Abstract

Procedures for calculating preference and risk indicators that were previously applied to mono interval objects are proposed within the collective-risk estimating method in the case of pairwise comparison for polyinterval objects, generalized interval, and fuzzy objects. The procedures are based on the defuzzification of interval estimates of preference and risk indicators related to mono intervals at alpha-levels in the case of fuzzy polyinterval objects and on the presentation of generalized interval estimates as a probabilistic mixture of the distributions forming such an estimate. Some differences and relationships in approach of generalized interval estimations and fuzzy approach for comparing alternatives are studied. It is established that generalized uniform distributions of probability in the approach of generalized interval estimates are obtained if we use the defuzzification methods for uniform distributions on alpha levels of fuzzy objects discussed in the paper. The manner is shown in which the defuzzification procedures lead to one-numeric estimates for the interval characteristics of fuzzy objects, similar to the numerical characteristics of distribution functions of probability theory, mathematical expectation, variance, and mean semideviation. Depending on the defuzzification method, different probability distributions in the formalism of generalized interval estimates can be obtained from uniform distributions on alpha-levels of fuzzy objects. However, the entire variety of probability distributions that arise in the last formalism is not exhausted by the distributions obtained in this manner.

中文翻译：

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多区间替代方案比较：集体风险估计

摘要

在多间隔对象，广义间隔和模糊对象成对比较的情况下，在集体风险估计方法中提出了计算先前应用于单间隔对象的偏好和风险指标的过程。该程序基于模糊多间隔对象的偏好区间估计和与alpha级别上的单区间相关的风险指标的去模糊化，以及基于广义区间估计作为形成这种估计的分布的概率混合的呈现。研究了广义区间估计与模糊方案比较中的一些差异和关系。如果我们使用去模糊化方法对本文讨论的模糊对象的α水平上的均匀分布使用去模糊化方法，则可以确定在广义间隔估计的方法中获得了概率的广义均匀分布。显示了一种方法，其中，去模糊过程导致对模糊对象的间隔特征进行一数字估计，类似于概率论，数学期望，方差和均值半偏差的分布函数的数值特征。根据反模糊化方法，可以从模糊对象的α级上的均匀分布中获得广义区间估计形式上的不同概率分布。然而，