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Open AccessArticle

Aggregation of L-Probabilistic Quasi-Uniformities

Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
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Mathematics 2020, 8(11), 1980; https://doi.org/10.3390/math8111980
Received: 30 September 2020 / Revised: 30 October 2020 / Accepted: 2 November 2020 / Published: 6 November 2020
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. View Full-Text
Keywords: filters; L-probabilistic quasi-uniformity; aggregation filters; L-probabilistic quasi-uniformity; aggregation
MDPI and ACS Style

Pedraza, T.; Rodríguez-López, J. Aggregation of L-Probabilistic Quasi-Uniformities. Mathematics 2020, 8, 1980. https://doi.org/10.3390/math8111980

AMA Style

Pedraza T, Rodríguez-López J. Aggregation of L-Probabilistic Quasi-Uniformities. Mathematics. 2020; 8(11):1980. https://doi.org/10.3390/math8111980

Chicago/Turabian Style

Pedraza, Tatiana; Rodríguez-López, Jesús. 2020. "Aggregation of L-Probabilistic Quasi-Uniformities" Mathematics 8, no. 11: 1980. https://doi.org/10.3390/math8111980

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