Fifth IEEE International conference on Fuzzy Systems, New Orleans (United States of America). 08-11 Septiembre 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
Publication date: September 1996.
Citation:
Villar, J., Conditions for equivalence between the compositional rule of inference and the compatibility modification inference, Fifth IEEE International conference on Fuzzy Systems, New Orleans (United States of America). 08-11 September 1996.
