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集值统计是模糊数学方法的应用,信号检测论之评价法与有无法实验满足集值统计条件,可用集值统计的程度函数表示辨别力或感受性的大小。本文提出两种计算程度函数的数学模型:(1)a=1/K[∑a_(k1·CP_(k1)(Y/SN)+∑a_(k2)·CP_(k2)(Y/N)],(2)f(u)=1/2[∑a_(k1)·P_(k1)(Y/SN)+∑a_(k2)·P_(k2)(Y/N)]。试验结果证实两种模型所计算的程度函数与信号检测论方法所计算的辨别力指数d’有高相关(r_(ad’)=0.842,r_f(u)d’=0.953、n=67),程度函数与d’一样,不仅可以作为辨别力的指标,而且可将判断标准与辨别力分开,不同的是程度函数用β=a_N/a_(SN)或β=f_N(u)/f_(SN)(U)计算的判断标准是一次性综合判断。此点不同于信号检测论可对每一个类别反应的判断标准进行计算。程度函数与d’的计算都利用了对信号与噪音的反应信息。除上述二者的共同之处外,程度函数比d’还具有以下一些优越性:(1)程度函数应用集值统计,无须信号检测论要求对信号与噪音的感觉分布为正态的基本假设,可认为是非参数的方法;(2)可克服信号检测论方法不同判断标准下d’不稳定又难以解释的困难;(3)可适当地减少试验次数;(4)程度函数取值在0-1之间,易于形成量表值方便比较,意义清晰、明确;(5)更符合心理判断的实际状态。
Set-valued statistics is the application of fuzzy mathematics method. The evaluation method of signal detection theory and the existence of experiment can satisfy the condition of set-valued statistics. The degree function of set-valued statistics can be used to express the size of discrimination or sensibility. In this paper, we propose two mathematic models for calculating the degree of function: (1) a = 1 / K [Σa_ (k1 · CP_ (k1) (Y / SN) + Σa_ (k2) · CP_ (k2) ], (2) f (u) = 1/2 [Σa_ (k1) · P_ (k1) (Y / SN) + Σa_ (k2) · P_ (k2) (Y / N)]. The degree functions calculated by the two models are highly correlated with the discriminant index d ’calculated by the signal detection method (r_ (ad’) = 0.842, r_f (u) d ’= 0.953, n = 67) d ’can be used not only as an index of discrimination but also as a criterion to distinguish it from discrimination, except that the degree function is defined by β = a_N / a_ (SN) or β = f_N (u) / f_ (SN) ) The calculated criterion is a one-time synthesis judgment, which differs from the signal detection theory in that it can calculate the criterion for each class reaction, and the degree function and d ’are both based on the signal and noise response information, Degree of function than d ’also has the following advantages: (1) The degree function of set-valued statistics, without the need for signal detection on the signal and noise perception of the distribution of the basic assumption is normal, Considered as a non-parametric method; (2) can overcome the different criteria of signal detection method d) instability and difficult to explain the difficulty; (3) can reduce the number of trials; (4) the degree of function values ?? between 0-1, easy to form a scale value for easy comparison, meaning clear and clear; (5) More in line with the actual state of mental judgments.