Abstract

For polyinterval objects, such as generalized interval estimates and fuzzy values, methods are proposed to calculate numerical characteristics, which are similar to characteristics of distribution functions of probability theory (mathematical expectation, variance, average semideviation). The methods are based on the defuzzification of interval estimates of the indicated numerical characteristics in the case of fuzzy polyinterval objects and on the representation of generalized interval estimations as a probability mixture of distributions forming such generalized estimations. These results allow extension of the well-known “mean-risk” method, which is usually used for comparing mono-interval values on their preference and risk, to the case of polyinterval estimates.

中文翻译：

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多区间替代方案比较：“均值风险”方法

摘要

对于广义区间估计和模糊值等多区间对象，提出了计算数值特征的方法，这些方法与概率论的分布函数特征（数学期望，方差，平均半偏差）相似。该方法基于模糊多间隔对象情况下所指示的数值特征的间隔估计值的去模糊化，以及基于作为形成这种广义估计值的分布的概率混合的广义间隔估计值的表示。这些结果允许将众所周知的“均值风险”方法扩展到多间隔估计的情况，该方法通常用于将单间隔值的偏好和风险进行比较。