Communication, Computer and Automation Engineering
Fuzzy reasoning algorithm and its application with three types of negation
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Abstract:
In fuzzy reasoning, both the compositional rule of inference (CRI) and the similarity-based approximate reasoning (SAR) methods are built on classical fuzzy sets with only one negation. With considering the characteristics of the generalized fuzzy set(GFScom) that possesses three types of negation (contradiction, opposite and medium negation), an extension is made to the implication operator of the CRI fuzzy reasoning method. The definition and formula of GFScom closeness degree, which incorporates three types of negation, are presented. A new computational method of fuzzy approximate reasoning, named GSAR(generalized similarity-based approximate reasoning), is proposed. The method is proven to have reducibility for fuzzy modus ponens (FMP). Through comparative examples, the new GSAR fuzzy reasoning method not only overcomes the subjectivity and arbitrariness of the CRI method in establishing fuzzy relation matrices, but also objectively and effectively reflects three types of negative information in fuzzy reasoning, thereby enriching the forms of fuzzy reasoning.
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Supported by National Natrual Science Foundation of China(61673301), Guizhou Provincial Science and Technology Foundation (Grant No. 1458), and Educational Commission of Guizhou Province (Grant 403 Contract KY）.
