两类模糊系统具有插值性的充要条件

Sufficient and necessary conditions for fuzzy systems possessing interpolation property

当模糊系统具有插值性时,它必具有泛逼近性.因此,由插值性可以分析模糊系统的逼近能力.本文讨论了由“交”和“并”的方式聚合推理规则所生成的两类模糊系统的插值性问题.首先,通过分析由“单点”模糊化方法、CRI(com positional ru le of inference)算法以及“重心法”构造的模糊系统,指出模糊系统是否具有插值性关键取决于模糊蕴含算子的第二个变量为0和1时的表达式或取值.在此基础上,得到两类模糊系统具有插值性的充要条件.最后给出了满足这两个充要条件的一些常用的蕴涵算子.

Fuzzy system is universally approximating when it possesses interpolation property, Approximation ability of fuzzy system can be studied by its interpolation property. In this paper, we discussed respectively the interpolation properties of two types of fuzzy systems generated by inference rules of combination of ＂intersection＂ and ＂union＂ . First, fuzzy systems adopting ＂singleton＂ fuzzification, compositional rule of inference （CRI） algorithm and ＂barycenter method＂ defuzzification are studied, and it is pointed out that interpolation properties of these fuzzy systems depend on the expressions or values of implication operator when its second variable take 0 and 1. Based on it, the sufficient and necessary conditions for fuzzy systems possessing interpolation properties are proposed. Furthermore, some commonly applied fuzzy implication operators that satisfy the sufficient and necessary conditions are given.