J4 ›› 2012, Vol. 47 ›› Issue (2): 93-97.

• Articles • Previous Articles     Next Articles

BR0-distributivity and its generalization

LI Ling-ling, WU Hong-bo*   

  1. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2011-04-07 Online:2012-02-20 Published:2012-12-24

Abstract:

BR0-distributivity has an important position in the structure of BR0algebras which says a→b∨c=(a→b)∨(a→c). It is proved that  residuated lattices with BR0-distributivity also have good properties.  BR0-distributivity is introduced in residuated lattices, and its equivalent form is given. Then the BR0-distributivity is generalized in complete residuated lattices, and  BR0-first infinite distributivity and BR0-second infinite distributivity are obtained. Finally, the properties and relationship between two kinds of BR0-infinite distributivity are  discussed in regular complete residuated lattices and the unite interval [0,1], respectively.

Key words: fuzzy logic; residuated lattice; BR0-algebras; BR0-distributivity; infinite distributivit

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