To prepare for mathematical modeling contest, I learned several online modeling algorithm, of course, there are many learned from some of the blog God, together with some of my understanding ,, in this sincerely thank those large share of God .
A algorithm: AHP,
We must first clear AHP can solve those problems, by definition level here can be understood as different factors, factors such as the impact of food prices, factors affecting the mobile phone market. In the analysis of these factors is the result of the degree of influence by the results finally come to make decisions, it is to provide programs and measures algorithms. This is a personal analysis of the conclusions derived from mathematical modeling Outstanding Paper (own understanding of it).
First, the authority for this algorithm is defined:
AHP depending on the nature of the problem and the overall goal to be achieved, the problem is decomposed into component elements, and in accordance with the interrelated influence between the factors and the affiliation will be factors at different levels of aggregation combined to form a multi-level analysis of the structural model and ultimately make the problem boils down to the bottom (for decision-making programs, measures, etc.) with respect to the highest level (overall objective) of weight relative importance of the right to determine the order or the relative merits of schedule.
Where: the purpose of decision-making problems to be solved: the top
The bottom: alternatives when decisions
Middle layer: factors to consider, the decision-making criteria.
Before delving into the analytic hierarchy process, a preparatory work needs to be done to understand what is consistent matrix method.
Second, consistent matrix method
Popular speaking, if I can now choose to travel several places, namely Guilin, Zhangjiajie, Qingdao, Sanya, and I want to go is the primary and secondary: Sanya> Zhangjiajie> Guilin> Qingdao, how you this will into a mathematical model so that everyone receives it, or quantify the extent of your willingness to do? Is consistent matrix
The core idea is consistent matrix method has two:
- Do not put all the factors put them together, but each pairwise comparison
- Relative scale use, to reduce the different properties as compared with each other in various factors difficult to improve accuracy.
The core idea of this table and what does it mean, a good example is the tourism, set up:
| Guilin | Zhangjiajie | Qingdao | Sanya |
| A1 | A2 | A3 | A4 |
I need to create a 4X4jdm.com matrix has been based on the idea of a matrix
| A1 | A2 | A3 | A4 | |
| A1 | 1 | 3 | 5 | 7 |
| A2 | 1/3 | 1 | 3 | 5 |
| A3 | 1/5 | 1/3 | 1 | 3 |
| A4 | 1/7 | 1/5 | 1/3 | 1 |
After this matrix to fill out the appropriate coefficients according to our subjective consciousness, and then add the rest of the space according to the reciprocal rule. We will be able to complete this consistency matrix.
Perhaps you will say, that the subjective awareness is very important eh. Yes, yes, AHP is actually a more subjective approach. So, when you need to fill in marked degree, try to review some more literature, so the results will be more accurate.
AHP:
Question: [Select] how to choose to travel in accordance with factors scenery, fees, living conditions in the three destinations.
solution:
1. First of all, in this problem, we have to solve the problem is to choose tourism, may wish to Z, this is our most senior = Z;
2. Next, in the title, we have only three selectable tourism, are denoted B . 1 , B 2 , B . 3 . This is our lowest level;
3. Finally, is our middle layer, by definition, the middle layer is in respect of the scenery, the cost of living, food, travel these conditions were set to A 1 , A 2 , A 3 , A 4 , A 5 .
Then we started to build a hierarchical model of it. As shown below
At this time we should appreciate the AHP is what kind of a way to the bar. If you look back at this time do not understand the official definition.
Well, that is, by calculating the weights between the various layers of heavy, again according to the outcome of our rights. , Which we need to list the five 3X3de consistency matrix, calculate the maximum value, that is where we're going.
Drunk problem model, is the removal of a large V's, he speaks well, accompanied by his blog address: https://www.cnblogs.com/Qling/p/9289580.html , I hope to see .