Entropy method of mathematical modeling - based model Topsis

Write the previous text : lazy Code is ready to participate in mathematical modeling, and is responsible for the programming part (matlab). Because time is limited, so the current personal opinion is programmed to learn (because it is white) based, supplemented by learning model (secondary here is to know how to use this model, it's how to write code). Of course, if you are interested in-depth study of the mathematical model, that is no problem. (Strongly agree)

Today is to introduce a number of indicators to determine the respective shares of the heavy weights of the method - Entropy Law.
Fuzzy Comprehensive analysis mentioned yesterday's index determined for each respective weights, here to write a detailed process with entropy weight method.
Before the blog has introduced a way to de-merits of distance method (Topsis model), entropy method is based on this model to extend.

Entropy Law ... the vernacular speaking, is to be evaluated according to a known value indicator to determine the weight of each index share of the weight. (Here we must note that you must have before they can use the numerical entropy method, if no values are not using this method)

Law of Entropy scenarios ... Simply put, that is, in the evaluation of objects, each object often have several indicators. That these indicators index weights which the largest share of the weight of it? (Of course, you can go to a fabricated their own, but this way seems a bit strong subjectivity.)
If you think you concoct just the right feeling a little inaccurate, it may wish to use patience to read here on Entropy Method.

Here it is to introduce, when several indicators to get the value of (a matrix), how to use MATLAB to determine its weight.

Fuzzy comprehensive evaluation of the data yesterday to take over. (If you do not know what this data means, please look at my previous blog "Mathematical modeling evaluation class model - Fuzzy Comprehensive Analysis")
data

① type judgment indicator

Before the merits of de-distance method (Topsis model) have speaking indicators are generally divided into very large, very small, middle and interval. That first step here is to determine the five indicators respectively, what type.
Obviously, the amount of mining, NPV is a very large one; investment in infrastructure, mining costs, the cost of instability is very small.

② The positive indicators of

Here there is a new word called forward of (in fact, I have written before in Topsis model years). Here again brief, it is forward of the very small, interval, intermediate, these indicators into very large.

The very small to very large conversion method is: max - x (intermediate and interval before the Topsis with a)

Here are three very small indicators (investment in infrastructure, mining costs, unstable expenses) converted at
the conversion results are as follows:
After the positive of the matrix

③ matrix of the normalized forward

This is the forward direction of the matrix (matlab represented):
After the positive of the matrix
normalized as follows: (z (ij) is the normalized matrix each element, x (ij) is a forward matrix of each element)
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matrix (normalized Z_ ) as follows:

Note: this normalized matrix obtained can not have a negative, i.e. the value must be greater than or equal to 0, if negative, need to be normalized in accordance with the following this method.

④ we are calculating the probability matrix P

Calculated as follows :( Z ~ (ij) is the front of Z (ij)) herein
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is calculated as follows:

⑤ calculate the entropy for each indicator

Calculated as follows:
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The results :( mylog custom function here, because matlab log (0) is negative infinity, is required here log (0) = 0)