A measure of consistency for fuzzy logic theories

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.

Automated summary

This paper discusses various ways to define the notion of inconsistency in fuzzy logic systems and provides a notion of inconsistency based on the absence of models, as well as two consistency measures that belong purely to the fuzzy paradigm. These measures coincide with the crisp notion of consistency when the set of truth values is {0, 1}, bringing back the spirit of fuzzy logic into the notion of consistency.