J4 ›› 2012, Vol. 47 ›› Issue (2): 86-92.

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The regularness of WBR0-algebras and relationship with other logic algebras

ZHOU  Jian-ren,  WU Hong-bo*   

  1. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062,  Shaanxi, China
  • Received:2011-09-23 Online:2012-02-20 Published:2012-12-24

Abstract:

Regular residuated lattices and WBR0-algebras are investigated in depth. The relationship between WBR0-algebras and other logic algebras is made  clearer and more definite than before. The main results of this paper are as follows: (1) It is proved that regular residuated lattices and WBR0algebras are the same algebraic structure. (2) The connection among WBR0-algebras with other classical logic algebras is given by the network, through which the roles of WBR0-algebras are explained. (3) The difference between WBR0-algebras and other logic algebras is revealed by constructing a special WBR0-algebra.

Key words:  fuzzy logic; logic algebra; regular residuated lattice; WBR0-algebra; BL-algebra

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