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Uncertain linear systems

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Abstract

In this paper, an uncertain linear system is defined and some special uncertain linear systems are studied by using uncertainty distributions. An approach for solving some special uncertain linear systems is designed and conditions for the existence of a solution to an uncertain linear system are presented. And, two examples are given to show the effectiveness of the proposed approach. Finally, an application to diet is given to show the practical significance of uncertain linear systems.

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References

  • Abbasbandy, S., Ezzati, R., & Jafarian, A. (2006). LU decomposition method for solving fuzzy system of linear equations. Applied Mathematics and Computation, 172(1), 633–643.

    Article  MATH  MathSciNet  Google Scholar 

  • Abbasbandy, S., Jafarian, A., & Ezzati, R. (2005). Conjugate gradient method for fuzzy symmetric positive definite system of linear equations. Applied Mathematics and Computation, 171(2), 1184–1191.

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo, T. (2004). Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation, 155(2), 493–502.

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo, T. (2005). Successive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation, 162(1), 189–196.

    Article  MATH  MathSciNet  Google Scholar 

  • Dehghan, M., Hashemi, B., & Ghatee, M. (2007). Solution of the fully fuzzy linear systems using iterative techniques. Chaos, Solitons and Fractals, 34(2), 316–336.

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman, M., Ma, M., & Kandel, A. (1998). Fuzzy linear systems. Fuzzy Sets and Systems, 96(2), 201–209.

    Article  MATH  MathSciNet  Google Scholar 

  • Li, P., & Fang, S. C. (2011). On the unique solvability of fuzzy relational equations. Fuzzy Optimization and Decision Making, 10(2), 115–124.

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.

    Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

    Google Scholar 

  • Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.

    Google Scholar 

  • Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, Article 1.

  • Ma, M., Friedman, M., & Kandel, A. (2000). Duality in fuzzy linear systems. Fuzzy Sets and Systems, 109(1), 55–58.

    Article  MATH  MathSciNet  Google Scholar 

  • Minc, H. (1988). Nonnegative matrices. New York: Wiley.

    MATH  Google Scholar 

  • Muzzioli, S., & Reynaerts, H. (2006). Fuzzy linear systems of the form \({\mathbf{A}}_{1} {\mathbf{x}}+{\mathbf{b}}_{1}= {\mathbf{A}}_{2} {\mathbf{x}}+ {\mathbf{b}}_{2}\). Fuzzy Sets and Systems, 157(7), 939–951.

  • Wang, S., Fang, S. C., & Nuttle, H. L. (2003). Solution sets of interval-valued fuzzy relational equations. Fuzzy Optimization and Decision Making, 2(1), 41–60.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, X., Zhong, Z., & Ha, M. (2001). Iteration algorithms for solving a system of fuzzy linear equations. Fuzzy Sets and Systems, 119(1), 121–128.

    Article  MATH  MathSciNet  Google Scholar 

  • Wu, C., & Ma, M. (1991). Embedding problem of fuzzy number space: Part I. Fuzzy Sets and Systems, 44(1), 33–38.

    Article  MATH  MathSciNet  Google Scholar 

  • Yao, K. (2013). Extreme values and integral of solution of uncertain differential equation. Journal of Uncertainty Analysis and Applications, 1, Article 2.

  • Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems: An International Journal, 41(7), 535–547.

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 61273009).

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Bo Li & Yuanguo Zhu

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  1. Bo Li
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  2. Yuanguo Zhu
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Correspondence to Yuanguo Zhu.

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Li, B., Zhu, Y. Uncertain linear systems. Fuzzy Optim Decis Making 14, 211–226 (2015). https://doi.org/10.1007/s10700-014-9197-x

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  • DOI: https://doi.org/10.1007/s10700-014-9197-x

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