Kaleva, Osmo On the convergence of fuzzy sets. (English) Zbl 0584.54004 Fuzzy Sets Syst. 17, 53-65 (1985). 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 Cited in 2 ReviewsCited in 40 Documents MSC: 54A40 Fuzzy topology 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:convex fuzzy set; locally compact metric space; Hausdorff metric; \(\alpha \) -level sets; fixed point property PDF BibTeX XML Cite \textit{O. Kaleva}, Fuzzy Sets Syst. 17, 53--65 (1985; Zbl 0584.54004) Full Text: DOI References: [1] Castaing, C.; Valadier, M., (Convex Analysis and Measurable Multifunctions (1977), Springer: Springer Berlin) · Zbl 0346.46038 [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., (Set Theory (1957), Chelsea: Chelsea New York) · Zbl 0060.12401 [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., (Real Analysis (1968), Macmillan: Macmillan London) · Zbl 0197.03501 [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., (Introduction to Functional Analysis (1964), Wiley: Wiley New York) [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 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.