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Measuring the difference between fuzzy numbers is often needed in many fuzzy optimization problems such as manufacturing system production line scheduling with uncertainty environments. In this paper, based on the distance function of plane R2 and the level importance function, we establish the UID-metric and LPID-metric of measuring the difference between fuzzy numbers, and discuss the basic properties of UID-metric and LPID-metric, and prove that fuzzy number spaces are metric spaces about UID-metric and LPID-metric if and only if the level importance function I(λ)≠0 almost everywhere on [0, 1]. Further, we discuss the convergence, separability and completeness of UID-metric and LPID-metric based on the norms of plane R2. Finally, we analyze the characteristics of UID-metric and LPID-metric by some application examples.
Measuring the difference between fuzzy numbers is often needed in many fuzzy optimization problems such as manufacturing system production line scheduling with uncertainty environments. In this paper, based on the distance function of plane R2 and the level importance function, we establish the UID-metric and LPID-metric of measuring the difference between fuzzy numbers, and discuss the basic properties of UID-metric and LPID-metric, and prove that fuzzy number spaces are metric spaces about UID-metric and LPID-metric if and only if the level importance function Further, we discuss the convergence, separability and completeness of UID-metric and LPID-metric based on the norms of plane R2. Finally, we analyze the characteristics of UID- metric and LPID-metric by some application examples.