摘要
在模糊数的结构元表示B~=f（E）中,要求f（x）在[-1,1]上单调,将f（x）扩展为[-1,1]上的连续函数,在证明f（E）是有界模糊数的基础上,给出了相应模糊数的隶属函数表达形式。由于单调性质在模糊数的运算表示中具有重要作用,还得出非单调连续函数f（x）的E-等价函数概念,并给出了E-等价函数的求法。对于算例,用结构元理论是无法求解的,用本文的方法给出解答。
When the fuzzy number is expressed by using structured element it is required that f（x） is monotone in [-1,1], this will be extended to continuous functions in [-1,1], it is proved that f（x） is bounded fuzzy number, on base of it, the membership function of fuzzy number is expressed correspondingly. As the monotonous nature play an important role in the operations of fuzzy numbers, the equivalent function concept of non-monotonic continuous function is concluded in this paper, and how to calculate equivalent function. When the example cannot be solved by using the structured element theory it can be solved by using this method.
出处
《模糊系统与数学》
CSCD
北大核心
2012年第1期20-24,共5页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(71071113)
关键词
模糊数
结构元
单调
Fuzzy Number
Structured Element
Monotone
