Completeness and compactness in type-2 fuzzy metric spaces

Abstract

In this paper completeness and compactness in type-2 fuzzy metric spaces are studied. Cantor’s intersection theorem characterizing the completeness of a type-2 fuzzy metric space is proved. Baire’s category theorem is also extended in this space. Notions of compactness, sequential compactness, total boundedness and Lebesgue number have been introduced. It is shown that a type-2 fuzzy metric space is compact if and only if it is totally bounded and complete. It is shown that in this space sequential compactness and compactness are equivalent to each other.