A Fuzzy Model to Optimise the Football Rule Assuring Spectacle, Fair Play, Objectivity and Ethics

The history of football, as in most sports, has always been accompanied by controversy caused by refereeing decisions, based on a set of rules and their interpretation which, rightly or wrongly, has on countless occasions been decisive in the final results of matches in which justice was to be done. Our proposal will provide, in an eminently theoretical way, those modifications to the football regulations that try to maximise the objectives that this sport requires, according to the experts interviewed, such as, among others, spectacle, fair play, objectivity and ethics. Once all the proposals had been compiled from the experts interviewed, we asked them to assess the feasibility and coherence of each of the proposals using real or uncertain numbers. This information, duly aggregated by means of expertons, has allowed us to establish a ranking that determines those changes that are most recommendable at a general level. However, by means of the theory of forgotten effects, we will find to what degree each proposal directly and indirectly affects the objectives sought in football, so that we can really know which changes in the regulations would be a priority. Finally, and in order to avoid too drastic modifications in a short time, we have obtained by means of Pichat’s affinity algorithm those ‘packages’ of necessary changes that make sense to carry them out together, thus being able to implement the improvements to the refereeing regulations gradually and adaptively.