Abstract
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]. The study of this class of operations has been extensively developed in the literature in the last 30 years from both theoretical and applicational points of view.
In our talk we will concentrate on many different applications of this class of functions. Firstly we will discuss some aspects of mathematical fuzzy logic. Next we will show they role in finding solutions of different fuzzy relational equations. In the next part we present their relevance in approximate reasoning and fuzzy control. In this section we will discuss various inference schemas and we will also show some results connected with fuzzy implications, which are related with reducing the complexity of inference algorithms. In the final part of our talk we will show the importance of fuzzy implication functions in fuzzy mathematical morphology and image processing.
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© 2013 Springer-Verlag Berlin Heidelberg
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Baczyński, M. (2013). On the Applications of Fuzzy Implication Functions. In: Balas, V., Fodor, J., Várkonyi-Kóczy, A., Dombi, J., Jain, L. (eds) Soft Computing Applications. Advances in Intelligent Systems and Computing, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33941-7_4
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DOI: https://doi.org/10.1007/978-3-642-33941-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33940-0
Online ISBN: 978-3-642-33941-7
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