定义在复模糊数上的复模糊值函数的收敛性

Convergence of Complex Fuzzy-valued Function Defined in Complex Fuzzy Number

把所有的关于y轴对称的模糊数都定义为零模糊数,在此基础之上给出了复模糊值函数的极限定义,并研究复模糊值函数的收敛性。得到了一系列关于收敛的复模糊值函数极限的结论,包括复模糊值函数的极限是唯一的,收敛的复模糊值函数具有局部有界性和局部保号性,以及复模糊值函数极限的线性运算性质;给出了复模糊值函数的收敛判别法,柯西收敛准则。此复模糊值函数是定义在复模糊数集F(C)上取值于F(C)(所有的复模糊数的集合)中的复模糊数的函数。

The author defines all fuzzy number which are symmetric respect to y-axis as zero fuzzy number, onthe basis, the author defines the limitation of complex fuzzy-valued function and discusses the properties ofconvergence. This pater obtains a series of results about limited complex fuzzy -valued function, including thelimitation of complex fuzzy-valued function is unique, the limited complex fuzzy-valued function has localboundedness and local protection, as well as the linear operation properties of the limitation. Furthermore, theconvergence criterion and the Cauchy convergence criterion of complex fuzzy-valued function are given. In thispaper, it is shown that the complex fuzzy-valued function is defined in a complex fuzzy set F（C） which valued thecomplex fuzzy number in F（C） （ set of all complex fuzzy number）.