Remarks on minimal solutions of a system of fuzzy relation equations over complete infinitely distributive lattices

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• 作者：Feng Sun ; Xiao-bing Qu ; Xue-ping Wang
• 关键词：Fuzzy relation ; Fuzzy relation equation ; Minimal solution ; Complete infinitely distributive lattice
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：20
• 期：2
• 页码：423-428
• 全文大小：466 KB
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• 作者单位：Feng Sun (1) (2)
  Xiao-bing Qu (2)
  Xue-ping Wang (1)
  
  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, Sichuan, People’s Republic of China
  2. College of Mathematics and Information Science, Leshan Normal University, Leshan, 614004, Sichuan, People’s Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479

文摘

In Section 3.6 of Fuzzy relation equations and their applications to knowledge engineering. Kluwer Academic Publishers, Boston (1989), Di Nola et al. presented a procedure to find a minimal solution from a fixed solution of a system of fuzzy relation equations over complete infinitely distributive lattices, and put the question: is the minimal solution found by the procedure unique or not? In this paper, we give a negative answer to the question and make some further remarks. We not only give a necessary and sufficient condition for the uniqueness of such minimal solutions, but also characterize the existence of the least solution and a unique solution of a system of fuzzy relation equations over complete infinitely distributive lattices.