Some remarks on distances between fuzzy numbers. (English) Zbl 0938.03088
Summary: We consider different approaches to assigning distances between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers arising from the idea of the value of a fuzzy number is described, and some of its topological properties are noted. Reducing functions are used to define a family of metrics on the space of fuzzy numbers; some convergent properties for these metrics are illustrated. Finally, a fuzzy distance between fuzzy numbers is introduced and its basic properties are studied.
References:
| [1] | Christenson, C.; Voxman, W., Aspects of Topology (1977), Dekker: Dekker New York · Zbl 0347.54001 |
| [2] | M. Delgado, A. Vila, W. Voxman, Canonical representations of fuzzy numbers, Fuzzy Sets and Systems, to appear.; M. Delgado, A. Vila, W. Voxman, Canonical representations of fuzzy numbers, Fuzzy Sets and Systems, to appear. · Zbl 0916.04004 |
| [3] | M. Delgdo, A. Vila, W. Voxman, A three parameter canonical representation of fuzzy numbers, Fuzzy Sets and Systems, to appear.; M. Delgdo, A. Vila, W. Voxman, A three parameter canonical representation of fuzzy numbers, Fuzzy Sets and Systems, to appear. |
| [4] | Goetschel, R.; Voxman, W., Topological properties of fuzzy numbers, Fuzzy Sets and Systems, 10, 87-99 (1983) · Zbl 0521.54001 |
| [5] | Kaleva, O., On the convergence of fuzzy sets, Fuzzy Sets and Systems, 17, 53-65 (1995) · Zbl 0584.54004 |
| [6] | Klir, G.; Floger, T., Fuzzy Sets, Uncertainty, and Information (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ |
| [7] | Kloeden, P., Compact supported endographs and fuzzy sets, Fuzzy Sets and Systems, 4, 193-201 (1980) · Zbl 0441.54008 |
| [8] | Lee, E. S.; Li, R. L., Comparison of fuzzy numbers based on the probability measure of fuzzy events, Comput. Math. Appl., 15, 887-896 (1988) · Zbl 0654.60008 |
| [9] | Nadler, S., Hyperspaces of Sets (1978), Dekker: Dekker New York · Zbl 0432.54007 |
| [10] | Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), North-Holland: North-Holland Amsterdam · Zbl 0546.60010 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
