A class of multiobjective linear programming model with fuzzy random coefficients.

*(English)*Zbl 1165.90701Summary: The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

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

90C29 | Multi-objective and goal programming |

##### Keywords:

fuzzy random variable; chance measure; possibility measure; fuzzy random simulation; genetic algorithm; compromise solution##### Software:

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\textit{J. Li} et al., Math. Comput. Modelling 44, No. 11--12, 1097--1113 (2006; Zbl 1165.90701)

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