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Perturbation Analysis of the Fully Fuzzy Linear Systems

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Advances in Computational Science and Computing (ISCSC 2018 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 877))

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Abstract

The main aim of this paper is to investigate perturbation analysis of the fully fuzzy linear systems (shown as FFLS) \(\tilde{A}\otimes \tilde{x}=\tilde{b}\), where \(\tilde{A}\) and \(\tilde{b}\) are respectively a fuzzy matrix and a fuzzy vector. For showing how the perturbation of the right hand vector impact the fuzzy approximate solution vector to FFLS. We first transform the original fully fuzzy linear systems into three crisp linear systems by the Dehghan’s method. Next, the situation that the right hand side is slightly perturbed while the coefficient matrix remains unchanged is discussed; Finally, the relative error bounds of perturbed fully fuzzy linear systems are obtained in terms of the distance of LR-type triangular fuzzy vector.

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Acknowledgements

Thanks to the support by Provincial Science and Technology Program Foundation of Gansu (18JR3RM238) and PhD Scientific Research Start-up Funded Projects of Longdong University (XYBY05).

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Authors and Affiliations

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

    Kun Liu, Hong-xia Li & Ying Guo

Authors
  1. Kun Liu
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  2. Hong-xia Li
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  3. Ying Guo
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Corresponding author

Correspondence to Kun Liu .

Editor information

Editors and Affiliations

  1. Division of Intelligent Future Technologies, Mälardalen University, Västerås, Sweden

    Ning Xiong

  2. School of Information Science and Technology, Hunan University, Changsha, Hunan, China

    Zheng Xiao

  3. School of Computer Science, Hunan Normal University, Changsha, Hunan, China

    Zhao Tong

  4. Hunan University of Chinese Medicine, School of Computer Science, Changsha, Hunan, China

    Jiayi Du

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

    Lipo Wang

  6. Design and Physical Sciences Brunel, Electronic and Computer Engineering, College of Engineering, Uxbridge, Middlesex, UK

    Maozhen Li

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Liu, K., Li, Hx., Guo, Y. (2019). Perturbation Analysis of the Fully Fuzzy Linear Systems. In: Xiong, N., Xiao, Z., Tong, Z., Du, J., Wang, L., Li, M. (eds) Advances in Computational Science and Computing. ISCSC 2018 2018. Advances in Intelligent Systems and Computing, vol 877. Springer, Cham. https://doi.org/10.1007/978-3-030-02116-0_12

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