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.
Highlights
The fuzzy set theory has numerous applications in a diverse array of complex systems
This paper proposes the analysis and computational evaluations of topological fuzzy measures in distributed monoid spaces
The analytic understanding of topological fuzzy measures facilitates the construction of specific measure spaces along with its applications
Summary
The fuzzy set theory has numerous applications in a diverse array of complex systems. The formation of fuzzy sets and fuzzy topology are constructed based on relational algebra, on a crisp set with an upper limit and lower limit [1]. The fuzzy set theory is applied to the topology in order to construct fuzzy topological spaces [5]. This formulation has created the structures of L-topology based on lattice models. The analysis of compactness of the fuzzy sets and topological spaces is important for formulating corresponding measures [9]. The fuzzy measure on any arbitrary topological space is constructed based on the general Borel sets [16]. This paper proposes the analysis and computational evaluations of topological fuzzy measures in distributed monoid spaces.
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