[Evaluation model] Topsis method (pros and cons distance method)

【Evaluate class models】Topsis法（优劣解距离法）

学习前言

TopsisThree-step approach to problem solving：

       第一步：将原始矩阵正向化

              最常见的四种指标：

              Very small indicators are converted to very large indicators：

              Intermediate indicators are converted to very large indicators：

              The range indicator is converted to a very large indicator： 

        第二步：Matrix normalization after forwarding

        第三步：计算得分并归一化

             核心公式：

             公式解释：

             总结：

牛刀小试：

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学习前言

        Topsisis a very interesting evaluation class model,This model is far superior to AHP,It is highly recommended to eat.抱着“若无必要,Do not add new knowledge”的想法,In the process of solving the problem below, bloggers try not to introduce unnecessary knowledge points,But it will be added at the end！

TopsisThree-step approach to problem solving：

        第一步：将原始矩阵正向化

               最常见的四种指标：

                This step is used to unify the indicator types,将所有的指标Converted to very large indicatorsIt is called index forwarding.

                Very small indicators are converted to very large indicators：

                The formula for converting a very small indicator to a very large one is simple,即：max -  x,如果所有元素均为正数,那么也可以用 1 / x .  

               Intermediate indicators are converted to very large indicators：

                The formula for converting an intermediate indicator to a very large indicator is a little more complicated：

The range indicator is converted to a very large indicator： 

        第二步：Matrix normalization after forwarding

                The purpose of standardization is to eliminate the influence of different index dimensions.

                假设有n个要评价的对象,m个评价指标（已经正向化了）构成的正向化矩阵如下：

                        那么,The matrices on which it is normalized are marked as Z,Z中的每一个元素：

        第三步：计算得分并归一化

             核心公式：

 

                   即：

            当看到这里,Presumably everyone has understood the origin of the term superior and inferior solution distance method,What is an optimal solution？就是x与最大值的距离,Bad solution is the opposite.

              公式解释：

            假设有n个要评价的对象,m个评价指标的标准化矩阵：

        总结：

牛刀小试：

        题目： Please rate four students.

        小case：在上述问题中, 对于成绩This indicator is naturally the bigger the better,We call such an indicator极大型指标.另外的,与他人争吵的次数This indicator is called 极小型指标.

        1、Convert the very small index to the very large index to get the positive matrix;

        2、将正向化矩阵标准化;

        3、The score is calculated by the formula.