Convergence of intuitionistic fuzzy sets

Abstract

We define pointwise convergence, uniform convergence, Γ-convergence and convergence in supremum metric for the intuitionistic fuzzy sets. The uniform convergence is in the topology induced by lower and upper pseudo metrics. The Γ-convergence is the Kuratowski–Painlevé convergence of the endographs of the intuitionistic fuzzy sets. The supremum metric is the supremum of Hausdroff distance among the ζ-cuts of the intuitionistic fuzzy sets. We discuss the mutual relationship of these convergences. Topological structures are also discussed in detail. Adequate number of examples are given to illustrate the relationship among these convergences.