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

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.

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

“…The corresponding topology in 1D space is denoted as τ x ⊆ P(X), maintaining the axioms of topological space [1]. Let n ∈ Z + , n > 1 be such that A n ⊂ X n is equipped with a closed group operation in n-dimensional subspace as o x : A 2n → A n , generating a G n = (A n , o x ) groupoid subspace [14]. Let I ⊂ Z + be an index set.…”

“…Let I ⊂ Z + be an index set. In G n = (A n , o x ), M is a distributed monoid (DM) if the following properties are satisfied [14]:…”

“…The fuzzy topological spaces are modified by integrating multiple functors maintaining fuzzy compactness [12]. The topological fuzzy measure in distributed monoid spaces is formulated under topological local isomorphism and local homeomorphism [14]. It is considered that the underlying space is Hausdorff in nature.…”

Topological Structures via Interval-Valued Neutrosophic Crisp Sets

“…Thus, this new concept is needed. Second, since the topology can be applied to high dimensional data sets, big data, and computational evaluations (see [31][32][33], respectively), we study topological structures based on interval-valued neutrosophic crisp sets. In order to accomplish such research, first, we recall some definitions related to intuitionistic sets, interval-valued sets, and neutrosophic crisp sets.…”