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Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces

Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju 660701, Korea
Symmetry 2019, 11(5), 671; https://doi.org/10.3390/sym11050671
Received: 30 March 2019 / Revised: 9 May 2019 / Accepted: 11 May 2019 / Published: 15 May 2019
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Abstract

The concepts of fuzzy sets and topology are widely applied to model various algebraic structures and computations. The dynamics of fuzzy measures in topological spaces having distributed monoid embeddings is an interesting topic in the presence of topological endomorphism. This paper presents the analysis of topological endomorphism and the properties of topological fuzzy measures in distributed monoid spaces. The topological space is considered to be Hausdorff and second countable in nature. The analysis of consistency of fuzzy measure in endomorphic topological spaces is formulated. The algebraic structures of endomorphic topological spaces having distributed cyclic monoids are constructed. The cyclic monoids contain specific generators, and a related cyclic topological endomorphism within the subspace is formulated. The analytical properties of fuzzy topological measures in the presence of cyclic topological endomorphism are presented. A comparative analysis of this proposed work with other related work in the domain is included. View Full-Text
Keywords: Hausdorff; monoid; fuzzy sets; fuzzy measures; topological space; endomorphism Hausdorff; monoid; fuzzy sets; fuzzy measures; topological space; endomorphism
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bagchi, S. Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces. Symmetry 2019, 11, 671.

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