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Structure of Uninorms with Continuous Diagonal Functions

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

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Abstract

The structure of uninorms which are continuous on some special parts of the unit square is discussed. After a summary of partial results achieved in the characterization of uninorms with continuous underlying t-norm and t-conorm in the past years, a full characterization of these uninorms is described. Representation theorems based on the set of discontinuity points of such a uninorm and the ordinal sum construction for semigroups are presented. Further generalizations yield uninorms with continuous diagonal functions. Several results related to uninorms with continuous diagonals are investigated. Further generalizations are also discussed.

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Acknowledgments

This work was supported by grants VEGA 2/0049/14, APVV-0178-11 and Program Fellowship of SAS.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia

    Andrea Mesiarová-Zemánková

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  1. Andrea Mesiarová-Zemánková
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Correspondence to Andrea Mesiarová-Zemánková .

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Editors and Affiliations

  1. Dept of Knowledge-Based Math. Systems, Johannes Kepler University Linz, Linz, Austria

    Susanne Saminger-Platz

  2. Dept. of Mathematics & Descriptive Geo., Slovak University of Technology, BRATISLAVA, Slovakia

    Radko Mesiar

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Mesiarová-Zemánková, A. (2016). Structure of Uninorms with Continuous Diagonal Functions. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_7

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  • Online ISBN: 978-3-319-28808-6

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