Confluence and related properties of fuzzy relations

  • Authors:

  • Radim Belohlavek;Tomas Kuhr;Vilem Vychodil

  • Affiliations:

  • SSIE Dept., T. J. Watson School, SUNY Binghamton, Binghamton, NY;Dept. Computer Science, Palacky University Olomouc, Olomouc, Czech Republic;SSIE Dept., T. J. Watson School, SUNY Binghamton, Binghamton, NY

  • Venue:
  • FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
  • Year:
  • 2009

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Abstract

Confluence and termination are essential properties of relations connected to the idea of rewriting and substituting which appear in abstract rewriting systems. This paper presents a preliminary study of 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 the two-valued Boolean algebra. The main motivation of this study is the fact that there are natural examples where the notion of substitutability is inherently fuzzy rather than crisp.