Modeling holistic fuzzy implication using co-copulas |
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Authors: | Ronald R Yager |
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Institution: | (1) Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA |
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Abstract: | Two related aggregation operators called copulas and co-copulas are introduced and various properties are described. The relationship,
of these operators to t-norms and t-conorms is noted. Generalizations of these, respectively, called conjunctors and disjunctors, are introduced. We suggest
the use of disjunctor operators for modeling the multi-valued implication operator in fuzzy logic. We point out that the selection
of operators used in fuzzy logic, in addition to having appropriate pointwise properties, should be holistic, this requires
consideration of the nature of the resulting fuzzy set as a whole. Focusing on the protoform of fuzzy modus ponens and looking
at the information contained in the inferred fuzzy set we show that the use of co-copulas has some desirable properties. Taking
advantage of the fact that the weighted sum of co-copulas is a co-copula we consider the problem of constructing customized
implication operators. |
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Keywords: | Fuzzy logic Granular objects Information Approximate reasoning Aggregation operators Fuzzy modus ponens Implication Specificity |
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