Solution of a system of linear equations with fuzzy numbers.

*(English)*Zbl 1183.65048This paper deals with system of linear equations whose parameters are fuzzy. It is inspired by results of interval arithmetic and tries to extend some of these to a fuzzy setting. The results are proved in monoidal T-norm based logic and the solutions to fuzzy linear equations are determined by the truth degree of membership formulas for the solution of the linear system in fuzzy logic. The paper includes computed examples and topics for further research.

Reviewer: Frank Uhlig (Auburn)

##### MSC:

65G40 | General methods in interval analysis |

15A06 | Linear equations (linear algebraic aspects) |

65F05 | Direct numerical methods for linear systems and matrix inversion |

15B15 | Fuzzy matrices |

08A72 | Fuzzy algebraic structures |

##### Keywords:

linear system; fuzzy numbers; fuzzy arithmetic; fuzzy interval; interval analysis; united solution set; numerical examples; fuzzy linear equations
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\textit{R. Horčík}, Fuzzy Sets Syst. 159, No. 14, 1788--1810 (2008; Zbl 1183.65048)

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