On Distributive Equations of Implications and Contrapositive Symmetry Equations of Implications Based on a Continuous t-Norm

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• 作者：Feng Qin (12) qinfeng923@163.com
  Meihua Lu (2)
• 关键词：Fuzzy connectives – ; Fuzzy implications – ; Continuous Archimedean t ; norms – ; Continuous t ; norms – ; Distributive equations of implications – ; Contrapositive symmetry equations of implications
• 刊名：Lecture Notes in Computer Science
• 出版年：2011
• 出版时间：2011
• 年：2011
• 卷：7027
• 期：1
• 页码：109-120
• 全文大小：195.8 KB
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• 作者单位：1. College of Mathematics and Information Science, Nanchang Hangkong University, 330063 Nanchang, P.R. China2. College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, P.R. China
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

In this paper, we summarize the sufficient and necessary conditions of solutions for the distributive equation of implication I(x,T ₁(y,z)) = T ₂(I(x,y),I(x,z)) and characterize all solutions of the functional equations consisting of I(x,T ₁(y,z)) = T ₂(I(x,y),I(x,z)) and I(x,y) = I(N(y),N(x)), when T ₁ is a continuous but not Archimedean triangular norm, T ₂ is a continuous and Archimedean triangular norm, I is an unknown function, N is a strong negation. We also underline that our method can apply to the three other functional equations closely related to the above-mentioned functional equations.