Confluence and termination of fuzzy relations

Confluence and termination are essential properties connected to the idea of rewriting and substituting which appear in abstract rewriting systems. The aim of the present paper is to investigate confluence, termination, and related properties from the point of view of fuzzy logic leaving the ordinary notions a particular case when the underlying structure of truth degrees is two-valued Boolean algebra. The main motivation of this study is the fact that in several natural situations, the notion of substitutability is inherently fuzzy rather than crisp.