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On Robustness of Min-Implication Fuzzy Relation Equation

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Fuzzy Engineering and Operations Research

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 147))

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Abstract

The robustness of solutions of min-implication fuzzy relation equation is investigated in this paper. After proposing the definition of perturbation of fuzzy sets based on some logic-oriented equivalence measure, we discuss the relationship for the existence of solutions between fuzzy relation equation and its fuzzy perturbation equation. When the solutions exist, the perturbation issues of the maximal and minimal solutions are presented in terms of δ–equalities, and the maximum of δ with the corresponding δ–equality satisfied is derived.

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Author information

Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Jian-hua Jin & Qing-guo Li

  2. College of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    Jian-hua Jin & Chun-quan Li

Authors
  1. Jian-hua Jin
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  2. Qing-guo Li
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  3. Chun-quan Li
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Corresponding author

Correspondence to Jian-hua Jin .

Editor information

Editors and Affiliations

  1. School of Mathematics and, Information Science, Guangzhou University, Wai Huan Xi Road, Guangdong, 510006, China, People's Republic

    Bing-Yuan Cao

  2. , School of Science, Southwest Petroleum University, Xindu Avenue 8#, Chengdu, 610500, China, People's Republic

    Xiang-Jun Xie

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© 2012 Springer-Verlag Berlin Heidelberg

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Jin, Jh., Li, Qg., Li, Cq. (2012). On Robustness of Min-Implication Fuzzy Relation Equation. In: Cao, BY., Xie, XJ. (eds) Fuzzy Engineering and Operations Research. Advances in Intelligent and Soft Computing, vol 147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28592-9_26

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  • DOI: https://doi.org/10.1007/978-3-642-28592-9_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28591-2

  • Online ISBN: 978-3-642-28592-9

  • eBook Packages: EngineeringEngineering (R0)

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