Archive for Mathematical Logic

, Volume 43, Issue 8, pp 1009–1039

Non-dual fuzzy connections

Article

DOI: 10.1007/s00153-004-0240-4

Cite this article as:
Georgescu, G. & Popescu, A. Arch. Math. Logic (2004) 43: 1009. doi:10.1007/s00153-004-0240-4

Abstract.

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions:

– some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results;

– interesting new concepts besides antitone and isotone ones (like, for instance, conjugated pair), that were classically reducible to the first, gain independency in fuzzy setting.

Key words or phrases:

Duality Isotone structure Fuzzy set theory Galois connection conjugated pair Closure operator 

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institute of MathematicsBucharestRomania
  2. 2.Fundamentals of Computer ScienceFaculty of MathematicsBucharestRomania

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