The Optimal Ordering And Its Algorithm Of Preference Relations

People always make the comparisons between strategies befor making decisions.,to establish the strategic relationship.Generally speaking,this relation is not necessarily totally ordered.There may have strategies which could hardly be compared,and situations like comparing cycle strategy.According to the obtained comparative information,the order of the expression is expressed by a function or a full order relation,which can cause errors.As the utility function,the minimum error function is used to guide people's decision making.In this paper,we construct a metric space which is based on the relationship of symmetry difference.There is a distance between each relationship and the totally order relation.All of the full order relations from this relation are called its totally order solutions.When the totally order of the solution is not unique,and then according to Shapley value profit value method to determine the final sort.Total order solutions are given for the partial order relationship,pre-order relation and general relations,and its algorithm.An example is given to illustrate its rationality.