$ r $-connectivity of $ L $-subsets in convex $ (L, M) $-fuzzy hull spaces

Hu Zhao; Bingnan Zhang; Jue Ma; Xiongwei Zhang; Hu Zhao; Bingnan Zhang; Jue Ma; Xiongwei Zhang

doi:10.3934/math.20251231

AIMS Mathematics

2025, Volume 10, Issue 11: 28020-28033. doi: 10.3934/math.20251231

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Research article

$ r $-connectivity of $ L $-subsets in convex $ (L, M) $-fuzzy hull spaces

1.
School of Science, Xi'an Polytechnic University, Xi'an 710048, China
2.
School of Mathematics and Statistics, Yulin University, Yulin 719000, Shaanxi, China

Received: 24 September 2025 Revised: 18 November 2025 Accepted: 24 November 2025 Published: 28 November 2025
MSC : 52A01

In general topology, connectedness is a fundamental concept. Convex structures, analogous to topological structures, enable the generalization of numerous properties from topological spaces. In this paper, we first define $ r $-connectivity for $ L $-subsets in convex $(L, M)$-fuzzy hull spaces based on convex $(L, M)$-fuzzy hull operators. We then establish several equivalent characterizations of $ r $-connected $ L $-subsets and explore their key properties. In particular, by leveraging these operators, we introduce the finite product property of $ r $-connecivity for product spaces within the framework of convex $(L, M)$-fuzzy hull spaces.
- $ r $-connected $ L $-subsets,
- convex $ (L, M) $-fuzzy hull operators,
- the finite product property
Citation: Hu Zhao, Bingnan Zhang, Jue Ma, Xiongwei Zhang. $ r $-connectivity of $ L $-subsets in convex $ (L, M) $-fuzzy hull spaces[J]. AIMS Mathematics, 2025, 10(11): 28020-28033. doi: 10.3934/math.20251231

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Abstract

In general topology, connectedness is a fundamental concept. Convex structures, analogous to topological structures, enable the generalization of numerous properties from topological spaces. In this paper, we first define $ r $-connectivity for $ L $-subsets in convex $(L, M)$-fuzzy hull spaces based on convex $(L, M)$-fuzzy hull operators. We then establish several equivalent characterizations of $ r $-connected $ L $-subsets and explore their key properties. In particular, by leveraging these operators, we introduce the finite product property of $ r $-connecivity for product spaces within the framework of convex $(L, M)$-fuzzy hull spaces.

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