Does expert system use algorithms?
Expert systems are called "Experts" for a reason. They are cable of doing a particular job at up most perfection. Not 100% but 99%. Now I am no expert on these systems (pun intended) but as far as these two algorithms go my answer would be to try to boil down to the exact purpose of your system. These two algorithms do two different things. All in all what I am saying is to find an concrete job that your expert system will do. Using the Stable Marriage algorithm you will be ranking and connecting vertices with edges accordingly to their respective weights. As for the Maximum Matching algorithm you will be trying to find the lone vertices and edges. At this point according to your needs I would try to find something in between or edit the Stable Marriage algorithm to fits your needs.

Good luck! You have chosen to tackle a very strong problem ;)