Some notes on Zadeh's extensions

Information Sciences

Volumn 180, Issue 19, 2010, Pages 3806-3813

  Huang, Huan ^a  

^a JIMEI UNIVERSITY   (China)

Author keywords

Continuity; Fuzzy functions; Fuzzy numbers; Sendograph metric; Zadeh's extensions

Indexed keywords

FUZZY SETS;

CONTINUITY; FUZZY FUNCTION; FUZZY NUMBERS; SENDOGRAPH METRIC; ZADEH'S EXTENSIONS;

FUZZY SET THEORY;

EID: 77958494105     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.05.023     Document Type: Article

References (19)

1. L.C. Barros, R.C. Bassanezi, P.A. Tonelli, On the continuity of the Zadeh's extension, in: Proc. IFSA'97 Congress, Prague, 1997.
2. P. Diamond, P. Kloeden, Metric Space of Fuzzy Sets - Theory and Application, World Scientific, Singapore, 1994.
3. D. Dubois, E. Kerre, R. Mesiar, H. Prade, Fuzzy interval analysis, in: D. Dubois, H. Prade (Eds.), Fundamentals of fuzzy sets, The Handbooks of Fuzzy Sets Series, Kluwer, Boston, Mass, 2000, pp. 483-581.
4. J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951) 353-367.
5. T. Fan, On the compactness of fuzzy numbers with sendograph metric, Fuzzy Sets Systems 143 (2004) 471-477.
6. G.H. Greco, M.P. Moschen, E. Quelho Frota Rezende, On the variational convergence of fuzzy sets in metric spaces, Annali dell'Universita di Ferrara 44 (1) (1998) 27-39.
7. G.H. Greco, Sendograph metric and relatively compact sets of fuzzy sets, Fuzzy Sets Systems 157 (2006) 286-291.
8. F. Hausdorff, Set Theory, Chelsea Press, New York, 1957.
9. H. Huang, J. Fang, A note on the relation between A[a,b] and B[a, b], Fuzzy Sets Systems 131 (2002) 415-416.
10. H. Huang, C. Wu, Characterizations of Γ-convergence on fuzzy number space, in: Proc. IFSA'05 Congress, Beijing, 2005, pp. 66-70.
11. Q. Mao, H. Huang, The relationships between some convergences on fuzzy number space (in Chinese), J. Fuzhou Univer. (Nat. Sci.) 32 (6) (2004) 669-672.
12. C. Negoita, D. Ralescu, Application of Fuzzy Sets to System Analysis, Wiley, New York, 1975.
13. H.T. Nguyen, A note on the extension principle for fuzzy sets, J. Math. Anal. Appl. 64 (1978) 369-380.
14. H. Román-Flores, L.C. Barros, R.C. Bassanezi, A note on Zadeh's extensions, Fuzzy Sets Systems 117 (2001) 327-331.
15. C. Wu, H. Li, X. Ren, A note on the sendograph metric of fuzzy numbers, Information Sciences 179 (2009) 3410-3417.
16. C. Wu, M. Ma, The Basic of Fuzzy Analysis (in Chinese), National Defence Industry press, Beijing, 1991.
17. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975) 199-249.
18. L. Zadeh, Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences 172 (1-2) (2005) 1-40.
19. L. Zadeh, Is there a need for fuzzy logic?, Information Sciences 178 (13) (2008) 2751-2779