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On Fuzzy RDM-Arithmetic

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Hard and Soft Computing for Artificial Intelligence, Multimedia and Security (ACS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 534))

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Abstract

The paper presents notion of horizontal membership function (HMF) and based on it fuzzy, relative distance measure (fuzzy RDM) arithmetic that is compared with standard fuzzy arithmetic (SF arithmetic). Fuzzy RDM-arithmetic possess such mathematical properties which allow for achieving complete fuzzy solution sets of problems, whereas SF-arithmetic, in general, delivers only approximate, partial solutions and sometimes no solutions of problems. The paper explains how to realize arithmetic operations with fuzzy RDM-arithmetic and shows examples of its application.

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Author information

Authors and Affiliations

  1. West Pomeranian University of Technology, Zolnierska Street 49, 71-210, Szczecin, Poland

    Andrzej Piegat

  2. Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland

    Marek Landowski

Authors
  1. Andrzej Piegat
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  2. Marek Landowski
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Corresponding author

Correspondence to Andrzej Piegat .

Editor information

Editors and Affiliations

  1. Graduate School of Science and Engineeri, Ehime University Graduate School of Science and Engineeri, Ehime, Japan

    Shin-ya Kobayashi

  2. West Pomeranian University of Technology in Szczecin , Szczecin, Poland

    Andrzej Piegat

  3. West Pomeranian University of Technology in Szczecin , Szczecin, Poland

    Jerzy Pejaś

  4. West Pomeranian University of Technology in Szczecin , Szczecin, Poland

    Imed El Fray

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

    Janusz Kacprzyk

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Piegat, A., Landowski, M. (2017). On Fuzzy RDM-Arithmetic. In: Kobayashi, Sy., Piegat, A., Pejaś, J., El Fray, I., Kacprzyk, J. (eds) Hard and Soft Computing for Artificial Intelligence, Multimedia and Security. ACS 2016. Advances in Intelligent Systems and Computing, vol 534. Springer, Cham. https://doi.org/10.1007/978-3-319-48429-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-48429-7_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48428-0

  • Online ISBN: 978-3-319-48429-7

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