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The Analysis of the Fuzzy Solution to Fully Fuzzy Linear Systems in Two Perturbation Situations

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Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1074))

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Abstract

The fuzzy solution to fully fuzzy linear systems \(\tilde{A}\otimes \tilde{x}=\tilde{b}\) (shown as FFLS) in two perturbation situations are discussed in detail in this paper, where \(\tilde{A}\) and \(\tilde{b}\) are respectively a fuzzy matrix and a fuzzy vector. This paper aims to show how the perturbations of the coefficient matrix or the right hand vector impact the fuzzy approximate solution vector to FFLS, we first transform the original fully fuzzy linear systems into tree crisp linear systems. And then two perturbation situations are studied: (I) the coefficient matrix is slightly perturbed while the right hand side remains unchanged; (II) the coefficient matrix and right hand side are all slightly perturbed. Finally, we deduce the relative error bounds to two perturbation situations based on the distance of LR-type triangular fuzzy vector.

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Acknowledgment

Thanks to the support by the Provincial Science and Technology Program Foundation of Gansu (18JR3RM238).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Longdong University, Qingyang, 745000, Gansu, China

    Kun Liu, Wei-peng Li & Yong-ling Li

  2. School of Information Engineering, Longdong University, Qingyang, 745000, Gansu, China

    Hong-ying Duan

Authors
  1. Kun Liu
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  2. Wei-peng Li
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  3. Yong-ling Li
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  4. Hong-ying Duan
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Corresponding author

Correspondence to Kun Liu .

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Editors and Affiliations

  1. School of Computer Science and Engineering, The University of Aizu, Aizu-Wakamatsu, Fukushima, Japan

    Yong Liu

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Lipo Wang

  3. Computer Science and Mathematics, University of Sao Paulo, Ribeirao Preto, Brazil

    Liang Zhao

  4. School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China

    Zhengtao Yu

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Liu, K., Li, Wp., Li, Yl., Duan, Hy. (2020). The Analysis of the Fuzzy Solution to Fully Fuzzy Linear Systems in Two Perturbation Situations. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_85

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