Abstract
In this paper, an attempt is made to define a Type-2 fuzzy metric on a nonempty set [Formula: see text] by allowing it to take fuzzy numbers as values of distance of a pair of points under a membership grade which is also a fuzzy number. Its type-1 counterpart is a fuzzy metric mostly similar to those defined by Kramosil and Michalek[Formula: see text] and also by George and Veeramani.6 It is shown that the topology induced by this fuzzy metric is Hausdorff in nature. In this type of fuzzy metric space, Banach’s fixed point theorem and Edelstein’s fixed point theorems are extended. Finally decomposition theorems for this fuzzy metric are proved from which a justification of type-2 behavior of this fuzzy metric can also be interpreted.
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