基于方差最小化的直觉模糊语言多属性决策方法

Multiple Attribute Decision-making Method of Intuitionistic Fuzzy Language Based on Variance Minimization

关键词:  多属性决策  不确定性  直觉模糊语言集  距离测度  方差最小化

Key words:  multiple attribute decision making  uncertainty  intuitionistic fuzzy linguistic set  distance measure  variance minimization

摘要:

针对语言型决策存在运算越界和不符合人们直觉等问题，采用直觉模糊语言距离测度，构建个体评价信息与集成结果之间的方差最小化模型，并通过求解该模型给出直觉模糊语言运算新方法，通过给出直觉模糊语言期望值、精确值和直觉模糊语言的序关系，进而给出一种属性权重已知或完全未知且属性值为直觉模糊语言的多属性决策方法。最后，将所获得的决策方法应用于具体的数值实例中，对比现有方法以验证其合理性与有效性。数值实例结果显示，所提方法在一定程度上克服了现有语言运算存在的越界以及不符合人们直觉的不足。

Abstract:

In view of the problems existed in linguistic decision making,such as boundary-crossing operation and inconsistent with people's intuition,the distance measure of intuitionistic fuzzy language is used to construct a variance minimization model between individual evaluation information and integration results. By solving the model,a new method of intuitionistic fuzzy linguistic operation is given,and the ranking relationship between the expected value,accurate value and intuitionistic fuzzy language is given.Then a multi-attribute decision making method is proposed,in which the attribute weights are known or completely unknown and the attribute values are intuitionistic fuzzy language. Finally,the obtained decision-making method is applied to specific numerical examples to verify its rationality and effectiveness by comparing with the existing methods. The results of numerical example shows that the proposed method overcomes the shortcomings of the existing linguistic operations that are beyond the bounds and do not conform to people's intuition.