关键词: 三角模糊数, 三元联系数, 组合预测, 联系数投影, CNGIOWA算子

Abstract: In the prediction process, the combined prediction model constructed by assembling several prediction methods together can obtain more accurate prediction results, which has been widely used in various fields of real life. Since the prediction is also accompanied by many uncertain and fuzzy phenomena, the triangular fuzzy numbers can portray the uncertain information more accurately than the interval numbers, which in turn makes it necessary to carry out the research on the innovative methods of triangular fuzzy number combination prediction.
In order to study the problem of triangular fuzzy number combination prediction, this paper firstly introduces the concept of connection number in set-pair analysis, finds out the transformation relationship between triangular fuzzy number and ternary connection number, and uses the ternary connection number combination prediction to study the triangular fuzzy number combination prediction. It also defines the arithmetic rules of ternary connection number, and cleverly avoids the ambiguity and complexity in the arithmetic of triangular fuzzy number combination prediction. Secondly, the contact number projection is constructed as a new index, and the triangular fuzzy number combination prediction model is established by maximizing the contact number projection with fixed weight coefficients from the sequence of actual values of connection number and the sequence of predicted values of connection number combination. This model is a better triangular fuzzy number prediction model because it is easy to calculate and can improve the prediction accuracy. Then we construct the contact number generalized induced ordered weighted average (CNGIOWA) operator, and study the properties of homogeneity, idempotence and substitution invariance of this operator. Aiming at the insufficiency of fixed weight coefficients in fixed-weight coefficient triangular fuzzy number combination prediction, according to the basic principle that high-precision prediction methods in combination prediction should be given larger weight coefficients, and combining with the criterion of contact number projection maximization, a variable-weight coefficient triangular fuzzy number combination prediction model based on the contact number projection and the CNGIOWA operator is established. The model can significantly improve the prediction accuracy, so it is a superior triangular fuzzy number prediction model.
In the empirical analysis, the least squares fuzzy linear regression method, quadratic polynomial fuzzy time series method and fuzzy time series autoregression method are constructed for the actual value sequence of the triangular fuzzy number, and the steps of constructing the two types of triangular fuzzy number combination prediction models are used to carry out the error evaluation analysis, the superiority analysis and the sensitivity analysis in turn. The results all show that the two types of combined prediction models are superior to both single prediction methods and prediction methods in the existing literature, while the variable weight coefficient triangular fuzzy number combination prediction is more effective in improving the accuracy of prediction than the fixed weight coefficient triangular fuzzy number combination prediction.
In this paper, when discussing the variable weight coefficient triangular fuzzy number combination prediction model, only the parameter sensitivity analysis is made in the limited interval, and only the CNGIOWA operator is constructed. If the parameter takes other values and constructs other connection number information aggregation operators, what will be the impact on the variable weight coefficient triangular fuzzy number combination prediction model? These contents can be studied in depth in the future.

Key words: triangular fuzzy number, ternary connection number, combination forecast, contact number projection, CNGIOWA operator