• DocumentCode
    433396
  • Title

    Partially ordered set with residuated t-norm

  • Author

    Kondo, Michiro ; Kawaguchi, Mayuka F.

  • Author_Institution
    Tokyo Denki Univ., Inzai, Japan
  • fYear
    2005
  • fDate
    19-21 May 2005
  • Firstpage
    26
  • Lastpage
    29
  • Abstract
    We consider properties of partially ordered sets with residuated t-norm and show that 1. If (X;T,0,1) is a bounded partially ordered set with residuated t-norm T, then (X;*,0X,1X) is a bounded BCK-algebra with condition (S); 2. Conversely, if (B;*,0B,1B) is a bounded BCK-algebra with (S), then (B;T,0,1) is the bounded partially ordered set with residuated t-norm. This means that the class of all bounded partially ordered sets with residuated t-norm coincides with the class of all bounded BCK-algebras with condition (S). Since the class of these algebras forms a variety, the class of partially ordered sets with residuated t-norm is represented by only equations.
  • Keywords
    category theory; fuzzy logic; process algebra; set theory; bounded BCK-algebra; partially ordered set; residuated t-norm; Algebra; Equations; Fuzzy logic; Lattices;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Multiple-Valued Logic, 2005. Proceedings. 35th International Symposium on
  • ISSN
    0195-623X
  • Print_ISBN
    0-7695-2336-6
  • Type

    conf

  • DOI
    10.1109/ISMVL.2005.37
  • Filename
    1423157
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=433396