Measuring the difference between fuzzy numbers is often needed in many fuzzy optimizationproblems such as manufacturing system production line scheduling with uncertainty environments. In thispaper, based on the distance function of plane R2 and the level importance function, we establish theUID-metric and LPID-metric of measuring the difference between fuzzy numbers, and discuss the basicproperties of UID-metric and LPID-metric, and prove that fuzzy number spaces are metric spaces aboutUID-metric and LPID-metric if and only if the level importance function /(λ) ≠ 0 almost everywhere on [0,1]. Further, we discuss the convergence, separability and completeness of UID-metric and LPID-metricbased on the norms of plane R2. Finally, we analyze the characteristics of UID-metric and LPID-metric bysome application examples.
