Detailed explanation of Analytic Hierarchy Process

In the comprehensive evaluation, the comprehensive evaluation function is always related to a weight vector. Analytic Hierarchy Process (AHP) is an effective method for determining weights. This

In addition, in some practical problems, we need to sort several objects under the specific targets, and select the most outstanding objects from them.

An Effective Method for sorting objects.
The Analytical Hierarchy Process was proposed by T. L. saaty, a professor of operations research in the United States in 1970s. saaty believes that if a practical problem involves

To determine the proportion of each factor in the whole, when the exact basis is inadequate, it is only determined based on the experience of experts.

Disconnected. However, as long as n> 3, it is difficult for any expert to express a set of exact data. However, if two factors are selected from all factors

In comparison, experts in the industry generally can use "equally important", "slightly important", "obviously important", "very important", and "extremely important"

To explain the importance of one factor over the other in general. Saaty recommends that you use these qualitative languages

Quantize and introduce the function f (x, y) to indicate the importance scale of factor X ratio factor y for the population. If f (x, y)> 1, x is more important than Y. If F

(X, y) <1 indicates that Y is more important than X. if and only when f (x, y) = 1, X and Y are equally important, f (y, x) = 1/f (x, y ). About

The list method is recommended for F (x, y) and saaty. See table 3-1.
For a given actual problem, x = {x1, x2,... xn} is the set of all factors. Please ask the experts according to the meanings of the items listed in the table,

Compare all factors, fill in matrix A, and call a as the judgment matrix.

Let's take an example to illustrate how to set all the cause sets of an actual problem to X = {x1, x2 ,... x5}, and the experts assessed that X4 and X5 are equally important for the overall goal. X2 and X4 are both equally important and slightly important. X1 is more important than X4, x5 is more important than X3. X1 is more important than X3. X2 is more important than X4 and X5. X2 is more important than X3. The judgment matrix is as follows: