基于直觉模糊测度的可测函数列依测度收敛研究  

Research on Convergence of Measurable Function Measure Based on Intuitionistic Fuzzy Measure

作　　者：毛明扬 MAO Mingyang(School of Date Science,Guangzhou Huashang College,Guangzhou 511300,China)

机构地区：[1]广州华商学院数据科学学院,广州511300

出　　处：《吉林大学学报（信息科学版）》2023年第4期639-645,共7页Journal of Jilin University（Information Science Edition）

基　　金：国家自然科学基金资助项目(61403219);广州华商学院校级导师制科研基金资助项目(2023HSDS02)。

摘　　要：为解决多属性群决策结果之间存在较大的差异问题,对基于直觉模糊测度的可测函数列依测度收敛进行了研究。基于可能性理论和直觉模糊集理论研究直觉模糊可能性测度,确定直觉模糊测度存在有界性、单调性以及直觉模糊可加性性质与直觉模糊测度依据接收、延迟和拒绝3项决策规则。研究结果明确给出可测函数列依测度收敛情况,可知集函数在可测空间中存在集值双零渐进可加的收敛状态。通过算例验证该方法可有效计算差异属性特征下不同决策的直觉模糊可能性测度,可有效获取最佳决策方案和解决多属性群决策问题,具有较好的实用性。In order to solve the large difference between the results of multi-attribute group decision making,the convergence of measurable functions is studied based on intuitionistic fuzzy measures.Based on the possibility theory and intuitionistic fuzzy set theory,the intuitionistic fuzzy possibility measure is studied,and the boundedness,monotonicity,additivity and intuitionistic fuzzy additive properties of the intuitionistic fuzzy measure are determined.The intuitionistic fuzzy measure is based on the three decision-making rules of receiving decision,delaying decision and rejecting decision.Based on the above research results,the convergence of measurable functions in terms of measure is clarified.It is known that there exists a convergence state of set-valued bizero asymptotically additive set function in measurable space.The example shows that this method can effectively calculate the intuitionistic fuzzy possibility measure of different decisions under different attribute characteristics,and can effectively obtain the best decision scheme,can effectively solve the multi-attribute group decision-making problem with good practicality.

关 键 词：直觉 模糊测度 可测 函数列 依测度 收敛 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]