Kybernetika 60 no. 1, 19-37, 2024

A new approach for fuzzy gyronorms on gyrogroups and its fuzzy topologies

Yu Shen and Conghua YanDOI: 10.14736/kyb-2024-1-0019

Abstract:

In this paper, a new approach for fuzzy gyronorms on gyrogroups is presented. The relations between fuzzy metrics(in the sense of Morsi), fuzzy gyronorms, gyronorms on gyrogroups are studied. Also, some sufficient conditions, which can make a fuzzy normed gyrogroup to be a topological gyrogroup and a fuzzy topological gyrogroup, are found. Meanwhile, the relations between topological gyrogroups, fuzzy topological gyrogroups and stratified fuzzy topological gyrogroups are studied. Finally, the properties of fuzzifying topological gyrogroups are studied.

Keywords:

fuzzy metric, fuzzy gyronorm, gyrogroup, topological gyrogroup, fuzzy topological gyrogroup, fuzzifying topological gyrogroup

Classification:

47H10, 58E30

paper.pdf

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