On interval fuzzy negations

Fuzzy Sets and Systems

Volumn 161, Issue 17, 2010, Pages 2290-2313

  Bedregal, Benjamín Callejas ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

Author keywords

Automorphisms; Equilibrium point; Fuzzy negations; Interval representations

Indexed keywords

AUTOMORPHISMS; CLASSICAL LOGIC; EQUILIBRIUM POINT; FUZZY IMPLICATIONS; LOGICAL PROPERTIES; T - NORM; T-CONORMS;

MATHEMATICAL OPERATORS;

EID: 77955038905     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2010.04.018     Document Type: Article

References (43)

1. B.M. Acióly, and B.C. Bedregal A quasi-metric topology compatible with inclusion monotonicity on interval space Reliable Computing 3 3 1997 305 313
2. K.T. Atanassov Intuitionistic fuzzy sets Fuzzy Sets and Systems 20 1 1986 87 96
3. M. Baczynski, and B. Jayaram Fuzzy Implications 2008 Springer-Verlag Berlin, Heildelberg
4. I. Batyrshin, and W. Wagenknecht Contracting and expanding negations on [0,1] Journal of Fuzzy Mathematics 6 1998 133 140
5. B.C. Bedregal, G.P. Dimuro, R.H.N. Santiago, and R.H.S. Reiser On interval fuzzy S-implications Information Sciences 180 8 2010 1373 1389
6. B.C. Bedregal, and A. Takahashi The best interval representation of t-norms and automorphisms Fuzzy Sets and Systems 157 24 2006 3220 3230
7. B.C. Bedregal, A. Takahashi, Interval valued versions of t-conorms, fuzzy negations and fuzzy implications, in: Proc. of IEEE Internat. Conf. on Fuzzy Systems (Fuzz-IEEE), Vancouver, July 16-21, 2006, pp. 1981-1987.
8. H. Bustince, P. Burillo, and F. Soria Automorphism negations and implication operators Fuzzy Sets and Systems 134 2003 209 229
9. H. Bustince, J. Montero, M. Pagola, E. Berrenechea, and D. Gomez A survey of interval-valued fuzzy sets Handbook of Granular Computing 2008 John Wiley & Sons West Sussex 491 515 (Chapter 22)
10. R. Callejas-Bedregal, and B.C. Bedregal Intervals as a domain constructor TEMA - Tendências em Matemática Aplicada e Computacional 2 1 2001 43 52
11. S. Cubillo, C. Torres, and E. Castiñeira Self-contradiction and contradiction between two Atanassov's intuitionistic fuzzy sets International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16 3 2008 283 300
12. G. Deschrijver A representation of t-norms in interval-valued L-fuzzy set theory Fuzzy Sets and Systems 159 13 2008 1597 1618
13. G. Deschrijver, C. Cornelis, and E.E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Transaction on Fuzzy Systems 12 1 2004 45 61
14. F. Esteva, E. Trillas, X. Domingo, Weak and strong negation function for fuzzy set theory, in: Eleventh IEEE Internat. Symp. on Multi-Valued Logic, Norman, Oklahoma, 1981, pp. 23-27.
15. J.C. Fodor A new look at fuzzy connectives Fuzzy Sets and Systems 57 1993
16. M. Gehrke, C. Walker, and E. Walker Some comments on interval valued fuzzy sets International Journal of Intelligent Systems 11 1996 751 759
17. M.B. Gorzalczany A method of inference in approximate reasoning based on interval-valued fuzzy sets Fuzzy Sets and Systems 21 1987 1 17
18. I. Grattan-Guiness Fuzzy membership mapped onto interval and many-valued quantities Zeitschrift für Mathematische Logik und Grundladen der Mathematik 22 1975 149 160
19. T. Hickey, Q. Ju, and M. van Emdem Interval arithmetic: from principles to implementation Journal of the ACM 48 5 2001 1038 1068
20. M. Higashi, and G.J. Klir On measure of fuzziness and fuzzy complements International Journal of General Systems 8 3 1982 169 180
21. K. Jahn Intervall-wertige mengen Mathematische Nachrichten 68 1975 115 132
22. L. Jaulin, M. Kieffer, O. Didrit, and E. Walter Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotic 2001 Springer-Verlag London
23. R.B. Kearfott Rigorous Global Search: Continuous Problems 1996 Kluwer Dordrecht
24. E. Klement, and M. Navara A survey on different triangular norm-based fuzzy logics Fuzzy Sets and Systems 101 1999 241 251
25. G.J. Klir, and B. Yuan Fuzzy Sets and Fuzzy Logics: Theory and Applications 1995 Prentice-Halls PTR Upper Saddle River, NJ
26. W.A. Lodwick Preface Reliable Computing 10 4 2004 247 248
27. R. Lowen On fuzzy complements Information Sciences 14 2 1978 107 113
28. R.E. Moore, Methods and Applications of Interval Arithmetic, Studies in Applied Mathematics - SIAM, Philadelphia, 1979.
29. M. Navara, How prominent is the role of Frank t-norms? in: Proc. Congress IFSA 97, Prague, June 1997, pp. 291-296.
30. M. Navara Characterization of measures based on strict triangular norms Journal of Mathematical Analysis and Applications 236 2 1999 370 383
31. H.T. Nguyen, and E.A. Walker A First Course in Fuzzy Logic second ed. 2000 Chapman & Hall, CRC Boca Raton
32. S. Raychowdhury, and W. Pedrycz An alternative characterization of fuzzy complement functional Soft Computing 7 2003 563 565
33. R. Sambuc, Fonctions φ -floues. application l'aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, University of Marseille, Marseille, 1975.
34. R.H. Santiago, B.C. Bedregal, and B.M. Acióly Formal aspects of correctness and optimality in interval computations Formal Aspects of Computing 18 2 2006 231 243
35. D.S. Scott, Outline of a mathematical theory of computation, in: 4th Annu. Princeton Conf. on Information Sciences and Systems, 1970, pp. 169-176.
36. M.B. Smyth Topology Handbook of Logic in Computer Science vol. 1 1992 Clarendon Press Oxford 641 761
37. M. Sugeno Fuzzy measures and fuzzy integrals: a survey Fuzzy Automata and Decision Processes 1977 North-Holland Amsterdam 89 102
38. A. Takahashi, and B.C. Bedregal T-normas, t-conormas, complementos e implicaões intervalares TEMA - Tendências em Matemática Aplicada e Computacional 7 1 2006 139 148
39. E. Trillas Sobre funciones de negación en la teoria de conjuntos difusos Stochastica 3 1979 47 59
40. M. Wagenknecht, and I. Batyrshin Fixed point properties of fuzzy negations Journal of Fuzzy Mathematics 6 1998 975 981
41. M. Wagenknecht, and I. Batyrshin On negations generated by compensations Journal of Fuzzy Mathematics 6 1998 141 150
42. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning - I Information Sciences 8 3 1975 199 249
43. L.A. Zadeh Fuzzy sets Information and Control 8 1965 338 353