Fuzzy Topological Partial Groups

Document Type : Original Article

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Faculty of Computers and Artificial Intelligence, Al-Sadat Egypt

Abstract

In this paper, we present a new concept, called fuzzy topological partial group, discussing some of its fundamental properties. We also examine some categorical properties of this notion. The notion of fuzzy sets, originally presented by Zadeh [1], was used to define fuzzy topological spaces [2,3,4]. Later, Rosenfeld [5] presented the fuzzification of groups, and Foster [6] followed by introducing fuzzy topological groups. Also, the fuzzification of partial groups was introduced by [7], using T-partial monoids on I = [0, 1]. Abd-Allah et al [8] presented the notion of topological partial groups, which we give the abbreviation ’TPG’. In the current paper, we examine the fuzzification
of TPGs, using the definition of fuzzy partial groups with the T-operation as the T−norm minimum. Also, we introduce the fundamental theorems of isomorphisms of fuzzy TPGs. Finally, the product of fuzzy TPGs was introduced in this paper and this category is a convenient categoty.

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