C模糊系统及其摄动性与稳定性  

C Fuzzy System and It's Perturbation and Stability

作　　者：谷敏强[1] 刘智斌[2] 程贞敏[3] 

机构地区：[1]汕头大学理学院数学系,汕头515063 [2]浙江师范大学数理与信息工程学院,金华324001 [3]北京联合大学商务学院,北京100025

出　　处：《应用数学学报》2009年第2期304-322,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60474023);汕头大学青年科研基金(YR08003)资助项目.

摘　　要：还原性、摄动性与稳定性是模糊系统的重要属性,对其进行深入研究将有助于研制具有良好性能的模糊控制器.称能保持推理还原性的模糊系统为C模糊系统.设"if x is A_((i)) then y is B_((i)),i=1,…,n"是一模糊规则组,模糊推理通过合成运算ο来实现,则C模糊系统的输入输出关系可表示为AοR=B,其中A是模糊输入,B是模糊输出,R是模糊关系方程组A_iοX=B)i(i=1,…,n)的一个解.本文在模糊划分的条件下,分别就ο为两种常用的合成算法∨-*和∧-→(*和→是BL代数中的伴随对)的情况讨论了上述方程组的解,从而给出C模糊系统可能存在的各种情形.在此基础上,给出了模糊系统的摄动性与稳定性的定义,并证明了基于前述两种合成运算的C模糊系统的若干特征定理,给出具有良好稳定性的C模糊系统的表示式.最后,研究了C模糊系统的解析形式,给出这类模糊系统的插值表示.Consistency, perturbation and stability are important properties of fuzzy systems. The investigation of these properties will help to develop excellent fuzzy controllers. The fuzzy systems which can keep consistency of fuzzy inference is called C fuzzy systems. Let ＂if x is Ai then y is Bi, i = 1,...,n＂ be agroupoffuzzyrules, fuzzy inference is realized by the composition operator o, then the input-output relation of C fuzzy system can be represented as A o R = B, where A is fuzzy input, B is fuzzy output, and R , a solution of fuzzy relation equations Ai o X = Bi（i = 1,..., n）.In this paper, under the condition of fuzzy partition, we discuss the solution of the upper relation equations in which o is ∨ - ＊ composition and ∧- → composition （where ＊ and → are conjunctions in BL algebra） respectively.Based on these solutions, we can construct many kind of C fuzzy systems. thereupon, new ideas of perturbation and stability of fuzzy systems are advanced, some characteristic theorems of C fuzzy systems are given, some C fuzzy systems with preferable stability are presented.At last, we study the analytic formulas of C fuzzy systems and give the interpolation representation of them.

关 键 词：C模糊系统 模糊关系方程 ∨-＊合成 ∧-→合成 摄动 稳定性 插值函数 

分 类 号：O159[理学—数学]