基于证据推理的不确定多属性决策方法

针对基本属性权重的不确定性,以及基本属性与广义属性评价集的不一致性等问题,提出一种基于证据推理的不确定多属性决策方法,将证据推理算法推广到更一般的决策环境中.根据决策矩阵的信息熵客观地获得属性的权系数；而对于基本属性与广义属性评价集不一致的情况,则通过对基本属性分布评价的模糊化及模糊变换,合理地实现到广义分布评价的统一形式；最后应用证据推理算法得到整个方案集的排序.实例结果表明,该方法是可行的、有效的.

Evidential Reasoning-Based Approach for Multiple Attribute Decision Making Problems under Uncertainty

The previous study shows that the evidential reasoning algorithm is an effective and rational method to solve MADM(Multiple Attribute Decision Making) problems under uncertainty.However,the method has constraints that attribute weights should be deterministic and evaluation grades assessing basic attributes and general attributes should be consistent.However,these constraints are not relevant to the actual decision-making problems,especially for basic qualitative attributes.Existing subjective and objective methods have defect for basic attribute weights.Most methods assume that the grade is the same in order to evaluate grades based on basic and general attributes.Therefore,these methods are not effective to assist the decision making process and solve problems. In consideration of the weakness of previous study,this study proposes a method based on the evidential reasoning for MADM under uncertainty with the goal of extending evidential reasoning algorithm into a more general decision environment. The first part is to determine basic attribute weights.We first briefly introduce the evidential reasoning algorithm,discussing two major issues related to its effective application for MADM under uncertainty:(1) how to totally determine basic attribute weights,and(2) how to fully implement the transformation of distributed assessment from basic attributes into general attributes.In addition,we calculate basic attribute weights using the information entropy of decision matrix to solve the first problem.In the second part,we implement the equivalent transformation of distributed assessments from basic attributes into general attributes by assuming that evaluation grades assessing basic attributes and general attributes are not the same. We first fuzz the distributed assessments of basic attributes according to different data types of basic attribute values,and then implement,based on fuzzy transformation theory,the unified form of general distributed assessments by combination of fuzzy distributed assessments of basic attributes with fuzzy relation between evaluation grades assessing basic attributes and general attributes,the second problem solved.Finally,we apply the evidential reasoning algorithm to rank all alternatives.An illustrative example is employed to examine the feasibility and validity of decision-making results based on the present approach. In summary,the evidential reasoning algorithm essentially establishes a nonlinear relationship between an aggregated assessment for a general attribute and an original assessment for basic attributes.The algorithm is still an effective and rational method to solve MADM problems under uncertainty and in an ideal environment.In this paper,we successfully tackle primary issues of the evidential reasoning algorithm that can be extended from an ideal decision environment into a more general decision environment so that the algorithm can resolve more sophisticated decision-making problems.