Title of article :
Hyperspace of a fuzzy quasi-uniform space
Author/Authors :
Pedraza, T. Instituto Universitario de Matem´atica Pura y Aplicada, Universitat Polit`ecnica de Val`encia - Camino de Vera, Valencia, Spain , ıguez-L´opez, Rodr Instituto Universitario de Matem´atica Pura y Aplicada, Universitat Polit`ecnica de Val`encia - Camino de Vera, Valencia, Spain
Abstract :
The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a
crisp quasi-uniformity. This process, based on previous works due to Morsi [25] and Georgescu [9], allows to extend
probabilistic and Hutton [0, 1]-quasi-uniformities on a set X to its power set. In this way, we obtain an endofunctor for
each one of the categories of those objects. We will demonstrate the commutativity of these endofunctors with Lowen
and Katsaras’ functors. Furthermore, we will prove the compatibility of our construction with the Hausdorff fuzzy
quasi-pseudometric introduced in
Keywords :
Fuzzy implication , Hausdorff quasi-uniformity , probabilistic quasi-uniformity , Hutton [0, 1]-quasi-uniformity , fuzzy quasi-pseudometric , Hausdorff fuzzy quasi-pseudometric
Journal title :
Iranian Journal of Fuzzy Systems (IJFS)
