5th EEE International Conference on Fuzzy Systems - FUZZ-IEEE '96, New Orleans (United States of America). 08-11 September 1996
Summary:
This paper shows that the compositional rule of inference reduces to the compatibility modification inference, when the antecedent of a fuzzy rule and its input fulfil some properties. Two main types of implications are investigated, those generalising the classical material conditional (residuated and strong implications), called in this paper m-implications, and those generalising the classical Cartesian product (t-norms and pseudo-conjunctions), called t-implications. For m-implications, when their maximum modus ponens generating function is used, the compatibility measure depends obviously on the relationship between input and antecedent, but also on the t-norm the implication comes from. Similarly, for t-implications, also used as their own modus ponens generating function, the compatibility measure depends again on the input and antecedent, but also on the t-norm they come from. As it could be expected, in the first case the compatibility measure is a degree of the inclusion of the input into the antecedent, while in the second one it is a degree of the intersection of both.
Keywords: Fuzzy inference, fuzzy implications, compostional rule of inference, compatibility modification, possibility and necessity measures
DOI: 
https://doi.org/10.1109/FUZZY.1996.551782
Published in FUZZ-IEEE '96, pp: 444-449, ISBN: 0-7803-3645-3
Publication date: 2002-08-06.
Citation:
J. Villar, Conditions for equivalence between the compositional rule of inference and the compatibility modification inference, 5th EEE International Conference on Fuzzy Systems - FUZZ-IEEE '96, New Orleans (United States of America). 08-11 September 1996. In: FUZZ-IEEE '96: Proceedings of IEEE 5th International Fuzzy Systems 1996, ISBN: 0-7803-3645-3
