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Intervals and More: Aggregation Functions for Picture Fuzzy Sets

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Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 835))

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Abstract

Picture fuzzy sets, recently introduced by B. C. Cuong and V. Kreinovich, are a special case of L-fuzzy sets. We discuss the set of truth values for these fuzzy sets as well as aggregation functions for these truth values, paying special attention to t-norms and t-conorms. The important role of representable t-norms and t-conorms is emphasized.

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Acknowledgements

The authors were supported by the “Technologie-Transfer-Förderung” of the Upper Austrian Government (Wi-2014-200710/13-Kx/Kai), the second author also by the Slovak grant VEGA 1/0006/19.

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Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria

    Erich Peter Klement

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

    Radko Mesiar

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  1. Erich Peter Klement
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  2. Radko Mesiar
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Correspondence to Erich Peter Klement .

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Editors and Affiliations

  1. Department of Teacher Education, University of Texas at El Paso, El Paso, TX, USA

    Olga Kosheleva

  2. Institute of Computational Technologies SB RAS, Novosibirsk, Russia

    Sergey P. Shary

  3. Johns Creek, GA, USA

    Gang Xiang

  4. Deptartment of Informatics, The State Russian Museum, Saint Petersburg, Russia

    Roman Zapatrin

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Klement, E.P., Mesiar, R. (2020). Intervals and More: Aggregation Functions for Picture Fuzzy Sets. In: Kosheleva, O., Shary, S., Xiang, G., Zapatrin, R. (eds) Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications. Studies in Computational Intelligence, vol 835. Springer, Cham. https://doi.org/10.1007/978-3-030-31041-7_10

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