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On the convergence of fuzzy sets. (English) Zbl 0584.54004
Three kinds of convergences of fuzzy sets are defined by using the Hausdorff metric for supported endographs (Kloeden e.a.) ore by using the Hausdorff distances of the \(\alpha\)-level sets (Heilpern, the author e.a.). For fuzzy subsets of \(R^ n\) the author studies the relationships of this convergences and the fixed point property.
Reviewer: B.Behrens

54A40 Fuzzy topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text: DOI
[1] Castaing, C.; Valadier, M., ()
[2] Goetschel, R.; Voxman, W., A pseudometric for fuzzy sets and certain related results, J. math. anal. appl., 81, 507-523, (1981) · Zbl 0505.54008
[3] Goetschel, R.; Voxman, W., Topological properties of fuzzy numbers, Fuzzy sets and systems, 10, 87-99, (1983) · Zbl 0521.54001
[4] Hausdorff, F., ()
[5] Heilpern, S., Fuzzy mappings and fixed point theorem, J. math. anal. appl., 83, 566-569, (1981) · Zbl 0486.54006
[6] Kaleva, O.; Seikkala, S., On fuzzy metric spaces, Fuzzy sets and systems, 12, 215-229, (1984) · Zbl 0558.54003
[7] Kloeden, P.E., Compact supported endographs and fuzzy sets, Fuzzy sets and systems, 4, 193-201, (1980) · Zbl 0441.54008
[8] Nguyen, H.T., A note on the extension principle for fuzzy sets, J. math. anal. appl., 64, 369-380, (1978) · Zbl 0377.04004
[9] Puri, M.L.; Ralescu, D.A., Differentials of fuzzy functions, J. math. anal. appl., 91, 552-558, (1983) · Zbl 0528.54009
[10] Royden, H.L., ()
[11] Rådström, H., An embedding theorem for spaces of convex sets, Proc. amer. math. soc., 3, 165-169, (1952) · Zbl 0046.33304
[12] Taylor, A.E., ()
[13] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, I. inform. sci., 8, 199-249, (1975) · Zbl 0397.68071
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