Modeling Algorithms (11)--Analytic Hierarchy Process

(i) Basic principles and steps of analytic hierarchy process

1. Building a hierarchical sub-structure model

2. Construct all judgment matrices in each level

3. Level single sort and consistency check

4, the level of the total ranking and consistency test

Second, the establishment and characteristics of the Class 1, stratification:

(1) The highest level: there is only one element in this level, generally it is the predetermined goal and ideal result of analyzing the problem.

(2) Middle layer: This level contains the intermediate link in order to achieve the goal, mainly is some consideration indicators and some criteria.

(3) At the bottom: This level includes a variety of options for achieving the goals.

2. Note:

Generally do not 1 layer not more than 9 factors

3, a demo

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Second, construct the judgment matrix

You should set a weight because the weights in each of the criteria layers may be different.

1. The element meaning of the comparative discriminant matrix

In order to compare the influence of n factors on a factor z, the ratio of the influence of Xi and XJ to Z is AIJ by using 22 comparison to establish a comparative discriminant matrix. Then the ratio of the effect of XJ to Xi is Aji=1/aij.

2. Definition of comparative discriminant matrix

3. Determination of the elements of the comparative discriminant matrix

Use the number 1-9 and its inverse as the scale.

Three, the level of single sorting and consistency test 1, principle

The judgment matrix A corresponds to the maximum characteristic of the characteristic vector W, which is the sort weights of the corresponding elements of the same level relative importance to the previous level element. Called Hierarchical single sort

Therefore, we have adopted To test whether a is a consistent matrix, The more the greater the number of a than n, the greater the degree of non-uniformity of a, so we can test the consistency by this method.

2. Steps

(1) Calculate consistency index CI

(2) Query average random consistency indicator RI, corresponding to n=1 to 9,ri values respectively

This is a set of standard metrics generated by random methods.

(3) Calculate consistency ratio CR

When cr<0.1, it is accepted that the consistency of the matrix is acceptable.

Iv. level of total sequencing and consistency test

1. Description

(1) A is the previous level (High level) andB is the current level

(2) a1,a2,a3......am is the total sort weight of a level.

(3) B1J......BNJ is a single-rank weight for AJ on layer B.

(4) from the highest level to the bottom

The weight of each factor in the B layer is asked for the total goal, that is to ask for the level of the total rank of each factor in B layer b1,b2......bn. Just follow the method in the calculation.

2, then for the level of the total sorting also to be consistent check.

When cr<0.10, it is considered that the results of hierarchical total sorting have more satisfactory consistency and accept the results of the analysis.

(ii) Application of analytic hierarchy process

1. The ranking matrix of the criterion layer

2, the scheme layer of the sorting matrix

3. Level sort Total Result

So the most satisfying job is 1.

MATLAB solution

Modeling Algorithms (11)--Analytic Hierarchy Process