Fuzzy logic has shown to be a suitable framework to handle contradictions in which, unsurprisingly, the notion of inconsistency can be defined in different ways. This paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is {0, 1}. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.

中文翻译：

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模糊逻辑理论一致性的度量

模糊逻辑已被证明是处理矛盾的合适框架，毫不奇怪，可以用不同的方式定义不一致的概念。本文首先对定义模糊逻辑系统中不一致概念的不同方法进行了简短的调查。因此，我们通过模型的缺失提供了第一个不一致的概念。随后，我们定义了两种纯粹属于模糊范式的一致性度量；当真值集为 {0, 1} 时，这两个度量都与一致性的明确概念一致。因此，我们可以说，所提供的两个一致性度量是基于程度的一致性概念，将模糊逻辑的精神带回到一致性概念中。