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Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications

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Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

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Abstract

In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered.

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Acknowledgment

The work on this paper for Michał Baczyński was partially supported by the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259. The work on this paper for Paweł Drygaś was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów, through Project Number RPPK.01.03.00-18-001/10. The work on this paper for Radko Mesiar was supported by the Grant APVV-14-0013.

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Authors and Affiliations

  1. Institute of Mathematics, University of Silesia in Katowice, ul. Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński

  2. Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, Poland

    Paweł Drygaś

  3. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Michał Baczyński
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  2. Paweł Drygaś
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  3. Radko Mesiar
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Corresponding author

Correspondence to Michał Baczyński .

Editor information

Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Baczyński, M., Drygaś, P., Mesiar, R. (2018). Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_20

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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