Linear optimization problem constrained by fuzzy max-min relation equations.

*(English)*Zbl 1284.90103Summary: Fang and Li introduced the optimization model with a linear objective function and constrained by fuzzy max-min relation equations. They converted this problem into a 0-1 integer programming problem and solved it using the jump-tracking branch-and-bound method. Subsequently, Wu et al. improved this method by providing an upper bound on the optimal objective value and presented three rules for simplifying the computation of an optimal solution. This work presents new theoretical results concerning this optimization problem. They include an improved upper bound on the optimal objective value, improved rules for simplifying the problem and a rule for reducing the solution tree. Accordingly, an accelerated approach for finding the optimal objective value is presented, and represents an improvement on earlier approaches. Its potential applications are discussed.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

##### Keywords:

linear optimization; branch-and-bound method; fuzzy relations; fuzzy relation equations; max-min composition
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\textit{C.-W. Chang} and \textit{B.-S. Shieh}, Inf. Sci. 234, 71--79 (2013; Zbl 1284.90103)

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##### References:

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