Abstract. In this paper, a novel decision-making trial and evaluation laboratory (DEMATEL) theory with a shrinkage coefficient of indirect relation matrix is proposed, and a useful validity index, called Liu's validity index, is also proposed for evaluating the performance of any DEMATEL model. If the shrinkage coefficient of an indirect relation matrix is equal to 1, then this new theory is identical to the traditional theory; in other words, it is a generalization of the traditional theory. Furthermore, the indirect relation is always considerably greater than the direct one in traditional DEMATEL theory, which is unreasonable and unfair because it overemphasizes the influence of the indirect relation. We prove in this paper that if the shrinkage coefficient is equal to 0.5, then the indirect relation is less than its direct relation. Because the shrinkage coefficient belongs to [0.5, 1], according to Liu's validity index, we can find a more appropriate shrinkage coefficient to obtain a more efficient DEMATEL method. Some crucial properties of this new theory are discussed, and a simple example is provided to illustrate the advantages of the proposed theory.

Abstract. The most important issue in DEMATEL theory is how to obtain a reliable initial direct relation matrix with order n, the traditional theory obtains it by using the pair-wise comparison method, in which, each respondent must answer n(n-1) times pair-wise comparisons of all of the direct influences, if n is a large number, the work of pair-wise comparing is becoming hard, time-consuming, and unreliable. In this paper, for overcoming above drawbacks, we replace the pair-wise comparison method with Liu's ordering theory to find the initial direct relation matrix. This new method without pair-wise comparing can be used for any order n, a simple example was also provided in this paper to illustrate the advantages of the proposed theory.

In this paper, a novel fuzzy measure, high order lambda measure, was proposed, based on the Choquet integral with respect to this new measure, a novel composition forecasting model which composed the GM(1,1) forecasting model, the time series model and the exponential smoothing model was also proposed. For evaluating the efficiency of this improved composition forecasting model, an experiment with a real data by using the 5 fold cross validation mean square error was conducted. The performances of Choquet integral composition forecasting model with the P-measure, Lambda-measure, L-measure and high order lambda measure, respectively, a ridge regression composition forecasting model and a multiple linear regression composition forecasting model and the traditional linear weighted composition forecasting model were compared. The experimental results showed that the Choquet integral composition forecasting model with respect to the high order lambda measure has the best performance.

In this paper, based on L-measure and O-density, a novel composition forecasting model is proposed. For evaluating this new composition forecasting model, a real data experiment by using the sequential mean square error was conducted. Based on O-density, the performances of Choquet integral composition forecasting model with the L-measure, Lambda-measure and P-measure, respectively, a ridge regression composition forecasting model and a multiple linear regression composition forecasting model and the traditional linear weighted composition forecasting model were compared. Experimental results show that the Choquet integral composition forecasting model with respect to the L-measure outperforms other 5 composition forecasting models.