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引入了R-Fuzzy集和Fuzzy系统范数的概念,在Fuzzy系统范数的意义下,可将Fuzzy系统分为3类,即正规Fuzzy系统、正则Fuzzy系统和奇异Fuzzy系统.证明了基于ZadehFuzzy集的Fuzzy系统和BernsteinFuzzy系统是正规Fuzzy系统,基于R-Fuzzy集的HermiteFuzzy系统是正则Fuzzy系统,基于R-Fuzzy集的LagrangeFuzzy系统是奇异Fuzzy系统.最后,通过构造BernsteinFuzzy系统,得到了一个广义Bernstein多项式.在较弱的条件下证明了广义Bernstein多项式在C[a,b]中具有泛逼近性,并通过反例说明:存在不具有泛逼近性的广义Bernstein多项式.
The concepts of R-Fuzzy sets and fuzzy system norm are introduced. Under the norm of fuzzy system norm, the fuzzy systems can be divided into three categories, that is, the normal fuzzy system, the regular fuzzy system and the singular fuzzy system. It is proved that the fuzzy set based on the ZadehFuzzy set Fuzzy system and BernsteinFuzzy system are regular fuzzy systems, HermiteFuzzy system based on R-fuzzy set is a regular fuzzy system, LagrangeFuzzy system based on R-fuzzy set is a singular fuzzy system.Finally, by constructing BernsteinFuzzy system, a generalized Bernstein polynomial Under weak conditions, we prove that the generalized Bernstein polynomials have the universal approximation in C [a, b], and the inverse example shows that there exists a generalized Bernstein polynomial without universal approximation.