定性映射诱导的转化及逆转化程度函数  

A Kind of Conversion Degree Functions and Inverse Conversion Degree Functions Induced by Qualitative-mapping

作　　者：徐晓林[1] 冯嘉礼[1] 

机构地区：[1]上海海运学院信息工程学院,上海200135

出　　处：《上海海运学院学报》2003年第4期364-367,共4页Journal of Shanghai Maritime University

基　　金：国家自然科学基金资助项目(60075016);广西自然科学基金资助项目(核科自9912010)。

摘　　要：文献[6～9]提出有关属性量—质特征转化关系,归结为一个定性映射的观点,并指出定性映射诱导出一个E R(QM)的等价关系,使得任一满足E R(QM)的转化程度函数(CDF),都构成一个能对该量—质转化进行模糊评判的隶属度函数。本文进一步给出了逆转化程度函数的概念。A definition of qualitative mapping(QM) is given in this paper, as follows :Definition: Let X={x|x is a quantity of attribute a(o) of object o}, P_o={p_i(o)| p_i(o) is a property of o, and i=1,n} the property set of object o, and Γ={(α_i,β_i)|(α_i,β_i) is a qualitative criterion(QC) of property p_i (o)} the criteria set of properties o, p:X×Γ→P_o is called a qualitative mapping by the criterion for a quantity x of a(o), if for any x∈X, there exists a criterion of property p_i(o) ∈Po , (α_i,β_i)∈Γ, so :p(x,)=x⊥(αi_,β_i)=p_i(o)iffx∈(α_i,β_i) -┐(or 0)p_i(o)iffx(α_i,β_i)=μ_i(x)p_i(o)where, μ_i(x)=1iffx∈(α_i,β_i) -┐(or 0)iffx(α_i,β_i)is the true value of property p_i(o),⊥ is the convert operation from the quantitative value x to the property p_i(o).It is shown that there exists an Equivalence Relation in the definition of QM, (E-R(QM)): x∈(α_i,β_i)=N(ζ_i,δ_i)|x-ζ_i|≤δ_i|x-ζ_i|δ_i≤1,N(ζ_i,δ_i) is a topologic neighborhood about ζ_i of radius δ_i, so any Qualitative Functions(QF) satisfying the relation E-R(QM), such as η_i(x)=exp12(x-ζ_iδ_i)~2]etc., is a conversion degree function.An inverse conversion degree function based on fuzzy membership function is proposed, too.

关 键 词：定性映射 逆转化程度函数 定性函数 模糊隶属函数 转化程度函数 量-质转换 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]