| Abstract: | When interactions among attributes exist in multiple decision-making problems?
the performance of the traditional additive scale method is poor. For example , in a
project?if two people work alone, the 1/20?1/30th of the project can be completed by
them separately every day ?If they work together?the 1/20+1/30=1/12th of the
project can be completed by them or not, according to the cooperating situation of
them in every day?Non-additive fuzzy measures and fuzzy integral can be applied to
improve this situation. The?-measure (Sugeno, 1974) and P-measure (Zadeh, 1978)
are two well-known fuzzy measures. Hsiang-Chuan Liu(2006a,b) also proposed some
improved non-additive fuzzy measures based on P-measure, the two valued
m-measure and the polyvalent m-measure can be used, Specially the polyvalent
m-measure has infinitely many solutions may be chosen?Choquet integral and Sugeno
integral with this proposed generalized m-measure is applied to obtain the aggregation
score of the entrance examination of graduate school. When effective dependent
variable existence?Hsiang-Chuan Liu suggested to use the fuzzy integral regression
model based on the most suitable improved fuzzy measures by only theoretical
analyses, In order to lacking of the practical experimental study?in this research, not
only the main concept and development of the fuzzy measure, the fuzzy integral and
fuzzy integral regression mode are given?but also an educational data experiment is
conducted for comparing the performances of the different forecasting models.
A real data set with 485 samples from a junior high school in Taiwan including
the independent variables, examination scores of three courses, physics and chemistry,
biology, and geoscience, and the dependent variable, the score of the Basic
Competence Test of junior high school is applied to evaluate the performances of
Sugeno and Choquet integral regression models based on the polyvalent m-measure,
?-measure, P-measure, a ridge regression model, and a multiple linear regression
model by using 5-fold cross validation method to compute the mean square error
(MSE) and the rooted mean square error (RMSE) of the dependent variable,
Responding the ratio of the credit hour for three courses, all of the fuzzy
measures about the independent variables are assigned the same singleton measures as
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0.5:0.25:0.25?experimental result confirmation?Fuzzy integral regression model
based on polyvalent m-measure has the best performance?other four kind of patterns
are in turn? measure Choquet of based on the integral regression model?ridge
regression model?multiple linear regression model?and based on P measure Choquet
of integral regression model? |
