Researches On Several Kinds Of Distance Between Interval-valued Fuzzy Sets

In this dissertation some researches on distancs of interval-valued fuzzy sets and metric space with respect to the distance are made. The main results as follow:(1) We give three kinds of distance of interval-valued fuzzy sets defined on real line R, denoted by d~*,d_p~* and d_∞~*, and study some properties, for example, homogeneity, translation invariant and so on. We investigate the completeness and separability of interval-valued fuzzy numbers metric spaces (IF~*(R),d~*), (IF~*(R),d_p~*) and (IF~*(R),d_∞~*). We show that the whole space (IF~*(R), d_∞~*) is complete metric space, and when K is a nonempty compact subset of R, the metric space (IF~*(K),d~*) and (IF~*(K),d_p~*) are complete. We discuss the relation between the convergence of sequence of interval-valued fuzzy numbers in the sence of the distance d~*, d_p~* and d_∞~*.(2) We generalize the concepts of two kinds of discrete distance of interval-valued fuzzy sets based on Hausdorff metric, and introduce a new distance of discrete interval-valued fuzzy sets based on Hausdorff metric and study some properties. We compare these three kinds of distance and give the max-min relation among them.