Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making
Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making
复制标题
梯形直觉模糊数的幂平均算子及其在多属性群决策中的应用
DOI：
10.1016/j.apm.2012.09.017
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发表时间：
2013-03-15
影响因子：
5
通讯作者：
Wan, Shu-ping
中科院分区：
文献类型：
--
作者：
Wan, Shu-ping
梯形直觉模糊数（TrIFNs）是实数集上的一种特殊直觉模糊集。 TrIFN 可用于处理决策数据和决策问题本身中未知的量。本文的重点是多属性群决策（MAGDM）问题，其中属性值用 TrIFN 表示，通过开发一种基于 TrIFN 功率平均算子的新决策方法来解决该问题。给出了 TrIFN 的新操作法则。从Hausdorff度量的角度来看，定义了TrIFN之间的汉明距离和欧几里得距离。至此，将实数功率平均算子推广为4种TrIFNs功率平均算子，包括TrIFNs功率平均算子、TrIFNs加权功率平均算子、TrIFNs功率有序加权平均算子、TrIFNs功率混合平均算子。在所提出的群体决策方法中，通过使用 TrIFN 的功率平均算子生成备选方案的个体总体评估值。应用TrIFNs的混合平均算子，将备选方案的个体总体评价值整合到集体评价值中，用于对备选方案进行排名。算例分析表明了该方法的实用性和有效性。 (C) 2012 Elsevier Inc. 保留所有权利。
Trapezoidal intuitionistic fuzzy numbers (TrIFNs) is a special intuitionistic fuzzy set on a real number set. TrIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The focus of this paper is on multi-attribute group decision making (MAGDM) problems in which the attribute values are expressed with TrIFNs, which are solved by developing a new decision method based on power average operators of TrIFNs. The new operation laws for TrIFNs are given. From a viewpoint of Hausdorff metric, the Hamming and Euclidean distances between TrIFNs are defined. Hereby the power average operator of real numbers is extended to four kinds of power average operators of TrIFNs, involving the power average operator of TrIFNs, the weighted power average operator of TrIFNs, the power ordered weighted average operator of TrIFNs, and the power hybrid average operator of TrIFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TrIFNs. Applying the hybrid average operator of TrIFNs, the individual overall evaluation values of alternatives are then integrated into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. (C) 2012 Elsevier Inc. All rights reserved.