Abstract
A system of fuzzy IF-THEN rules is considered as a knowledge-base system where inference is made on the basis of three rules of inference,namely Compositional Rule of Inference ,Modus Ponens and Generalized Modus Ponens. The problem of characterizing models of such systems is investigated.We propose an analytical theory of fuzzy IF-THEN rules where all the above mentioned rules of inference work properly.Modus Ponens and Generalized Modus Ponens formally express interpolation between fuzzy nodes and continuity at fuzzy nodes,respec-tively.We show that the validity of Modus Ponens and thus,interpolation between fuzzy nodes lead to the problem of solvability of fuzzy relation equations.We prove that if the computation is based on sup −composition then the validity of Modus Ponens implies the validity of Generalized Modus Ponens.
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Perfilieva, I. (2007). Analytical Theory of Fuzzy IF-THEN Rules with Compositional Rule of Inference. In: Wang, P.P., Ruan, D., Kerre, E.E. (eds) Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71258-9_9
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DOI: https://doi.org/10.1007/978-3-540-71258-9_9
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