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Symmetry 2019, 11(1), 9; https://doi.org/10.3390/sym11010009

On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces

Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju 660701, Korea
Received: 3 December 2018 / Revised: 19 December 2018 / Accepted: 20 December 2018 / Published: 22 December 2018
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Abstract

The computational applications of fuzzy sets are pervasive in systems with inherent uncertainties and multivalued logic-based approximations. The existing fuzzy analytic measures are based on regularity variations and the construction of fuzzy topological spaces. This paper proposes an analysis of the general fuzzy measures in n-dimensional topological spaces with monoid embeddings. The embedded monoids are topologically distributed in the measure space. The analytic properties of compactness and homeomorphic, as well as isomorphic maps between spaces, are presented. The computational evaluations are carried out with n = 1, considering a set of translation functions with different symmetry profiles. The results illustrate the dynamics of finite fuzzy measure in a monoid topological subspace. View Full-Text
Keywords: fuzzy sets; fuzzy measures; monoid topological subspace; compactness; computational applications fuzzy sets; fuzzy measures; monoid topological subspace; compactness; computational applications
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Bagchi, S. On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces. Symmetry 2019, 11, 9.

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