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Triangular Operations, Negations, and Scalar Cardinality of a Fuzzy Set

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Computing with Words in Information/Intelligent Systems 1

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 33))

Abstract

Scalar approaches to cardinality of a fuzzy set are very simple and convenient, which justifies their frequent use in many areas of applications instead of more advanced and adequate forms such as fuzzy cardinals. On the other hand, theoretical investigations of scalar cardinalities in the hitherto existing subject literature are rather occasional and fragmentary, and lacking in closer references to triangular norms and conorms. This paper is an attempt at filling that gap by constructing an axiomatized theory of scalar cardinality for fuzzy sets with triangular norms and conorms. It brings together all standard scalar approaches, including the so-called sigma-counts and p-powers, and offers infinitely many new alternative options.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769, Poznań, Poland

    Maciej Wygralak

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  1. Maciej Wygralak
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Editors and Affiliations

  1. Berkeley Initiative in Soft Computing (BISC) Computer Science Division and Electronics Research Laboratory Department of Electrical and Electronics Engineering and Computer Science, University of California, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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© 1999 Springer-Verlag Berlin Heidelberg

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Wygralak, M. (1999). Triangular Operations, Negations, and Scalar Cardinality of a Fuzzy Set. In: Zadeh, L.A., Kacprzyk, J. (eds) Computing with Words in Information/Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol 33. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1873-4_14

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  • DOI: https://doi.org/10.1007/978-3-7908-1873-4_14

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11362-2

  • Online ISBN: 978-3-7908-1873-4

  • eBook Packages: Springer Book Archive

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