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Decomposition and Resolution of Fuzzy Relation Equations (II) Based on Boolean-Type Implications

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AI 2005: Advances in Artificial Intelligence (AI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3809))

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Abstract

The problem of solving fuzzy relation equations (II) based on Boolean-type implications is studied in the present paper. Decomposition of fuzzy relation equations (II) based on Boolean-type implications is first presented in a finite case. Then, the solution existence of fuzzy relation equations (II) based on Boolean-type implications is discussed, and for nice Boolean-type implications, some new solvability criteria based upon the notion of ”solution matrices” are given. It is also shown that for each solution a of a fuzzy relation equation (II) based on Boolean-type implication, there exists a minimal solution a * of this equation, such that a * is less than or equal to a, whenever the solution set of this equation is nonempty. The complete solution set of fuzzy relation equation (II) based on Boolean-type implication can be determined by all minimal solutions of this equation. Finally, an effective method to solve fuzzy relation equations (II) based on Boolean-type implications is proposed.

This work is sponsored by the 973 program of China under grant No.2002CB312200, the National Science Foundation of China under grant No.60474045, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Zhejiang Province and Zhejiang University.

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Author information

Authors and Affiliations

  1. National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027, China

    Yanbin Luo, Chunjie Yang & Daoying Pi

  2. Institute of Fuzzy Systems, College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an, 710062, China

    Yongming Li

Authors
  1. Yanbin Luo
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  2. Chunjie Yang
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  3. Yongming Li
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  4. Daoying Pi
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Editor information

Editors and Affiliations

  1. Guangxi Normal University, College of CS and IT, Guilin, China, and University of Technology, Faculty of Engineering and Information Technology, Sydney, Australia

    Shichao Zhang

  2. Department of Electrical and Computer Systems Engineering, Monash University, 3800, Melbourne, Victoria, Australia

    Ray Jarvis

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© 2005 Springer-Verlag Berlin Heidelberg

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Luo, Y., Yang, C., Li, Y., Pi, D. (2005). Decomposition and Resolution of Fuzzy Relation Equations (II) Based on Boolean-Type Implications. In: Zhang, S., Jarvis, R. (eds) AI 2005: Advances in Artificial Intelligence. AI 2005. Lecture Notes in Computer Science(), vol 3809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589990_33

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  • DOI: https://doi.org/10.1007/11589990_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30462-3

  • Online ISBN: 978-3-540-31652-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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