Lipschitz functions and fuzzy number approximations

Fuzzy Sets and Systems

Volumn 200, Issue , 2012, Pages 116-135

  Coroianu, Lucian ^a,b  

^a UNIVERSITY OF ORADEA   (Romania)

^b BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Ambiguity; Approximation; Convexity; Fuzzy number; Lipschitz constant; Trapezoidal fuzzy number; Value

Indexed keywords

AMBIGUITY; APPROXIMATION; CONVEXITY; FUZZY NUMBERS; LIPSCHITZ CONSTANT; TRAPEZOIDAL FUZZY NUMBERS; VALUE;

VECTOR SPACES;

FUZZY RULES;

EID: 84861101237     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2012.01.001     Document Type: Article

References (38)

1. S. Abbasbandy, and M. Amirfakhrian The nearest trapezoidal form of a generalized left right fuzzy number Int. J. Approx. Reason. 43 2006 166 178 (Pubitemid 44345153)
2. S. Abbasbandy, and M. Amirfakhrian The nearest approximation of a fuzzy quantity in parametric form Appl. Math. Comput. (New York) 172 2006 624 632 (Pubitemid 43132866)
3. S. Abbasbandy, and B. Asady The nearest trapezoidal fuzzy number to a fuzzy quantity Appl. Math. Comput. (New York) 156 2004 381 386
4. S. Abbasbandy, and T. Hajjari Weighted trapezoidal approximation- preserving cores of a fuzzy number Comput. Math. Appl. 59 2010 3066 3077
5. T. Allahviranloo, and M. Adabitabar Firozja Note on "Trapezoidal approximation of fuzzy numbers" Fuzzy Sets Syst. 158 2007 755 756 (Pubitemid 46215754)
6. A.I. Ban, and S.G. Gal Defects of Properties in Mathematics. Quantitative Characterizations 2002 World Scientific New Jersey
7. A.I. Ban Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval Fuzzy Sets Syst. 159 2008 1327 1344
8. A.I. Ban On the nearest parametric approximation of a fuzzy number-Revisited Fuzzy Sets Syst. 160 2009 3027 3047
9. A.I. Ban Trapezoidal and triangular approximations of fuzzy numbers - inadvertences and corrections Fuzzy Sets Syst. 160 2009 3048 3058
10. A.I. Ban, A. Brândaş, L. Coroianu, C. Negruţiu, and O. Nica Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the value and ambiguity Comput. Math. Appl. 61 2011 1379 1401
11. A.I. Ban, L. Coroianu, Continuity and linearity of the trapezoidal approximation preserving the expected interval operator, in: IFSA-EUSFLAT World Congress, 20-24 July 2009, pp. 798-802.
12. A.I. Ban, and L. Coroianu Discontinuity of the trapezoidal fuzzy number-valued operators preserving core Comput. Math. Appl. 62 2011 3103 3110
13. A.I. Ban, and L. Coroianu Metric properties of the nearest extended parametric fuzzy number and applications Int. J. Approx. Reason. 52 2011 488 500
14. C. Bertoluzza, N. Corall, and A. Salas On a new class of distances between fuzzy numbers Mathware Soft Comput. 2 1995 71 84
15. S. Chanas On the interval approximation of a fuzzy number Fuzzy Sets Syst. 122 2001 353 356 (Pubitemid 32590560)
16. L. Coroianu Best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval Fuzzy Sets Syst. 165 2011 81 97
17. P. Diamond, and P. Kloeden Metric Spaces of Fuzzy Sets. Theory and Applications 1994 World Scientific Singapore
18. M. Delgado, M.A. Vila, and W. Voxman On a canonical representation of a fuzzy number Fuzzy Sets Syst. 93 1998 125 135
19. R. Goetschel Jr., and W. Voxman Topological properties of fuzzy numbers Fuzzy Sets Syst. 10 1983 87 99
20. P. Grzegorzewski Metrics and orders in space of fuzzy numbers Fuzzy Sets Syst. 97 1998 83 94 (Pubitemid 128654881)
21. P. Grzegorzewski Nearest interval approximation of a fuzzy number Fuzzy Sets Syst. 130 2002 321 330 (Pubitemid 34862876)
22. P. Grzegorzewski, and E. Mrówka Trapezoidal approximations of fuzzy numbers Fuzzy Sets Syst. 153 2005 115 135 (Pubitemid 40612574)
23. P. Grzegorzewski, and E. Mrówka Trapezoidal approximations of fuzzy numbers-revisited Fuzzy Sets Syst. 158 2007 757 768 (Pubitemid 46215760)
24. P. Grzegorzewski, New algorithms for trapezoidal approximations of fuzzy numbers preserving the expected interval, in: L. Magdalena, M. Ojeda, J. L. Verdegay (Eds.), Proceedings of IPMU'08, pp. 117-123.
25. P. Grzegorzewski Trapezoidal approximations of fuzzy numbers preserving the expected interval - Algorithms and properties Fuzzy Sets Syst. 47 2008 1354 1364
26. P. Grzegorzewski, L. Stefanini, Non-linear shaped approximation of fuzzy numbers, in: IFSA-EUSFLAT World Congress, 20-24 July 2009, pp. 1535-1540.
27. S. Heilpern Representation and application of fuzzy numbers Fuzzy Sets Syst. 91 1997 259 268 (Pubitemid 127683719)
28. E.N. Nasibov, and S. Peker On the nearest parametric approximation of a fuzzy number Fuzzy Sets Syst. 159 2008 1365 1375 (Pubitemid 351466979)
29. P. Prakash, and M.R. Sertel Topological semivector spaces. Convexity and fixed point theory Semigroup Forum 9 1974 117 138
30. H. Rådström An embedding theorem for spaces of convex sets Proc. Am. Math. Soc. 3 1952 165 169
31. W. Trutschnig, G. González-Rodríguez, A. Colubi, and M.A. Gil A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread Inf. Sci. 179 2009 3964 3972
32. C.-T. Yeh A note on trapezoidal approximations of fuzzy numbers Fuzzy Sets Syst. 158 2007 747 754 (Pubitemid 46223512)
33. C.-T. Yeh, Approximation by interval, triangular and trapezoidal fuzzy numbers, in: IFSA-EUSFLAT World Congress, 20-24 July 2009, pp. 143-148.
34. C.-T. Yeh On improving trapezoidal and triangular approximations of fuzzy numbers Int. J. Approx. Reason. 48 2008 297 313 (Pubitemid 351324072)
35. C.-T. Yeh Trapezoidal and triangular approximations preserving the expected interval Fuzzy Sets Syst. 159 2008 1345 1353 (Pubitemid 351466982)
36. C.-T. Yeh Weighted semi-trapezoidal approximations of fuzzy numbers Fuzzy Sets Syst. 165 2011 61 80
37. C.-T. Yeh Weighted trapezoidal and triangular approximations of fuzzy numbers Fuzzy Sets Syst. 160 2009 3059 3079
38. W. Zeng, and H. Li Weighted triangular approximation of fuzzy numbers Int. J. Approx. Reason. 46 2007 137 150 (Pubitemid 47285667)