Cluster points of sequences of fuzzy real numbers. (English) Zbl 1200.40002

Summary: Properties of cluster points of sequences of fuzzy real numbers are investigated. It is shown that some similar theorems like in the case of real sequences hold. On the other hand, some differences from the real case are discussed.


40A99 Convergence and divergence of infinite limiting processes
26E50 Fuzzy real analysis
Full Text: DOI


[1] Burgin M (2000) Theory of fuzzy limits. Fuzzy Sets Syst 115:433–443 · Zbl 0960.26009 · doi:10.1016/S0165-0114(98)00338-8
[2] Hutton B (1975) Normality in fuzzy topological spaces. J Math Anal Appl 50:74–79 · Zbl 0297.54003 · doi:10.1016/0022-247X(75)90039-6
[3] Kaleva O, Seikkala S (1984) On fuzzy metric spaces. Fuzzy Sets Syst 12:215 –229 · Zbl 0558.54003 · doi:10.1016/0165-0114(84)90069-1
[4] Klement EP, Mesiar R, Pap E (2000) Triangular norms. Trends in Logic–Studia Logica Library 8. Kluwer, Dordrecht
[5] Lowen R (1983) On (R(L), \(\boldsymbol{\oplus}\) ). Fuzzy Sets Syst 10:203–209 · Zbl 0527.54006 · doi:10.1016/S0165-0114(83)80115-8
[6] Lowen R (1984) Fuzzy integers, fuzzy rationals and other subspaces of the fuzzy real line. Fuzzy Sets Syst 14:231–236 · Zbl 0579.54006 · doi:10.1016/0165-0114(84)90083-6
[7] Rodabaugh SE (1982) Fuzzy addition in the L-fuzzy real line. Fuzzy Sets Syst 8:39–52 · Zbl 0508.54002 · doi:10.1016/0165-0114(82)90028-8
[8] Rodabaugh SE (1982) The L-fuzzy real line and its subspaces. In: Yager RR (ed) Recent development in fuzzy set and possibility theory. Pergamon Press, Oxford, pp 402–418
[9] Wang G (1988) Fuzzy addition in the Lowen fuzzy real line. Fuzzy Sets Syst 27:303–315 · Zbl 0656.54004 · doi:10.1016/0165-0114(88)90056-5
[10] Wang G, Xiaoyong X (2002) Convergence of sequences on the fuzzy real line. Fuzzy Sets Syst 127:323–331 · Zbl 1001.40001 · doi:10.1016/S0165-0114(01)00110-5
[11] Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[12] Zhang D (2001) A natural topology for fuzzy numbers. J Math Anal Appl 264:344–353 · Zbl 1020.54005 · doi:10.1006/jmaa.2001.7662
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