模糊系统与数学
模糊繫統與數學
모호계통여수학
FUZZY SYSTEMS AND MATHEMATICS
2009年
6期
74-79
,共6页
模糊数%联合隶属函数%截集%积分变换
模糊數%聯閤隸屬函數%截集%積分變換
모호수%연합대속함수%절집%적분변환
Fuzzy Number%Joint Membership%Cut-sets%Integral Transform
使用模糊数的联合隶属函数定义了模糊数的积分变换和逆积分变换,证明了模糊数在积分变换后的模糊数与原模糊数有相同的支撑与核.另外讨论了在积分变换和逆积分变换下保持不变时积分中基函数满足的充要条件,最后给出积分变换的两个应用.
使用模糊數的聯閤隸屬函數定義瞭模糊數的積分變換和逆積分變換,證明瞭模糊數在積分變換後的模糊數與原模糊數有相同的支撐與覈.另外討論瞭在積分變換和逆積分變換下保持不變時積分中基函數滿足的充要條件,最後給齣積分變換的兩箇應用.
사용모호수적연합대속함수정의료모호수적적분변환화역적분변환,증명료모호수재적분변환후적모호수여원모호수유상동적지탱여핵.령외토론료재적분변환화역적분변환하보지불변시적분중기함수만족적충요조건,최후급출적분변환적량개응용.
Integral transform and inverse integral transform of fuzzy numbers are defined by using the joint membership of two fuzzy numbers. It is proved that the fuzzy number obtained by integral transforming a fuzzy number has the same support and kernel as that of the original one. Moreover, a necessary and sufficient condition under that a given fuzzy number with bounded support will not changed after integral transforming and inverse integral transforming is given. Additionally, two applications illustrate integral transform of of fuzzy numbers.
