Fuzzy Topological Partial Groups | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 32, Issue 1, 2024, Page 11-21 PDF (443.34 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/joems.2024.319201.1007 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Ahmed Fathy 
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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. | ||||
| Keywords | ||||
| Fuzzy Topology; Fuzzy Group; Fuzzy Partial Group; Fuzzy Topological Group; Topological Partial Group | ||||
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