基于模糊相似度的广义Mamdani模糊系统及其逼近  

Generalized Mamdani Fuzzy System Based on Fuzzy Similarity Degree and Its Approximation

作　　者：高彤 王贵君[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《模糊系统与数学》2018年第1期137-143,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61374009)

摘　　要：模糊相似度是通过局部信息来刻画两个模糊集相似程度的度量,它是进一步研究模糊控制的重要理论工具。本文基于模糊相似度重新给出后件模糊集的计算公式,进而依据广义模糊化、乘积推理机和中心平均解模糊化获得多输入单输出广义Mamdani模糊系统模型及其表示,并通过实例得到该模糊系统的表达式.此外,利用多元微分中值定理证明了广义Mamdani模糊系统对连续可微函数具有一阶逼近性。Fuzzy similarity degree is a metric of the similar degree between two fuzzy sets through describing local information, it is an important theoretical tool for further research on fuzzy control. In this paper, the calculation formula of the consequent fuzzy sets is given based on the fuzzy similarity degree, and then, according to the generalized fuzzification,product inference engine and center average defuzzifier, the multiple inputs single output generalized Mamdani fuzzy system model is obtained, and an expression of the fuzzy system can be got by an example. In addition, using the multivariate differential mean value theorem, it is proved that the generalized Mamdani fuzzy system has a first order approximation to a continuous differentiable function.

关 键 词：模糊相似度 模糊化 中心平均解模糊化 广义Mamdani模糊系统 逼近性 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O159[自动化与计算机技术—控制科学与工程]