Fuzzy number on subset of $ \mathbb{R} $ and application

Man Huang; Guixiang Wang; Chengjia Li; Mengmeng Song; Man Huang; Guixiang Wang; Chengjia Li; Mengmeng Song

doi:10.3934/math.20261339

AIMS Mathematics

2026, Volume 11, Issue 10: 34323-34340. doi: 10.3934/math.20261339

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Research article

Fuzzy number on subset of $ \mathbb{R} $ and application

1.
Liberal Arts and Sciences College, Hangzhou Dianzi University Information Engineering College, No. 1 Hangdian Road, Qingshanhu Street, Hangzhou 311305, Zhejiang, China
2.
School of Sciences, Hangzhou Dianzi University, No. 1158 2nd Avenue, Baiyang Street, Hangzhou 310018, Zhejiang, China
3.
Hangzhou Wenhui School, No. 518 Jinqiao Street, Hangzhou 310018, Zhejiang, China

Received: 06 April 2026 Revised: 19 September 2026 Accepted: 10 October 2026 Published: 22 October 2026
MSC : 03E72, 90B50, 90C70, 93C42

In this paper, some issues related to fuzzy numbers on number sets were studied. The definition of fuzzy numbers on number sets was given. Continuous fuzzy numbers and discrete fuzzy numbers are fuzzy numbers defined on the set of real numbers. The fuzzy numbers defined on the number set are sometimes neither continuous fuzzy numbers nor discrete fuzzy numbers (for example, they may be fuzzy rational numbers). Therefore, the definition of fuzzy numbers on number sets unifies the definition forms of continuous fuzzy numbers and discrete fuzzy numbers, and also expands the scope of fuzzy numbers. The representation theorem of fuzzy numbers on number sets was given, and the operation rules of fuzzy numbers on number sets were discussed. Then, a binary relation was defined based on the center of mass of fuzzy numbers on number sets. Next, specific implementation steps for sorting target objects with mixed uncertain multi-channel digital information characteristics were presented, and these steps were applied to a specific example.
- continuous fuzzy numbers,
- discrete fuzzy numbers,
- discrete set,
- operation closure,
- mixed multi-channel uncertain digital information,
- ranking
Citation: Man Huang, Guixiang Wang, Chengjia Li, Mengmeng Song. Fuzzy number on subset of $ \mathbb{R} $ and application[J]. AIMS Mathematics, 2026, 11(10): 34323-34340. doi: 10.3934/math.20261339

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Abstract

In this paper, some issues related to fuzzy numbers on number sets were studied. The definition of fuzzy numbers on number sets was given. Continuous fuzzy numbers and discrete fuzzy numbers are fuzzy numbers defined on the set of real numbers. The fuzzy numbers defined on the number set are sometimes neither continuous fuzzy numbers nor discrete fuzzy numbers (for example, they may be fuzzy rational numbers). Therefore, the definition of fuzzy numbers on number sets unifies the definition forms of continuous fuzzy numbers and discrete fuzzy numbers, and also expands the scope of fuzzy numbers. The representation theorem of fuzzy numbers on number sets was given, and the operation rules of fuzzy numbers on number sets were discussed. Then, a binary relation was defined based on the center of mass of fuzzy numbers on number sets. Next, specific implementation steps for sorting target objects with mixed uncertain multi-channel digital information characteristics were presented, and these steps were applied to a specific example.

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