Necessary or Sufficient Conditions of F-bounded and Separability in Fuzzy alpha-Metric Space

Zicky, Lukman (2021) Necessary or Sufficient Conditions of F-bounded and Separability in Fuzzy alpha-Metric Space. Masters thesis, Universitas Negeri Sebelas Maret.

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Abstract

Metrics have an important role in mathematics, both in analysis as well as applications. One of the new concepts of metric space is fuzzy α-metric space. This metric space is an expansion of the fuzzy metric space by adding α generator. In this thesis, we discuss about characterization of F-bounded and separability in the fuzzy α-metric space. The property of F-bounded is obtained from the compact subset of given universe set, while the separability is obtained from the countable and dense subset of given universe set. These two characteristics have been discussed by Changqing and Kedian in Hausdorff fuzzy metric spaces. In this thesis, the necessary and sufficient conditions are obtained so that the fuzzy α metric space satisfies the properties of F-bounded. and separable ============================================================================================== Metrics have an important role in mathematics, both in analysis as well as applications. One of the new concepts of metric space is fuzzy α-metric space. This metric space is an expansion of the fuzzy metric space by adding α generator. In this thesis, we discuss about characterization of F-bounded and separability in the fuzzy α-metric space. The property of F-bounded is obtained from the compact subset of given universe set, while the separability is obtained from the countable and dense subset of given universe set. These two characteristics have been discussed by Changqing and Kedian in Hausdorff fuzzy metric spaces. In this thesis, the necessary and sufficient conditions are obtained so that the fuzzy α metric space satisfies the properties of F-bounded and separable.

Item Type: Thesis (Masters)
Subjects: Q Science > QA Mathematics > QA611.28 Metric spaces
Q Science > QA Mathematics > QA248_Fuzzy Sets
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User: Zicky Lukman
Date Deposited: 11 Feb 2022 01:59
Last Modified: 11 Feb 2022 01:59
URI: https://repository.its.ac.id/id/eprint/92967

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