Abstract: Experiments and theories were used to suggest that: (a) as the reliability of the degree functioned, the value of θsatisfied the relationship: 1/m≤θ≤1/m and changed conversely to the reliability(i,e, if the reliability of a is large, will be small; otherwise, if the reliability of a is small,θ will be large). Usually the value of θ is about half of the upper bound plus lower bound. (b) when the fuzzy statistic model or the probabilistic statistic model was applied to the multi-step rating scale method to deal with group data, the means of degree function were almost the same. Their correlation coefficient, was very conspicuous, reaching high to the value of 0.997. (c)when the probabilistic statistic model was applied to multi-step rating scale method to deal with group data, the standard deviation only reflected the difference among the degree function of the dependants, and showed no relationship to the reliability of degree function. (the correlation coefficient equalled 0.0024 and was not conspicuous). To the personal results, if the value of reliability θwas calculated by using the formula θ=1/m∑θj, following the calculation of the mean and standard variance, how the deviation of θ changed could also be obtained.

Key words: multi-step rating scale method, degree function, reliability, fuzzy statistic model and the probabilistic statistic model, correlation