Maximum entropy principle for uncertain sets with expectation and variance constraints

Chenyan Liu; Guanzhong Ma; Chenyan Liu; Guanzhong Ma

doi:10.3934/math.2026384

AIMS Mathematics

2026, Volume 11, Issue 4: 9303-9318. doi: 10.3934/math.2026384

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Research article

Maximum entropy principle for uncertain sets with expectation and variance constraints

Chenyan Liu ^{1
,
,},
Guanzhong Ma ²

1.
Department of General Education, Luoyang Polytechnic, No. 6 Keji Avenue, Luolong District, Luoyang, Henan, China
2.
School of Mathematics and Statistics, Anyang Normal University, No. 436 Xiange Avenue, Anyang, Henan, China

Received: 26 July 2025 Revised: 10 March 2026 Accepted: 27 March 2026 Published: 07 April 2026
MSC : 60A40, 94A17

Up to now, the entropy of uncertain sets has found many applications in areas including uncertain finance, uncertain inference, and learning curves. Providing a maximum entropy principle for uncertain sets is helpful for selecting appropriate membership functions in these areas. This paper proposes the maximum entropy principle for uncertain sets and obtains the membership function which achieves the maximum entropy by using the Euler equation in the calculus of variations. Additionally, the entropy of some commonly used uncertain sets is computed in the manuscript.
- entropy,
- maximum entropy principle,
- uncertainty theory,
- uncertain set,
- membership function,
- Euler equation
Citation: Chenyan Liu, Guanzhong Ma. Maximum entropy principle for uncertain sets with expectation and variance constraints[J]. AIMS Mathematics, 2026, 11(4): 9303-9318. doi: 10.3934/math.2026384

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Abstract

Up to now, the entropy of uncertain sets has found many applications in areas including uncertain finance, uncertain inference, and learning curves. Providing a maximum entropy principle for uncertain sets is helpful for selecting appropriate membership functions in these areas. This paper proposes the maximum entropy principle for uncertain sets and obtains the membership function which achieves the maximum entropy by using the Euler equation in the calculus of variations. Additionally, the entropy of some commonly used uncertain sets is computed in the manuscript.

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