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A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees

机译：带有犹豫模糊真度的混合多准则群决策的犹豫模糊数学规划方法

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This paper aims to develop a new hesitant fuzzy mathematical programming method for hybrid multi criteria group decision making (MCGDM) with hesitant fuzzy truth degrees and incomplete criteria weight information. In this method, the types of assessment information on criteria are expressed by Atanassov intuitionistic fuzzy sets, hesitant fuzzy sets, trapezoidal fuzzy numbers, intervals and real numbers, respectively. Firstly, the distances of each alternative to positive ideal solution (PIS) and negative ideal solution (NIS) are calculated. Then the hesitant fuzzy positive ideal group consistency index (HFPGCI) and hesitant fuzzy positive ideal group inconsistency index (HFPGICI), the hesitant fuzzy negative ideal group consistency index (HFNGCI) and hesitant fuzzy negative ideal group inconsistency index (HFNGICI) are defined, respectively. To derive the PIS, NIS and the criteria weights simultaneously, a new four-objective hesitant fuzzy mathematical programming model is constructed by minimizing the HFPGICI and HFNGICI as well as maximizing the HFPGCI and HFNGCI. Using the geometric-mean score functions of hesitant fuzzy sets, the four-objective programming model is transformed to a single objective program to resolve. Subsequently, the relative closeness degrees of alternatives for each decision maker (DM) are obtained and applied to derive the individual ranking order of alternatives. To generate the collective ranking order of alternatives, a multi-objective assignment model is established and converted into a single objective programming model to resolve. Thus, a new hesitant fuzzy mathematical programming method is proposed to solve hybrid MCGDM. Finally, a real example is provided to demonstrate the applicability and validity of the proposed method. (C) 2017 Published by Elsevier B.V.
机译：本文旨在开发一种具有犹豫模糊真度和不完全准则权重信息的混合多准则群决策（MCGDM）的犹豫模糊数学规划方法。在这种方法中，关于标准的评估信息的类型分别由Atanassov直觉模糊集，犹豫模糊集，梯形模糊数，区间和实数表示。首先，计算每个替代方案到正理想解（PIS）和负理想解（NIS）的距离。然后分别定义了犹豫的模糊正理想群一致性指数（HFPGCI）和犹豫的模糊正理想群一致性指数（HFPGICI），犹豫的模糊负理想群一致性指数（HFNGCI）和犹豫的模糊负理想群一致性指数（HFNGICI）。 。为了同时导出PIS，NIS和标准权重，通过最小化HFPGICI和HFNGICI以及最大化HFPGCI和HFNGCI构造了一个新的四目标犹豫模糊数学规划模型。使用犹豫模糊集的几何平均得分函数，将四目标规划模型转换为单个目标规划进行求解。随后，获得每个决策者（DM）的备选方案的相对接近度，并将其应用于得出备选方案的各个排名顺序。为了生成备选方案的集体排名顺序，建立了多目标分配模型并将其转换为单个目标编程模型以进行求解。因此，提出了一种新型的犹豫模糊数学规划方法来求解混合MCGDM。最后，提供了一个真实的例子来说明该方法的适用性和有效性。 （C）2017由Elsevier B.V.发布

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