三角模糊数在多属性决策中的建模

Modeling of triangular fuzzy number in multi-attribute decision-making

为了获得三角模糊数的多属性决策数学模型,将语言变量和三角模糊数引入到多属性决策中,用语言变量或三角模糊数表示多属性决策中的属性值和各属性的权重,采用加权和法求得每个备选方案的三角模糊数最终评价值,并应用三角模糊数的减法运算定义任意两个三角模糊数的优越度,在方案两两对比求得优越度后建立方案的互补判断矩阵,采用最小平方法求得方案排序向量,根据排序向量元素的大小进行方案排序。

In order to obtain the mathematical model of Multi-Attribute Decision Making（MADM）under condition of group decision making, linguistic variable and triangular fuzzy number is introduced into MADM in this research. The entries in decision matrix and weights of all attributes are represented by triangular fuzzy number or linguistic variable. The final evaluation value of each alterative is achieved by means of Simple Additive Weighting method（SAW）. The degree of dominance between alternatives is defined by the way of difference of two triangular fuzzy numbers. The complementary judgment matrix is built up on degree of dominance between alternatives. The ordering vector of alternatives is figured out by using the least-square method. The order of alternatives is gained according to the value of element of the order vector.