D-Matrix: A Novel Ranking Procedure for Prioritizing Data Items

In this article, we propose a ranking method based on a matrix, called D-matrix, with the special identical diagonal values. This ranking system has five properties: (1) it can provide both biased and bias-free ranking, and except for that, the working matrix can be built in two ways: results merging and results separating for both biased and bias-free matrices. (2) it can perform the webpage ranking with a sparse matrix to generate ratings for pages instead of constructing complicated, irreducible, and stochastic matrices as the Google PageRank matrix does, thereby accelerating the computation speed. (3) this D-matrix has a solution no matter how much data is selected. If there are no comparisons among items, then all the items end up with the same equal ratings. (4) the ranking system has the least effects on data variation. If one item changes, only those connecting to it get different ratings, those without connection retain the same ratings. (5) this D-matrix has a $\ddot {R}$ support matrix with a delicate diagonal value which may or may not appear crucial. These five features are illustrated with five different and comprehensive examples. Besides that, a 2017 game of the National Football League data is tested where the D-matrix generates a reasonable result. Furthermore, we introduce a new approximate non-dominated sorting method based on D-matrix and thereby put forth a new algorithm for solving the multi-objective optimization problems. Experimental results indicate that our algorithm can maintain a better spread of solutions on many standard test functions.