On D-implications solutions of equation [I(x,y)=I(x,I(x,y))]

Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (29): 46-50.

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On D-implications solutions of equation [I(x,y)=I(x,I(x,y))]

LI Weicai1, SHANG Meijuan1, QIN Feng2, CAO Feng3

1.Department of Mathematics and Information Science, Shijiazhuang University, Shijiazhuang 050035, China
2.School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
3.Department of Computer Science and Technolgy, Tangshan College, Tangshan, Hebei 063000, China

Online:2012-10-11 Published:2012-10-22

关于满足[I(x,y)=I(x,I(x,y))] D-蕴涵的解

李伟才1，商美娟1，覃锋2，曹锋3

1.石家庄学院数学与信息科学系，石家庄 050035
2.江西师范大学数学与信息科学学院，南昌 330022
3.唐山学院计算机科学与技术系，河北唐山 063000

Abstract

Abstract: In this paper, function equation [I(x,y)=I(x,I(x,y))] is discussed, where D-implication [I] is generated by a continuous t-norm [T], a continuous t-conorm [S], and a strong negation [n], i.e.[I(x,y)=S(T(n(x),n(y)),y)].It proposes the solutions of the [I(x,y)=I(x,I(x,y))] which is satisfied.

Key words: fuzzy sets, t-norms；t-conorms, D-implications, function equations

摘要： 研究了[I(x,y)=I(x,I(x,y))]方程，[I]为由连续三角模[T]、连续三角余模[S]和强否定[n]生成的D-蕴涵，即[I(x,y)=S(T(n(x),n(y)),y)]，给出了满足方程[I(x,y)=I(x,I(x,y))]的解。

关键词: 模糊集, 三角模, 三角余模, D-蕴涵, 函数方程

LI Weicai1, SHANG Meijuan1, QIN Feng2, CAO Feng3. On D-implications solutions of equation [I(x,y)=I(x,I(x,y))][J]. Computer Engineering and Applications, 2012, 48(29): 46-50.

李伟才1，商美娟1，覃锋2，曹锋3. 关于满足[I(x,y)=I(x,I(x,y))] D-蕴涵的解[J]. 计算机工程与应用, 2012, 48(29): 46-50.

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On D-implications solutions of equation [I(x,y)=I(x,I(x,y))]

关于满足[I(x,y)=I(x,I(x,y))] D-蕴涵的解

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