Similarity issues of confluence of fuzzy relations

Abstract

We study similarity issues of confluence and related properties of fuzzy relations. The ordinary notions of divergence, convergence, convertibility, and confluence are essential properties of relations which appear in abstract rewriting systems. In a graded setting, we can introduce analogous notions related to the idea of approximate rewriting. This paper is a continuation of our previous paper (Belohlavek et al. 2010), where we have introduced such notions using residuated structures of truth degrees, leaving the ordinary notions a particular case when the underlying structure of truth degrees is the two-valued Boolean algebra. In this paper, we focus on similarity issues of confluence and present formulas which provide approximations of degrees of confluence and related properties based on similarity of the original fuzzy relations.

Keywords:

• confluence
• estimation
• fuzzy relations
• similarity
• residuated lattices

Acknowledgement

This study was supported by project reg. no. CZ.1.07/2.3.00/20.0059 of the European Social Fund in the Czech Republic, which is gratefully acknowledged.