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International Summer School on Aggregation Operators

AGOP 2017: Aggregation Functions in Theory and in Practice pp 9–20Cite as

Point-Interval-Valued Sets: Aggregation and Construction

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

Abstract

The concept of a point-interval-valued set (PIV set) is proposed as a tool for summary characterization of data from a two-way table. A PIV set is an L-fuzzy set whose membership labels can be numbers as well as special subintervals from the unit interval. Two relations of partial order of PIV sets are introduced and corresponding operations of union and intersection are studied. Aggregation of PIV sets by bounded t-norms is suggested.

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Acknowledgements

The work of Martin Kalina has been supported from the Science and Technology Assistance Agency under contract No. APVV-14-0013, and from the VEGA grant agency, grant No. 2/0069/16.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, MSC 172, Kingsville, TX, 78363, USA

    Slavka Bodjanova

  2. Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava, Slovakia

    Martin Kalina

Authors
  1. Slavka Bodjanova
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  2. Martin Kalina
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Corresponding author

Correspondence to Martin Kalina .

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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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Bodjanova, S., Kalina, M. (2018). Point-Interval-Valued Sets: Aggregation and Construction. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_2

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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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