摘要
本文在分析灰数的内在含义的基础上,通过隶属函数给出了灰数的抽象定义及其表示方法;讨论了灰数的分类情况及灰数与糊模数、实数的关系;给出了有理灰数的运算法则,并论证了在加强条件下乘法对加法的分配律。
An abstract definition of the grey number is given and the following problems are discussed:1. The subordinating degree of a grey number is 'sandwiched' between the two subordinating degrees μ(x) and μ(x) (μ(x) ≥μ(x)).2. There are three categories of grey numbers: the upper unbounded, lower unbounded, and bounded grey numbers.3. The grey numbers in current use are Deng's grey number and the internal grey number, called rational grey numbers. The operational rule of the rational grey number is given and it is proved that the distributive law[a, b] ([c, d] + [e,f]) = [a, b][c, d] + [a, b][e,f] holds if and only if the following conditions hold: a,b,c,d,e,f≥0 or a, b,c, d, e,f≤0.4. The theories of the grey function, grey limit, grey matrix, grey determinant, grey topology, etc. can be worked out on the basis of the abstract definition of the grey number.5. Let G be a grey number, F a fuzzy number, and R a real number. Then G F R.
出处
《华中理工大学学报》
CSCD
北大核心
1990年第1期47-53,共7页
Journal of Huazhong University of Science and Technology
关键词
灰色系统
灰数
模糊数
映射
模糊集
Grey system
Grey number
Cantor's set
Fuzzy set
Grey set
Mapping
Grey-zone
Rational grey number
