Abstract
Boolean implications are employed in inference schemas like modus ponens, modus tollens, etc., where the reasoning is done with statements or propositions whose truth-values are two-valued. Fuzzy implications play a similar role in the generalizations of the above inference schemas, where reasoning is done with fuzzy statements whose truth-values lie in [0, 1] instead of 0, 1.
One of the best known application areas of fuzzy logic is approximate reasoning (AR) ( Driankov et al. [84]), wherein from imprecise inputs and fuzzy premises or rules we obtain, often, imprecise conclusions. Approximate reasoning with fuzzy sets encompasses a wide variety of inference schemes and have been readily applied in many fields, among others, decision making, expert systems and fuzzy control.
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© 2008 Springer-Verlag Berlin Heidelberg
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Baczyński, M., Jayaram, B. (2008). Fuzzy Implications in Approximate Reasoning. In: Fuzzy Implications. Studies in Fuzziness and Soft Computing, vol 231. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69082-5_8
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DOI: https://doi.org/10.1007/978-3-540-69082-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69080-1
Online ISBN: 978-3-540-69082-5
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