Weightable quasi-metrics related to fuzzy sets

Authors : Mj CAMPİÓN, R G CATALÁN, E INDURÁİN, O VALERO

Pages : 1184-1195

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Publication Date : 2018-10-16

Article Type : Research Paper

Abstract :We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the  membership function of a fuzzy set or from the disymmetry function of a quasi-metric.
Keywords : Fuzzy sets, weightable quasi metrics, functional equations, representable total preorders