and moreover is computationally very easy to apply.

When predicates are crisp, the rule of inference for deduction is the Modus Ponens. In order to perform such an inference when predicatec are f u z ~y , ZadehsX6 proposed a compositional rule of inference, also called the Generalized Modus Ponens (GMP). But, this GMP does not yield to a unique model because it presents several degrees of freedom such as the choice of the compo-*Senior research assistant at the National Fund for Scientific Research (Belgium).