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为克服模糊数运算的复杂性引入折线模糊数的定义,利用折线模糊数的优良性质获得了两个重要不等式,并给出实例说明折线模糊数的逼近能力有效.其次,引进K-拟可加积分和K-积分模概念,在折线模糊数空间满足可分性的基础上,借助于模糊值简单函数和模糊值Bernstein多项式研究了若干函数空间的稠密性问题,获得了可积有界模糊值函数类依K-积分模构成完备可分的度量空间.最后,在K-积分模意义下讨论了四层正则折线模糊神经网络对模糊值简单函数的泛逼近性,进而得到该网络对可积有界函数类也具有泛逼近性.该结果表明正则折线模糊神经网络对连续模糊系统的逼近能力可以推广为对一般可积系统的逼近能力.
In order to overcome the complexity of fuzzy number operation, the paper introduces the definition of polygon number, and uses the excellent property of polygon number to obtain two important inequalities, and gives an example to show that the approximation ability of polygon number is effective.Secondly, Integral and K-integral modules are introduced. On the basis of the satisfiability of the line number of the fuzzy line, the denseness of several function spaces is studied by means of the simple fuzzy function and the Bernstein polynomial of the fuzzy value, and the integrable bounded fuzzy values The function class forms a complete separable metric space by K-integral modules.Finally, we discuss the general approximation of the four-level regular polyline fuzzy neural network to the fuzzy value simple function in the sense of K-integral modules, The bounded function class also has the function of universal approximation, which shows that the approximation ability of the regular polyline fuzzy neural network to continuous fuzzy systems can be generalized to the approximation ability of general integrable systems.