基于正态云期望和方差距离的语言型多属性决策方法研究

Research on Linguistic Multi-attribute Decision Making Method Based on Normal Cloud Expectation and Variance Distance

针对属性权重完全未知,属性指标值为不确定语言值的多属性决策问题,提出一种基于云模型的决策方法。首先,引入正态云的不确定度概念和正态云的期望方差距离(Manhattan距离);其次,将不确定语言值转化为正态云信息,建立基于正态云不确定度最小化的优化模型确定各属性客观权重;然后,通过云加权算术平均(CWAA)算子实现正态云信息综合集成,并通过基于Manhattan距离的TOPSIS方法得到各方案的排序;最后,运用企业竞争情报实例说明该方法的可行性和有效性。

Linguistic multi-attribute decision-making(MADM)problems are widespread in the areas such as economics,management,the social sciences,engineering,and military applications.However,traditional methods are not robust enough to convert qualitative concepts to quantitative information in linguistic MADM problems,neither can they completely reflect the fuzziness and randomness inherent in qualitative concepts.Fortunately,these difficulties can be overcome by using a cloud model.The cloud model,which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations,has attracted considerable attention from researchers studying multi-criteria decision-making problems involving linguistic information.In the process of linguistic MADM based on cloud model,there are two key problems:one is the determination of attribute weight,and the other is the quantitative comparison or ranking of decision-making schemes represented by normal cloud,which involves the distance measurement methods between different cloud models.Therefore,cloud distance measurement plays an important role in linguistic multi-attribute decision-making.A good distance measurement method can greatly improve the scientificity and rationality of decision-making.Aiming at the multi-attribute decision making problem in which the attribute weight is unknown and the attribute value is uncertain linguistic value,a decision-making method based on cloud model is proposed.Firstly,according to the statistical characteristics of the cloud model,fully considering the shape and location of the normal cloud,taking the expectation and variance distance of the normal cloud expectation curve and the entropy expectation curve as the starting point,a Manhattan distance of the expectation and variance of the normal cloud is given.The conversion between linguistic variables and clouds is introduced.Then,the uncertain linguistic value is transformed into the normal cloud information,and the optimization model based on the minimum uncertainty of normal cloud is established to determine the weight value of each attribute.The cloud weighted arithmetic average(CWAA)operator is used to realize the integration of normal cloud information.Secondly,the technique for order preference by similarity to ideal solution(TOPSIS)method based on cloud Manhattan distance is used to examine the similarity between candidate schemes and positive and negative ideal schemes from the perspective of normal cloud distance measurement,and the linguistic MADM method based on normal cloud expectation and variance distance is proposed.Finally,the feasibility and effectiveness of this method are illustrated by an example of enterprise competitive intelligence.