Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making
Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making
复制标题
梯形直觉模糊数幂几何算子及其在多属性群决策中的应用
DOI：
10.1016/j.asoc.2014.12.031
复制
发表时间：
2015-04-01
影响因子：
8.7
通讯作者：
Dong, Jiu-Ying
中科院分区：
文献类型：
--
作者：
Wan, Shu-Ping;Dong, Jiu-Ying
梯形直觉模糊数（TrIFNs）作为实数集上的一种特殊直觉模糊集，具有更好的对未知量进行建模的能力。本文的目的是开发一些 TrIFN 的幂几何算子，并将其应用于 TrIFN 的多属性群决策（MAGDM）。首先，介绍TrIFNs的下限和上限加权可能性均值以及加权可能性均值。据此，开发了一种新的词典编排方法来对 TrIFN 进行排序。定义了 TrIFN 之间的 Minkowski 距离。然后，研究了4种TrIFNs幂几何算子，包括TrIFNs幂几何算子、TrIFNs幂加权几何算子、TrIFNs幂有序加权几何算子和TrIFNs幂混合几何算子。讨论了它们理想的特性。针对属性和DM的权重向量已知或未知的四种情况，分别提出了四种使用TrIFN的MAGDM方法。在这些方法中，替代方案的各个整体属性值是通过使用 TrIFN 的幂几何或幂加权几何算子生成的。通过构建多目标优化模型确定备选方案的集体整体属性值，并转化为目标规划模型进行求解。这样，根据备选方案的综合整体属性值就得到了备选方案的排名顺序。最后，对绿色供应商选择问题进行了说明，以展示所提方法的应用和验证。 (C) 2015 Elsevier B.V. 保留所有权利。
As a special intuitionistic fuzzy set on a real number set, trapezoidal intuitionistic fuzzy numbers (TrIFNs) have the better capability to model ill-known quantities. The purpose of this paper is to develop some power geometric operators of TrIFNs and apply to multi-attribute group decision making (MAGDM) with TrIFNs. First, the lower and upper weighted possibility means of TrIFNs are introduced as well as weighted possibility means. Hereby, a new lexicographic method is developed to rank TrIFNs. The Minkowski distance between TrIFNs is defined. Then, four kinds of power geometric operators of TrIFNs are investigated including the power geometric operator of TrIFNs, power weighted geometric operator of TrIFNs, power ordered weighted geometric operator of TrIFNs and power hybrid geometric operator of TrIFNs. Their desirable properties are discussed. Four methods for MAGDM with TrIFNs are respectively proposed for the four cases whether the weight vectors of attributes and DMs are known or unknown. In these methods, the individual overall attribute values of alternatives are generated by using the power geometric or power weighted geometric operator of TrIFNs. The collective overall attribute values of alternatives are determined through constructing the multi-objective optimization model, which is transformed into the goal programming model to solve. Thus, the ranking order of alternatives is obtained according to the collective overall attribute values of alternatives. Finally, the green supplier selection problem is illustrated to demonstrate the application and validation of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.