This paper considers fuzzy multi-state systems (MSSs) with performance sharing between adjacent units, in which each fuzzy multi-state unit has a random performance and a random demand. If the performance of a unit exceeds its individual demand (performance > demand), its surplus performance can be transmitted to its adjacent unit that experiences performance deficiency (performance < demand). The performance/demand of a unit is represented by the performance/demand levels and the corresponding state probabilities. It is usually difficult to estimate the precise state probabilities due to the inaccuracy and insufficiency of data, therefore, fuzzy state probabilities are given instead of precise state probabilities. This paper proposes a fuzzy universal generating function (FUGF)-based method to evaluate the fuzzy reliability of series systems with performance sharing between adjacent units considering the parametric uncertainty related to the state probabilities of the performance/demand levels of units. The originality of this work lies in two aspects: i) the surplus performance of a unit can only be shared with its adjacent units which experience deficiency; ii) the parametric uncertainty related to the state probabilities is considered. An illustrative example is provided to validate the proposed method.

本文考虑了相邻单元之间具有性能共享的模糊多状态系统（MSS），其中每个模糊多状态单元具有随机性能和随机需求。如果一个单位的绩效超过其个人需求（绩效>需求），则其剩余绩效可以传递给遇到绩效不足的相邻单位（绩效<需求）。一个单元的性能/需求由性能/需求水平和相应的状态概率表示。由于数据的不准确和不足，通常很难估计精确的状态概率，因此，给出模糊状态概率而不是精确状态概率。本文提出了一种基于模糊通用生成函数 (FUGF) 的方法，用于评估相邻单元之间性能共享的串联系统的模糊可靠性，考虑与单元性能/需求水平的状态概率相关的参数不确定性。这项工作的独创性在于两个方面：i) 一个单元的剩余性能只能与相邻的不足的单元共享；ii) 考虑与状态概率相关的参数不确定性。提供了一个说明性示例来验证所提出的方法。i) 一个单元的超额性能只能与其相邻的有缺陷的单元共享；ii) 考虑与状态概率相关的参数不确定性。提供了一个说明性示例来验证所提出的方法。i) 一个单元的超额性能只能与其相邻的有缺陷的单元共享；ii) 考虑与状态概率相关的参数不确定性。提供了一个说明性示例来验证所提出的方法。