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Rough Approximation Operations Based on IF Sets

  • Conference paper
Artificial Intelligence and Soft Computing – ICAISC 2006 (ICAISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4029))

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Abstract

Intuitionistic fuzzy sets, originally introduced by Atanassov, allow for representation both degrees of membership and degrees of non–membership of an element to a set. In this paper we present a generalisation of Pawlak’s rough approximation operations taking Atanassov’s structures as a basis. A special class of residuated lattices is taken as a basic algebraic structure. In the signature of these algebras we have abstract counterparts of two main classes of fuzzy implications. We show that basing on these lattices we can express degrees of weak and strong certainties and possibilities of membership and non–membership of an element to a set.

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Radzikowska, A.M. (2006). Rough Approximation Operations Based on IF Sets. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2006. ICAISC 2006. Lecture Notes in Computer Science(), vol 4029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785231_56

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  • DOI: https://doi.org/10.1007/11785231_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35748-3

  • Online ISBN: 978-3-540-35750-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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