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Can We Detect Crisp Sets Based Only on the Subsethood Ordering of Fuzzy Sets? Fuzzy Sets and/or Crisp Sets Based on Subsethood of Interval-Valued Fuzzy Sets?

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Fuzzy Logic in Intelligent System Design (NAFIPS 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 648))

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Abstract

Fuzzy sets are naturally ordered by the subsethood relation \(A\subseteq B\). If we only know which set which fuzzy set is a subset of which – and have no access to the actual values of the corresponding membership functions – can we detect which fuzzy sets are crisp? In this paper, we show that this is indeed possible. We also show that if we start with interval-valued fuzzy sets, then we can similarly detect type-1 fuzzy sets and crisp sets.

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References

  1. Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)

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  2. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2006)

    MATH  Google Scholar 

  3. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

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Author information

Authors and Affiliations

  1. Computer Science and Information Technology Systems Department, El Paso Community College, 919 Hunter, El Paso, TX, 79915, USA

    Christian Servin

  2. Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, 79968, USA

    Gerardo Muela & Vladik Kreinovich

Authors
  1. Christian Servin
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  2. Gerardo Muela
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  3. Vladik Kreinovich
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Corresponding author

Correspondence to Christian Servin .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Reformat

  5. Laboratory of Computational Intelligence and Automation, University of Waterloo, Waterloo, Ontario, Canada

    William Melek

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Servin, C., Muela, G., Kreinovich, V. (2018). Can We Detect Crisp Sets Based Only on the Subsethood Ordering of Fuzzy Sets? Fuzzy Sets and/or Crisp Sets Based on Subsethood of Interval-Valued Fuzzy Sets?. In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_35

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  • DOI: https://doi.org/10.1007/978-3-319-67137-6_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67136-9

  • Online ISBN: 978-3-319-67137-6

  • eBook Packages: EngineeringEngineering (R0)

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