Evaluation - analytic hierarchy process

1、 effect

Analytic hierarchy process (AHP) is a decision analysis method combining qualitative and quantitative methods to solve multi-objective complex problems . This method combines quantitative analysis with qualitative analysis , Use the experience of the decision-maker to judge the relative importance of the standards for whether the objectives can be achieved , For example, by building evaluation indicators （ scenery 、 cost , live , diet 、 Journey ） For candidate tourist destinations （ guilin 、 huangshan , peitaiho ） Quantitative evaluation , Make a selection .

2、 Input / output description

Input ： Compare the indicators or schemes according to the prompts .
Output ： The quantitative score of each scheme or the index weight of the same level .

3、 Case example

Case study ： By constructing evaluation indicators （ scenery 、 cost , live , diet 、 Journey ） For candidate tourist destinations （ guilin 、 huangshan , peitaiho ） Quantitative evaluation , Make a selection .

4、 Modeling steps

1 Build a multi-level hierarchical structure model
The evaluation index system is established from top to bottom according to the dominant relationship ：
（1） At the top ： Also called the target layer or the target layer , It is the goal or result that the system wants to achieve , It is the primary criterion of system evaluation .
（2） Criterion layer ： It is the criterion set for the realization of the target layer , The number is m.
（3） At the bottom ： Also called scheme layer . It is a variety of schemes adopted to achieve the goal 、 Measures, etc , The number is n.

2 Construct pairwise comparison judgment matrix

Construct comparison matrix for criterion layer and scheme layer .
For elements of the same level , Each element of the above level is compared pair by pair for the comparison objective , Establish a judgment matrix .
Compare in pairs , use aij Representation element Bi And elements Bj To the goal A The ratio of the degree of influence ：

Symmetric matrix A=(aij) Is the element judgment matrix . Judgment matrix A Medium i Elements and j The ratio of relative importance of elements is aij Express , And has the following relationship ：

The greater the ratio , be i The more important it is .
In order to quantify judgment , according to 1-9 The scale determines the relative importance of each element .

 

3 Weight calculation
（1） Find the matrix A And its corresponding eigenvector .
（2） The weight can be obtained by normalizing the feature vector .

4 Consistency check
To ensure the correctness and rationality of the weight obtained , Consistency checks are also required , Consistency test is to judge whether the subjective logical weighting is beyond the reasonable range .
Calculate the consistency index C.I.

among ,

obviously ,n The bigger it is ,C.I. The greater the error . therefore , The random consistency ratio is introduced in the test C.R.

among R.I. Is a random consistency index , From the table below

When the random consistency ratio C.R.< 0.1 It is considered that the calculated hierarchical sorting weight is correct 、 reasonable , otherwise , The judgment matrix needs to be readjusted , Until the conformity inspection is passed .

5、 Calculate the scheme layer weight

The first i Scheme weights ： For the first time j The weight of the criteria , For the first time i The first scheme is in the j A score of three criteria , among

Finally, the schemes are sorted .