Measures of compactness in L-fuzzy pretopological spaces

This paper presents a new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness based on L-fuzzy α-open operators introduced by Nannan and Ruiying [1] and implication operation. The proposed representation extends the properties of α-openness, α-continuity, α-irresoluteness, and α-compactness to the setting of L-fuzzy pretopological spaces based on graded concepts. Moreover, we introduce and establish the relationships among the new concepts.

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“…De nition 2.12. [24] For an L-fpt σ on X and an L-subset A ∈ L X , the degree of fuzzy compactness com(A) of A is given by:…”

Section: Be An L-fuzzy α-Open Operator Induced By L-fpt σ On Xmentioning

confidence: 99%

A new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness in L-fuzzy pretopological spaces

2019

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“…Compact fuzzy topological spaces are proposed, and the respective measures on L-fuzzy pretopological spaces are constructed [10][11][12][13]. The fuzzy topological spaces are modified by integrating multiple functors maintaining fuzzy compactness [12].…”

Section: Introductionmentioning

confidence: 99%

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

Bagchi

2019

Symmetry

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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.

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“…The analysis of compactness of the fuzzy sets and topological spaces is important for formulating corresponding measures [9]. The degree of compactness and countability in L-fuzzy pretopological spaces can be analyzed [10]. The formulation of pretopological spaces is based on the combination of a non-distributive lattice and implication operator algebra.…”

Section: Introductionmentioning

confidence: 99%

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

Bagchi

2018

Symmetry

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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.

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Measures of compactness in L-fuzzy pretopological spaces

Cited by 12 publications

References 14 publications

A new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness in L-fuzzy pretopological spaces

A new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness in L-fuzzy pretopological spaces

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

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

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