论文部分内容阅读
利用平面上的距离函数及水平重要性函数,建立了衡量模糊数之间差异的UID度量和LPID度量,讨论了UID度量和LPID度量的基本性质,证明了模糊数空间关于UID度量和LPID度量成为度量空间的充分必要条件是水平重要性函数在区间[0,1]上几乎处处不为零.进而讨论了由平面上的范数确定的UID度量和LPID度量的收敛性、可分性和完备性问题.最后通过实例进一步分析了UID度量和LPID度量的特性.
The UID measure and LPID measure, which measure the difference between fuzzy numbers, are established by using distance function and horizontal importance function on the plane. The basic properties of UID measure and LPID measure are discussed. It is proved that the UID measure and LPID measure of fuzzy number space become The necessary and sufficient condition for metric space is that the horizontal importance function is almost non-zero in the interval [0,1], and then discusses the convergence, separability and completeness of the UID metric and LPID metric determined by the norm in the plane Finally, the characteristics of UID measurement and LPID measurement are further analyzed by examples.