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Mathematics
Volume 12
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10.3390/math12131945
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Article

The Intrinsic Characterization of a Fuzzy Consistently Connected Domain

by
Chongyun Zhao
and
Guanghao Jiang
*
School of Mathematics and Statistics, Huaibei Normal University, Huaibei 235000, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(13), 1945; https://doi.org/10.3390/math12131945
Submission received: 15 April 2024 / Revised: 4 June 2024 / Accepted: 21 June 2024 / Published: 23 June 2024
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
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Abstract

The concepts of a fuzzy connected set (fc set) and a fuzzy consistently connected set (fcc set) are introduced on fuzzy posets, along with a discussion of their basic properties. Inspired by some equivalent conditions of crisp connected sets, the characterizations of the fc sets are given, and we also explore fuzzy completeness and fuzzy compactness in addition to defining a new fuzzy way-below relation based on fcc complete sets. Using this relationship as a basis, the fcc domain is also provided and studied, and its equivalent characterizations are obtained. In summary, we develop a method to establish fcc completeness from a continuous poset.
Keywords: fuzzy connected sets; fuzzy consistently connected sets; fuzzy connected complete sets; fuzzy connected continuous domain fuzzy connected sets; fuzzy consistently connected sets; fuzzy connected complete sets; fuzzy connected continuous domain

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MDPI and ACS Style

Zhao, C.; Jiang, G. The Intrinsic Characterization of a Fuzzy Consistently Connected Domain. Mathematics 2024, 12, 1945. https://doi.org/10.3390/math12131945

AMA Style

Zhao C, Jiang G. The Intrinsic Characterization of a Fuzzy Consistently Connected Domain. Mathematics. 2024; 12(13):1945. https://doi.org/10.3390/math12131945

Chicago/Turabian Style

Zhao, Chongyun, and Guanghao Jiang. 2024. "The Intrinsic Characterization of a Fuzzy Consistently Connected Domain" Mathematics 12, no. 13: 1945. https://doi.org/10.3390/math12131945

APA Style

Zhao, C., & Jiang, G. (2024). The Intrinsic Characterization of a Fuzzy Consistently Connected Domain. Mathematics, 12(13), 1945. https://doi.org/10.3390/math12131945

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