Iterative ordering using fuzzy logic and application to ranking college football teams

Ranking of sports teams has been the interest of many people. Ranking of college sports teams (in the US) has its special challenge in that most teams do not play each other, and there is no lack of argument regarding how to compare two teams which have not played each other. We present here an algorithm that utilizes fuzzy sets to represent the teams\´ strengths, hence incorporating the uncertainty that is intrinsic in such a problem. The membership values of these fuzzy sets are adjusted iteratively according to the opponents and results of games played. After the process converges, we generate the final ranking using the centroids of these fuzzy sets. In addition, we present another set of fuzzy rules for predicting, with some degree of confidence, the winning/losing of games not included in the "training set," which consist of games used to generate the team strengths. We also discuss the selection of parameters for making the confidence of predictions mimic the actual percentage of correct predictions.