Weightable quasi-metrics related to fuzzy sets

Year 2018, Volume: 47 Issue: 5, 1184 - 1195, 16.10.2018

M.j. Campión R. G. Catalán E. Induráin O. Valero

https://izlik.org/JA89JW68DN

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

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