Advances in Fuzzy Implication Functions
By: edited by Michał Baczyński, Gleb Beliakov, Humberto Bustince Sola, Ana Pradera
Contributors: Beliakov, Gleb; Bustince Sola, Humberto; Pradera, Ana; SpringerLink (Online service)
Series: Studies in Fuzziness and Soft Computing -- 300
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2013
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 210
ISBN-13: 9783642356773
Subjects: Engineering; Computational intelligence; Artificial intelligence; Artificial Intelligence (incl. Robotics)
Description: <p>Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0,1}, to fuzzy logic, where the truth values belong to the unit interval [0,1]. These functions are not only fundamental for fuzzy logic systems, fuzzy control, approximate reasoning and expert systems, but they also play a significant role in mathematical fuzzy logic, in fuzzy mathematical morphology and image processing, in defining fuzzy subsethood measures and in solving fuzzy relational equations.</p><p>This volume collects 8 research papers on fuzzy implication functions.</p><p>Three articles focus on the construction methods, on different ways of generating new classes and on the common properties of implications and their dependencies. Two articles discuss implications defined on lattices, in particular implication functions in interval-valued fuzzy set theories. One paper summarizes the sufficient and necessary conditions of solutions for one distributivity equation of implication. The following paper analyzes compositions based on a binary operation * and discusses the dependencies between the algebraic properties of this operation and the induced sup-* composition. The last article discusses some open problems related to fuzzy implications, which have either been completely solved or those for which partial answers are known. These papers aim to present today’s state-of-the-art in this area.</p>
Table of contents: title: An Overview of Construction Methods of Fuzzy Implications; title: Fuzzy Implications: Classification and a New Class; title: A Survey of the Distributivity of Implications over Continuous T-norms and the Simultaneous Satisfaction of the Contrapositive Symmetry; title: Implication Functions in Interval-valued Fuzzy Set Theory; title: (S;N)-Implications on Bounded Lattices; title: Implication Functions Generated Using Functions of one Variable; title: Compositions of Fuzzy Implications; title: Fuzzy Implications: Some Recently Solved Problems.