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Transactions on Rough Sets II pp 201–207Cite as

A Non-controversial Definition of Fuzzy Sets

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3135))

Abstract

Already in the early stages of the development of fuzzy set theory, it has been recognized that fuzzy sets can be defined and represented in several different ways. In this paper we first define fuzzy sets within the classical set theory by suitable nested families of sets, and then we discuss how this definition is related to the usual definition by membership functions.

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Author information

Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modelling, University of Ostrava, Czech Republic

    Jaroslav Ramík

  2. Institute of Information Theory and Automation, Praha, Czech Republic

    Milan Vlach

Authors
  1. Jaroslav Ramík
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  2. Milan Vlach
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institut de Recherche en Informatique de Toulouse, France

    Didier Dubois

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  5. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  6. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

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© 2004 Springer-Verlag Berlin Heidelberg

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Ramík, J., Vlach, M. (2004). A Non-controversial Definition of Fuzzy Sets. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_11

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  • DOI: https://doi.org/10.1007/978-3-540-27778-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23990-1

  • Online ISBN: 978-3-540-27778-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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