顺序量表、间隔量表和比率量表数学定义的改进

Mathematical definition improvement on prdinal scaling,interval scaling and ordio scaling

对顺序量表、间隔量表和比率量表的数学定义存在的某些不足加以改进。以上确界a、b、c∈X的存在导出以有界集构成的顺序量表的定义;通过关系式d=kσ的引入使定义可以表达k≠1的多间隔情况,当k=1时即为原量表的定义。间隔d通过设计j的指标集J获得,无需计算标准差σ但又包含着标准差σ的信息;比率量表的比率r,通过设计某一Aj值和令AJ=xn的条件,解方程组获得。给出3种量表的检验式Aj≠,当出现Aj=时需要重新设计。

Because of mathmatical definition of ordinal scaling,interval scaling and ordio scaling existed not enough,so in this paper the authors improve it.The improvement as follows：form the existence of supermum a、b、c∈X lead to definition of ordinal scaling of bounded set construction.Through lead relation formula d=kσ make the definition may expressed manifold intervlal of k≠1,then k=1 namely original definition.Interval d was got by design index set J of j,and doesn＇t need computed standard deviation σ but it includes the information of standard deviation σ.Ordio r of ordio scaling through design an Aj value and make AJ=xn as condition,after get r with model of solve system of equations.The authors have given a test formula Aj≠ of three scalings,then appear Aj= need design again.