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Aggregation of L -Probabilistic Quasi-Uniformities

Author

Listed:
  • Tatiana Pedraza

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Jesús Rodríguez-López

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L -probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L -probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L = { 0 , 1 } , which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.

Suggested Citation

  • Tatiana Pedraza & Jesús Rodríguez-López, 2020. "Aggregation of L -Probabilistic Quasi-Uniformities," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1980-:d:441042
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    References listed on IDEAS

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    1. Tareq M. Al-shami & Ljubiša D. R. Kočinac & Baravan A. Asaad, 2020. "Sum of Soft Topological Spaces," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
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    Cited by:

    1. Zoltán Kovács & Tibor Csizmadia & István Mihálcz & Zsolt T. Kosztyán, 2022. "Multipurpose Aggregation in Risk Assessment," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    2. Tatiana Pedraza & Jesús Rodríguez-López, 2021. "New Results on the Aggregation of Norms," Mathematics, MDPI, vol. 9(18), pages 1-19, September.

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