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Some Remarks About Polynomial Aggregation Functions

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

There exist a great quantity of aggregation functions at disposal to be used in different applications. The choice of one of them over the others in each case depends on many factors. In particular, in order to have an easier implementation, the selected aggregation is required to have an expression as simple as possible. In this line, aggregation functions given by polynomial expressions were investigated in [22]. In this paper we continue this investigation focussing on binary aggregation functions given by polynomial expressions only in a particular sub-domain of the unit square. Specifically, splitting the unit square by using the classical negation, the aggregation function is given by a polynomial of degree one or two in one of the sub-domains and by 0 (or 1) in the other sub-domain. This is done not only in general, but also requiring some additional properties like idempotency, commutativity, associativity, neutral (or absorbing) element and so on, leading to some families of binary polynomial aggregation functions with a non-trivial 0 (or 1) region.

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Acknowledgments

This paper has been partially supported by the Spanish Grant TIN2016-75404-P AEI/FEDER, UE.

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Authors and Affiliations

  1. SCOPIA Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa, km. 7.5, 07122, Palma, Spain

    Sebastia Massanet, Juan Vicente Riera & Joan Torrens

  2. Balearic Islands Health Research Institute (IdISBa), 07010, Palma, Spain

    Sebastia Massanet, Juan Vicente Riera & Joan Torrens

Authors
  1. Sebastia Massanet
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  2. Juan Vicente Riera
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  3. Joan Torrens
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Correspondence to Sebastia Massanet .

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Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Massanet, S., Riera, J.V., Torrens, J. (2019). Some Remarks About Polynomial Aggregation Functions. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_5

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