Hesitant Fuzzy 2-Dimension Linguistic Term Set and its Application to Multiple Attribute Group Decision Making
Hesitant Fuzzy 2-Dimension Linguistic Term Set and its Application to Multiple Attribute Group Decision Making
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DOI：
10.1007/s40815-017-0384-0
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发表时间：
2017-09
影响因子：
4.3
通讯作者：
Xiaoyue Liu;Yanbing Ju;Qixing Qu
中科院分区：
文献类型：
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作者：
Xiaoyue Liu;Yanbing Ju;Qixing Qu
犹豫模糊语言术语集 (HFLTS) 是一种强大的工具，用于解决决策者在几个连续的语言术语之间犹豫是否提供他或她对替代方案的偏好的情况。为了反映HFLTS中所有可能的语言术语的不同重要性程度或权重，通过添加概率提出了称为概率语言术语集（PLTS）的HFLTS扩展。请注意，对于 PLTS，所有可能的语言术语的重要性信息均由清晰的数字描述。然而，在实际应用中，尤其是在不确定的环境下，决策者可能很难通过清晰的数字来提供重要信息。为了准确保存决策者提供的完整评价信息，受二维语言变量思想的启发，本文提出犹豫模糊二维语言术语集的概念，它不仅包括表达对对象评价值的可能语言术语，还包括语言术语所表示的每个语言术语的重要程度。首先，定义了犹豫模糊二维语言元素（HF2DLE）之间的运算和比较规律。然后，提出了一些广义聚合算子用于聚合HF2DLE，例如广义犹豫模糊二维语言加权平均（G-HF2DLWA）算子、广义犹豫模糊二维语言有序加权平均（G-HF2DLOWA）算子和广义犹豫模糊二维语言混合加权平均（G-HF2DLHWA）算子。此外，还讨论了这些运算符的一些理想属性和特殊情况。基于G-HF2DLOWA和G-HF2DLWA算子，提出了一种犹豫模糊二维语言环境下的多属性群决策方法。最后给出数值算例验证了该方法的实用性和有效性。
Hesitant fuzzy linguistic term set (HFLTS) is a powerful tool for solving the situations in which a decision maker hesitates among several consecutive linguistic terms in providing his or her preference to an alternative. To reflect the different importance degrees or weights of all possible linguistic terms in a HFLTS, an extension of HFLTS called probabilistic linguistic term set (PLTS) is proposed through adding probabilities. Note that for a PLTS, the importance information of all possible linguistic terms is described by crisp numbers. However, in practical applications, especially under uncertain environment, it may be difficult for decision makers to provide the importance information by crisp numbers. To accurately preserve the complete evaluation information provided by decision makers, motivated by the idea of 2-dimension linguistic variables, this paper proposes the concept of hesitant fuzzy 2-dimension linguistic term set, which includes not only possible linguistic terms expressing the evaluation value to an object, but also the importance degree of each linguistic term denoted by a linguistic term. Firstly, the operations and comparison laws between hesitant fuzzy 2-dimension linguistic elements (HF2DLEs) are defined. Then, some generalized aggregation operators are proposed for aggregating HF2DLEs, such as generalized hesitant fuzzy 2-dimension linguistic weighted average (G-HF2DLWA) operator, generalized hesitant fuzzy 2-dimension linguistic ordered weighted average (G-HF2DLOWA) operator and generalized hesitant fuzzy 2-dimension linguistic hybrid weighted average (G-HF2DLHWA) operator. Furthermore, some desirable properties and special cases of these operators are discussed. Based on the G-HF2DLOWA and G-HF2DLWA operators, an approach to multiple attribute group decision making is developed under hesitant fuzzy 2-dimension linguistic environment. Finally, a numerical example is given to verify the practicality and effectiveness of the proposed method.