Type-2 Fuzzy Metric Spaces

Upasana Samanta ()
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Upasana Samanta: Department of Mathematics, BIT Mesra, Ranchi, PIN-835215, India

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 03, 917-933

Abstract: In this paper, an attempt is made to define a Type-2 fuzzy metric on a nonempty set X 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 cite10 and also by George and Veeramani cite6. 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.

Keywords: Fuzzy metric; type-2 fuzzy metric; fixed points; fuzzy numbers (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005724500480

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