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What is Fuzzy Implication

Chapter 1
Handbook of Research on Fuzzy Information Processing in Databases
Function computing the fulfillment degree of a rule expressed by IF X THEN Y, where the antecedent and the consequent are fuzzy. These functions must comply with certain basic properties and the most typical is the Kleene-Dienes implication, based on the classical implication definition (x?y = ¬x ? y), using the Zadeh’s negation and the maximum s-norm, but other fuzzy implication functions exist (Table 3).
Published in Chapter:
Introduction and Trends to Fuzzy Logic and Fuzzy Databases
José Galindo (University of Málaga, Spain)
Copyright: © 2008 |Pages: 33
DOI: 10.4018/978-1-59904-853-6.ch001
Abstract
This chapter presents an introduction to fuzzy logic and to fuzzy databases. With regard to the first topic, we have introduced the main concepts in this field to facilitate the understanding of the rest of the chapters to novel readers in fuzzy subjects. With respect to the fuzzy databases, this chapter gives a list of six research topics in this fuzzy area. All these topics are briefly commented on, and we include references to books, papers, and even to other chapters of this handbook, where we can find some interesting reviews about different subjects and new approaches with different goals. Finally, we give a historic summary of some fuzzy models, and we conclude with some future trends in this scientific area.
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Chapter 22
Imprecise Functional Dependencies
It is an extension of the classical implication in which the two values involved are not necessarily true or false (1 or 0), but can be also two degrees of truth (belonging to [0,1]). The result is another degree of truth. More precisely, it is a function ?f: [0,1] ? [0,1].
Published in Chapter: Imprecise Functional Dependencies; From: Handbook of Research on Innovations in Database Technologies and Applications: Current and Future Trends
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Chapter 6
On the Versatility of Fuzzy Sets for Modeling Flexible Queries
Operator generalizing the usual material implication, whose arguments and result are valued in the unit interval [0, 1].
Published in Chapter: On the Versatility of Fuzzy Sets for Modeling Flexible Queries; From: Handbook of Research on Fuzzy Information Processing in Databases
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