Fuzzy linear systems.

*(English)*Zbl 0805.04005Summary: Fuzzy linear systems of equations and inequalities over a bounded chain are studied both from theoretical and computational points of view. A unified approach is presented for solving such systems, completed with polynomial time algorithms. The main results are concerned with establishing the consistency of the system, computing all kinds of solutions, or marking the contradictory equations (respectively inequalities) if the system is inconsistent. Applications in fuzzy linear programming, multivalued logic, fuzzy matrix equations or inequalities, fuzzy relation equations or inclusions, fuzzy automata and medicine are presented.

##### MSC:

03E72 | Theory of fuzzy sets, etc. |

68Q25 | Analysis of algorithms and problem complexity |

15A99 | Basic linear algebra |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

##### Keywords:

fuzzy linear systems of equations and inequalities; polynomial time algorithms; fuzzy linear programming; multivalued logic; fuzzy matrix equations; fuzzy relation equations; fuzzy automata; medicine
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##### References:

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