Distance of special multi-dimensional fuzzy number space and its application

In this paper, distances of the special multi-dimensional fuzzy ellipsoid number spaces are studied. The characteristic calculation formulas of distances for the special fuzzy ellipsoid number spaces are obtained. Formulas for Propositions 1 and 2 can be easily realized by computer program in applications and the completeness of the special fuzzy ellipsoid number spaces about the distance are proved. A practical example is given to demonstrate its application in pattern recognition problems.