Comparison of topological and uniform structures for fuzzy numbers and the fixed point problem |
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| Institution: | 1. Institute of Geosciences, Christian-Albrechts University, 24118 Kiel, Germany;2. Seminar of the Archaeology of Prehistory to the Early Middle Ages, Friedrich-Schiller University, 07743 Jena, Germany;3. Institute of Geography, Leipzig University, 04103 Leipzig, Germany;4. Leibniz Institute of Photonic Technology (Leibniz-IPHT), 07745 Jena, Germany |
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| Abstract: | The goal of this paper is to compare certain topological and uniform structures on sets of fuzzy numbers. Since fuzzy sets can be viewed as a kind of subsets they can be endowed with uniform structures in ways similar to those used for classic subsets. The Hausdorff construction is one such approach. The structures we study are the myope structure, the uniform convergence of the cuts in the sense of Hausdorff, and a structure induced by a metric defined by Goetschel and Voxman. We show how these structures are related to fixed point problems for some classes of fuzzy numbers. |
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