Abstract: The prediction results are always real numbers or interval numbers in traditional combination forecasting methods. In fact, triangular fuzzy numbers can depict the characteristics of complicated things better under uncertain surroundings. Therefore, this paper proposes a new method in which the prediction information is expressed by triangular fuzzy numbers. The relative error between triangular fuzzy numbers is defined in this paper, and meanwhile, in order to embody the interactions of primitive forecasting data, the triangular fuzzy weighted power averaging(TFWPA)operator is introduced, and the fuzzy optimal combination forecasting model is developed based on TFWPA operator, triangular fuzzy weighted power geometric(TFWPG)operator and max-min criterion. The concepts of non-inferior combination forecasting and superior combination forecasting are presented, and it is proved that the proposed model is with non-inferior property. An example is also illustrated to show that the effectiveness of the proposed method is guaranteed, and sensitivity analysis is given to some parameters.

Key words: triangular fuzzy number, TFWPA operator, fuzzy optimal, combination forecasting

摘要： 传统的组合预测中,预测对象往往是实数或区间数,实际上,三角模糊数则更能刻画不确定环境下复杂事物的某些量的特征。因此,本文提出一种预测信息为三角模糊数的模糊优化组合预测新方法。定义了两个三角模糊数的相对误差,同时考虑到预测数据之间的交叉影响,基于三角模糊加权Power平均(TFWPA)算子、三角模糊加权Power几何(TFWPG)算子和max-min准则,分别构建模糊优化组合预测模型。提出非劣性和优性组合预测的概念,证明所提模糊组合预测模型具有非劣性质。最后通过实例分析说明了该模糊组合预测方法的有效性,并对参数做了灵敏度分析。

关键词: 三角模糊数, TFWPA算子, 模糊优化, 组合预测