Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (4): 36-38.DOI: 10.3778/j.issn.1002-8331.2010.04.011

• 研究、探讨 • Previous Articles     Next Articles

On distributivity equations’solutions of QL- and D-implications

LI Wei-cai1,3,WU Hai-xiang2,QIN Feng3,WEI Xi-feng1   

  1. 1.Department of Mathematics and Information Science,Shijiazhuang University,Shijiazhuang 050035,China
    2.Department of Foundation Teaching,Jiangxi Institute of Economic Administrators,Nanchang 330088,China
    3.College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China
  • Received:2008-09-18 Revised:2009-06-23 Online:2010-02-01 Published:2010-02-01
  • Contact: LI Wei-cai

关于QL-、D-蕴涵的分配性方程的解

李伟才1,3,吴海翔2,覃 锋3,魏喜凤1   

  1. 1.石家庄学院 数学与信息科学系,石家庄 050035
    2.江西经济管理干部学院 基础教学部,南昌 330088
    3.江西师范大学 数学与信息科学学院,南昌 330022
  • 通讯作者: 李伟才

Abstract: Four distributivity equations[r→(t∧s)]≡[(r→t)∧(r→s)],[r→(t∨s)]≡[(r→t)∨(r→s)],[(p∧q)→r]≡[(p→r)∨(q→r)],[(p∨q)→r]≡[(p→r)∧(q→r)] are discussed.The generalized versions of these distributivity equations are I(r,T1(t,s))=T2(I(r,t),I(r,s)),I(r,S1(t,s))=S2(I(r,t),I(r,s)),I(T1(p,q),r)=S1(I(p,r),I(q,r)),I(S1(p,q),r)=T1(I(p,r),I(q,r)),p,q,r,s,t∈[0,1],where T1,T2 are a t-norm,S1,S2 are a t-conorm.Then this paper proposes the sufficient and necessary conditions for QL-,D-implications to satisfy these distributivity equations.

摘要: 研究了[r→(t∧s)]≡[(r→t)∧(r→s)],[r→(t∨s)]≡[(r→t)∨(r→s)],[(p∧q)→r]≡[(p→r)∨(q→r)],[(p∨q)→r]≡[(p→r)∧(q→r)]4个分配性方程,它们在模糊集理论中的形式分别是I(r,T1(t,s))=T2(I(r,t),I(r,s)),I(r,S1(t,s))=S2(I(r,t),I(r,s)),I(T1(p,q),r)=S1(I(p,r),I(q,r)),I(S1(p,q),r)=T1(I(p,r),I(q,r)),其中p,q,r,s,t∈[0,1],T1、T2为任意三角模,S1、S2为任意三角余模,给出了I为QL-、D-蕴涵时满足分配性方程的充要条件。

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