集对模糊联系数构建与因素影响重要性分析

Construction of set pair fuzzy connection numbers and analysis of the factor influence importance

为研究系统及其在因素影响下的安全性特征,必须考虑各方面的数据模糊性和不确定性。因此需要一种能同时表示系统及数据模糊性和不确定性的方法,为此提出了一种结合模糊数学隶属函数和集对分析联系数的方法。首先,论述了两者的等效关系;然后,通过将各模糊语义分级中隶属函数的积分与总积分的比值作为该语义对应集对联系数的系数,建立单因素集对模糊联系数;使用同、异、反三状态逻辑真值表将单因素集对模糊联系数耦合形成多因素集对模糊联系数;最后,提出使用单因素集对模糊联系数的系统安全因素影响分析方法。通过两因素五级语义划分以系统安全为目标构建了集对模糊类联系数,并分析了两因素对系统安全影响的程度和排序。研究表明,将模糊数学隶属函数与集对分析联系数关联起来能同时描述数据的模糊性和不确定性,具有较好的研究性质和前景。

To research the system and its safety characteristics under the influence of factors,the data fuzziness and uncertainty brought by man-machine environment management must be considered.Therefore,a method that can represent the fuzziness and uncertainty of the system and data at the same time is needed.This paper proposes a mathematical method that combines fuzzy mathematical membership function and set pair analysis connection number.Firstly,the equivalence relationship between the two is discussed.The relationship includes three items.The fuzzy degree of the fuzzy membership function is equivalent to the determination and uncertainty of set pair analysis;The fuzzy semantic classification is the same as the item number of connection numbers;The membership function integral of each semantic level is the same as the item coefficient of the corresponding connection number.This to some extent indicates that the membership function is a density function corresponding to the coefficients of the connection number items.The ratio of the integral of the membership function to the total integral in each fuzzy semantic classification is used as the connection number of the set pair connection number of the corresponding semantic element,to establish a single factor to determine the fuzzy connection number.An identical discrepancy contrary three-state logic truth table is used to couple the single-factor set fuzzy connection number to form the multi-factor set fuzzy connection number.Finally,an analysis method involving system safety factors using a single factor set pair fuzzy connection numbers is proposed.Through the two factors of five-level semantic division,the set pair fuzzy connection number is constructed to ensure system safety,and the degree of influence and ranking of the two factors on system safety can then be analyzed.The research shows that associating the membership function of fuzzy mathematics with the connection number of set pair analysis can describe the fuzziness and uncertainty of data at the same time,suggesting that this method has good potential for future research and applications.