摘要
对广义模糊子环和广义模糊理想给出了一种等价的定义，证明了原广义模糊理想的定义中对任何的模糊点ｘｔ，ｙｓ∈Ａ都有Ａ（ｘ＋ｙ）≥Ｍ（Ａ（ｘ），Ａ（ｙ），０．５），Ａ（－ｘ）≥Ｍ（Ａ（ｘ），０．５），Ａ（ｘｙ）≥Ｍ（ｍａｘ（Ａ（ｘ），Ａ（ｙ）），０．５）这三个条件等价于（ｘ＋ｙ）Ｍ（ｔ，ｓ）∈Ａ或（ｘ＋ｙ）１－Ｍ（ｔ，ｓ）∈Ａ，（－ｘ）ｔ∈Ａ或（－ｘ）１－ｔ∈Ａ，（ｘｙ）Ｍ（ｔ，ｓ）∈Ａ或（ｘｙ）１－Ｍ（ｔ，ｓ）∈Ａ这３个新条件。利用上述等价定义推导出了广义模糊（左，右，双边）理想的“和”与“积”的若干运算性质。
The equivalent definition is introduced on the generalized fuzzy subrings and the generalized fuzzy ideals. It is proved that“A(x+y)≥M(A(x),A(y),0.5), A(-x)≥M(A(x),0.5), A(xy)≥M(max(A(x),A(y)),0.5)” and “(x+y)M(t,s)∈A or (x+y)1-M(t,s)∈A, (-x)t∈A or (-x)1-t∈A, (xy)M(t,s)∈A or (xy)1-M(t,s)∈A” are equivalent. Some operational properties of the “sum” and “product” of two generalized fuzzy (left, right, two side) ideals of the ring X is inferred based on this equivalent definition.
出处
《抚顺石油学院学报》
EI
1998年第2期65-69,共5页
Journal of Fushun Petroleum Institute
