基于离差最大化模型的模糊多属性决策投影法

针对属性权重完全未知且属性值为三角模糊数的模糊多属性决策问题,提出了一种基于线性规划和模糊向量投影的决策方法。该方法给出了三角模糊数距离、三角模糊数向量投影等概念,给出了两个属性值规范化公式。基于加权属性值离差最大化建立一个线性规划模型,通过求解此模型得到属性的权重,从而利用各方案的加权属性值在模糊正理想点上的投影对方案进行排序。该方法不仅避免了模糊数的比较,而且具有操作简便和易于计算的优点。最后,通过算例说明模型及方法的可行性和有效性。

Projection method of fuzzy multi-attribute decision-making based on the maximal deviation model

With regard to the fuzzy multi-attribute decision making(FMADM) problems,in which the information about attribute weights are unknown completely and the attribute values are in the form triangular fuzzy numbers,a method based on the linear programming model and projection of fuzzy numbers vectors is proposed.Some concepts such as the distance between two triangular fuzzy numbers,the projection of triangular fuzzy numbers vectors,etc,are given.Two normalized formula of attribute values are also presented.A linear programming model based on the maximal deviation of weighted attribute values is established,and then the attribute weights are obtained by solving the model.Furthermore,the alternatives are ranked by using the projection of the weighted attribute values of every alternative on the fuzzy positive ideal point of alternatives.The method not only avoids comparing for fuzzy numbers,but also has the advantages of simple operation and easy calculation.A numerical example is illustrated to show the feasibility and effectivity of the developed model and method.