基于熵和协相关度的直觉模糊多属性决策方法

针对决策信息为直觉模糊集且属性权重完全未知的多属性决策问题,提出了一种基于直觉模糊熵和协相关度的决策方法。对于直觉模糊集的直觉性和模糊性,从公理化定义出发,给出了一种改进的直觉模糊熵的定义。然后基于所有属性总不确定信息量最小化准则,利用提出的直觉模糊熵建立非线性规划模型,从而得到属性权重公式。接着,由统计学中变量间相关系数的构造思想,提出直觉模糊集协相关度的概念,并探讨了与相关系数类似的性质,且进一步得出各对象与理想对象加权的协相关度公式。最后给出了一种新的多属性决策途径,并将所提方法成功应用于教授评选的实例中,通过计算各个教师的协相关度确定最佳候选人,实现最优决策。该方法操作合理,算法易于实现,计算结果可靠,可用于多种决策问题。

Multi-attribute decision-making method of intuitionistic fuzziness based on entropy and co-correlation degree

The multi-attribute decision-making has the problems that the decision information is Intuitionistic Fuzzy Set (IFS) and the attribute weights are completely unknown. In order to solve the problems, a decision-making method based on Intuitionistic Fuzzy (IF) entropy and co-correlation degree was proposed. Considering the intuitionism and fuzziness of IFS, an improved IF entropy was defined from the axiomatic definition. Furthermore, based on the criterion that the total uncertain information of all the attributes kept minimization, a nonlinear programming model was established by utilizing the proposed IF entropy, and the formula of attribute weights was obtained. From the structure of the correlation coefficients in statistics between the variables, the concept of co-correlation degree of IFS was proposed, and the similar properties with correlation coefficient were also discussed. Moreover, the formula of co-correlation degree weighted between each object and the ideal object was acquired. Finally, a new multi-attribute decision-making approach was presented, which was successfully applied to the example of teachers' election. By calculating the co-correlation degree of each teacher, the best candidate was determined, and the optimal decision was achieved. With the advantages of reasonable operation, reliable calculation result, and easy to implement, the proposed method can be used for a variety of decision problems.