Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 47)
A fuzzy conditional statement (or conditional rule, or fuzzy if-then rule) assumes the form:
where A and B are linguistic values of linguistic variables X and Y, defined by fuzzy sets A and B, respectively. Proposition “X is A” is called the premise or antecedent, and “Y is B” is called conclusion or consequence. In classical logic the statement “if P then Q” is written with implication P ⇒ Q. Implication is a connective defined by Table 2.1.
$$IF X is A THEN y is B,$$
KeywordsMembership Function Fuzzy Relation Aggregation Operation Inference Result Fuzzy Rule Base
Unable to display preview. Download preview PDF.
- Demirli, K., Türksen, I.B. (1994): A review of implications and the generalized modus ponens. Proceedings of the Third IEEE International Conference on Fuzzy Systems IEEE Press, 1440–1445Google Scholar
- Fodor, J.C., Keresztfalvi, T. (1996): Generalized modus ponens and fuzzy connectives. Proceedings on International Panel Conference on Soft and Intelligent Computing, Technical University of Budapest, 99–106Google Scholar
- Wang, L.-X, Mendel, J.M. (1992): Genetating fuzzy rules by learning from examples. IEEE Trans. Systems, Man and Cybernetics 22, 1414–1427Google Scholar
- Marichal, J.,-L., Mathonet, P. (1999): A characterization of the ordered weighted averagingGoogle Scholar
- Whalen, T., Schott, B. (1992): Presumption, prejudice, and regularity in fuzzy material implication. In: Zadeh, L.A., Kacprzyk, J. (eds.) Fuzzy logic for the management of uncertainty. Wiley, New YorkGoogle Scholar
- Czogala, E., Lgski, J. (1999): On equivalence of approximate reasoning results using different interpretations of if-then rules. Fuzzy Sets and Systems, (in print)Google Scholar
© Physica-Verlag Heidelberg 2000