Matching training with Neural Network I have a matching algorithm that is based on making an comparison score. This score is divided into parts.
Example:

5 - Points for attributes (lets say they have 3 common attributes, would the score be ((3/5)*5) = 3 Points

5 - Points for location

10 - Points for content

Theses points are just something i have set though guessing, and they work well. 
But to find what values would be best would i like to implement a kind of AI to test this, i have created 20+ test cases where i know what the correct matching is, so i though that i will be able to train my algorithm to have better values for the different value.
I am no expert in AI, i have only have one course about it, but would a neural network be able to help me here, or should i go with another AI?
I would suggest you use linear regression, or simply grid search (you can search over all possible number of points for each category, from 1..20; that's only $2^{13}$ possibilities, all of which can be easily tested one-by-one).

Make sure to use cross-validation: split the data set into training and test, and use the training data to derive the best parameters, then evaluate it on the test part.