On Fuzzy Retract of a Fuzzy Loop Space

Haçat, Gülnur

doi:10.14445/22315373/ijmtt-v65i2p512

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…Also, he presented some theorems and corollaries about the fuzzy fundamental groups of the limit of foldings and the variant and invariant of the fuzzy fundamental group under the folding of the fuzzy manifold into itself. Later, Haçat [25] studied fuzzy H-space and fuzzy H-group and shown that a fuzzy deformation retract of a fuzzy loop space is a fuzzy H-group. e background of this paper is considered as a continuation of the above efforts in following the study of fuzzy groups by Rosenfild's [6], and it starts from the definition of isometric folding map of Riemannian manifolds by Robertson [26], who defined this map between two Riemannian manifolds and stated some of its properties such as the continuity property and the property of conservativeness on the length of piecewise geodesic paths.…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Fundamental Groups and Fuzzy Folding of Fuzzy Minkowski Space

Talafha

Alqaraleh

El-Ahmady

et al. 2021

Advances in Fuzzy Systems

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In this paper, we studied the relations between new types of fuzzy retractions, fuzzy foldings, and fuzzy deformation retractions, on fuzzy fundamental groups of the fuzzy Minkowski space M ˜ 4 . These geometrical transformations are used to give a combinatorial characterization of the fundamental groups of fuzzy submanifolds on M ˜ 4 . Then, the fuzzy fundamental groups of the fuzzy geodesics and the limit fuzzy foldings of M ˜ 4 are presented and obtained. Finally, we proved a sequence of theorems concerning the isomorphism between the fuzzy fundamental group and the fuzzy identity group.

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Section: Introductionmentioning

confidence: 99%

On Fuzzy Fundamental Groups and Fuzzy Folding of Fuzzy Minkowski Space

Talafha

Alqaraleh

El-Ahmady

et al. 2021

Advances in Fuzzy Systems

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Fuzzy Closure Hopf Space

Demiralp

2024

TJMCS

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In this study, we introduce the concepts of fuzzy closure Hopf space and fuzzy closure Hopf group within the framework of fuzzy closure spaces, using homotopy theory. We investigate the relationships between the fuzzy closure Hopf group and its homotopy equivalence. Furthermore, we demonstrate the existence of a contravariant functor from the category of fuzzy closure Hopf spaces and the continuous functions, to the category of groups and homomorphisms. This is demonstrated by illustrating that the set of homotopy function classes among fuzzy closure Hopf groups constitutes a group.

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On Fuzzy Retract of a Fuzzy Loop Space

Cited by 2 publications

References 4 publications

On Fuzzy Fundamental Groups and Fuzzy Folding of Fuzzy Minkowski Space

On Fuzzy Fundamental Groups and Fuzzy Folding of Fuzzy Minkowski Space

Fuzzy Closure Hopf Space

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