Abstract
Uncertainty theory is a branch of axiomatic mathematics concerned with human’s belief degree. The maximum entropy principle states that the probability distribution with maximal information entropy is the best choice on the basis of partial information. In this paper, the unimodal entropy of uncertain variable is introduced, which unifies most of the classical entropy in uncertainty theory. And the Boundary Decay Condition of an uncertain variable is proposed. Based on the Boundary Decay Condition and Cauchy–Schwarz inequality, the maximum entropy principle of the unimodal entropy is established. Different from the known methods in dealing with the maximum entropy principles in uncertainty theory, we do not apply the Euler–Lagrange equation of the calculus of variations, which is only a necessary but not sufficient condition for the extrema of functionals. As applications, the classical maximum entropy principles in uncertainty theory are deduced from the maximum entropy principle of the unimodal entropy.
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This work is supported by the Key Project of Natural Science Foundation of Educational Committee of Henan Province (No. 20A110010).
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Ma, G. A remark on the maximum entropy principle in uncertainty theory. Soft Comput 25, 13911–13920 (2021). https://doi.org/10.1007/s00500-021-06333-9
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DOI: https://doi.org/10.1007/s00500-021-06333-9