概率语言术语集中包含语言信息和语言术语的概率信息,相比犹豫模糊语言术语集, 其不确定性测度更加复杂.文章针对概率语言术语集提出了新的模糊熵、犹豫熵和综合熵度量方法,以分别测量概率语言术语集的模糊性、犹豫性和整体不确定性.首先基于概率语言术语集的距离,提出了概率语言术语集的模糊熵的公理化定义和熵公式;然后定义了概率语言术语集的偏离度,给出了新的犹豫熵公式;在此基础上给出了概率语言术语集的综合熵的公理化定义和熵公式,并和现有的公式进行比较,说明所提熵公式的合理性.

The probabilistic linguistic term sets (PLTSs) contain linguistic terms and probability information of the linguistic terms. Compared with the hesitant fuzzy linguistic term sets, the uncertainty measures of PLTSs are more complicated. This paper proposes new fuzzy entropy, hesitant entropy and comprehensive entropy for PLTSs to measure their fuzziness, hesitation, and overall uncertainty, respectively. Firstly, based on the distance of PLTSs, the axiomatic definition and entropy formula of fuzzy entropy for PLTSs are proposed. Then the deviation degree of PLTSs is defined, and a new hesitant entropy formula is given. On this basis, the axiomatic definition and entropy formula of the comprehensive entropy of PLTSs are given, which are compared with the existing formulas to illustrate the rationality of the proposed entropy formulas.