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Soft Computing Algorithm for Arithmetic Multiplication of Fuzzy Sets Based on Universal Analytic Models

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Information and Communication Technologies in Education, Research, and Industrial Applications (ICTERI 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 469))

Abstract

This paper deals with the investigations of increasing dependability of computing operations for fuzzy numbers with triangular and bell-shape membership functions (MFs). Special attention is paid to the synthesis of analytic models of the MFs for the results of fuzzy arithmetic operations. New analytical models of the result’s MFs with the description of synthesis procedures for the multiplication operation with triangular fuzzy numbers in R + and R are presented in a universal style. The general analytic models for determination of \( \alpha \)-cuts parameters (direct and inverse approaches) for result fuzzy sets are given. Modeling results confirm the efficiency of the proposed models and fuzzy arithmetic algorithms for fuzzy information processing.

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Author information

Authors and Affiliations

  1. Department of Intelligent Information Systems, Petro Mohyla Black Sea State University, 68-th Desantnykiv Str. 10, Mykolaiv, 54003, Ukraine

    Yuriy Kondratenko

  2. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, USA

    Volodymyr Kondratenko

Authors
  1. Yuriy Kondratenko
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  2. Volodymyr Kondratenko
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Correspondence to Yuriy Kondratenko .

Editor information

Editors and Affiliations

  1. Zaporizhzhya National University, Zaporizhzhya, Ukraine

    Vadim Ermolayev

  2. Institute of Applied Informatics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Heinrich C. Mayr

  3. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Mykola Nikitchenko

  4. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

  5. V.N. Karazin Kharkiv National University, Kharkov, Ukraine

    Grygoriy Zholtkevych

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Kondratenko, Y., Kondratenko, V. (2014). Soft Computing Algorithm for Arithmetic Multiplication of Fuzzy Sets Based on Universal Analytic Models. In: Ermolayev, V., Mayr, H., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2014. Communications in Computer and Information Science, vol 469. Springer, Cham. https://doi.org/10.1007/978-3-319-13206-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-13206-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13205-1

  • Online ISBN: 978-3-319-13206-8

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