Algebraic structures of interval-valued fuzzy (S, N) -implications

International Journal of Approximate Reasoning

Volumn 53, Issue 6, 2012, Pages 892-900

  Li, Dechao ^a,b   Li, Yongming ^b  

^a ZHEJIANG OCEAN UNIVERSITY   (China)

^b SHAANXI NORMAL UNIVERSITY   (China)

Author keywords

Fuzzy negation; Interval valued fuzzy implication; Laws of contraposition; S Implication; s Norm

Indexed keywords

FUZZY IMPLICATIONS; FUZZY NEGATION; LAWS OF CONTRAPOSITION; S-IMPLICATION; S-NORM;

ARTIFICIAL INTELLIGENCE;

SOFTWARE ENGINEERING;

EID: 84861797307     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2012.03.003     Document Type: Article

References (28)

1. M. Mas, M. Monserrat, and J. Torrens A survey on fuzzy implication functions IEEE Transactions on Fuzzy Systems 15 6 2007 1107 1121 (Pubitemid 350284156)
2. Sebastia Massanet, and Joan Torrens Intersection of Yager's implications with QL and D-implications International Journal of Approximate Reasoning 53 4 2012 467 479
3. M. Baczyński, and B. Jayaram Fuzzy implications, studies in fuzziness and soft computing vol. 231 2008 Berlin Heidelberg NY
4. M. Baczyński, and B. Jayaram (S,N)-and R-implications: A state of the art survey Fuzzy Sets and Systems 159 2008 1836 1859
5. H. Bustince, P. Burillo, and F. Soria Automorphisms, negations and implication operators Fuzzy Sets and Systems 134 2003 209 229
6. M. Baczyński, and B. Jayaram (U,N)-implications and their characterizations Fuzzy Sets and Systems 160 2009 2049 2062
7. M. Mas, M. Monserrat, and J. Torrens A characterization of (U,N),RU,QL and D-implications derived from uninorms satisfying the law of importation Fuzzy Sets and Systems 161 2010 1369 1387
8. I. Aguiló, J. Suñer, and J. Torrens A characterization of residual implications derived from left-continuous uninorms Information Sciences 180 2010 3992 4005
9. D.W. Pei, Formalization of implication based fuzzy reasoning method, International Journal of Approximate Reasoning, http://dx.doi.org/10.1016/j. ijar.2012.01.007.
10. Feng Qin, and Li Yang Distributive equations of implications based on nilpotent triangular norms International Journal of Approximate Reasoning 51 8 2010 984 992
11. L.A. Zadeh Quantitative fuzzy semantics Information Science 3 1971 159 176
12. J.M. Mendel, Fuzzy sets for words: a new beginning, in: IEEE International Conference on Fuzzy Systems, St. Louis, MO, 2003.
13. J.R. Castro, O. Castillo, and P. Melin A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks Information Sciences 179 13 2009 2175 2193
14. M.Y. Hsiao, T.S. Li, and J.-Z. Lee Design of interval type-2 fuzzy sliding-mode controller Information Sciences 178 6 2008 1696 1716
15. O. Linda, and M. Manic Interval type-2 fuzzy voter design for fault tolerant systems Information Sciences 181 14 2011 2933 2950
16. G.M. Mendez, and M.D.L.A. Hernandez Hybrid learning for interval type-2 fuzzy logic next term systems based on orthogonal least-squares and backpropagation method Information Sciences 179 13 2009 2146 2157
17. D.C. Li, Y.M. Li, and Y.J. Xie Interval-valued fuzzy inference Information Sciences 181 20 2011 4754 4764
18. C. Alcalde, A. Burusco, and R. Fuentes-Gonzalez A constructive method for the definition of interval-valued fuzzy implication operators Fuzzy Sets and Systems 153 2005 211 227 (Pubitemid 40644714)
19. C. Cornelis, G. Deschrijver, and E.E. Kerre Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application International Journal Approximate Reasoning 35 1 2004 55 95
20. C. Cornelis, G. Deschrijver, and E.E. Kerre Advances and challenges in interval-valued fuzzy logic Fuzzy Sets and Systems 157 2006 622 627 (Pubitemid 43189821)
21. 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
22. G. Deschrijver, C. Cornelis, and E.E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Transactions on Fuzzy Systems 12 1 2004 45 61
23. G.J. Klir, and B. Yuan Fuzzy sets and fuzzy logic, theory and applications 1995 Prentice-Hall PTR, NJ
24. 1)-conditional functions? Fuzzy Sets and Systems 134 2003 305 310
25. D. Dubois, and H. Prade Fuzzy sets in approximate reasoning. Part 1: inference with possibility distributions Fuzzy Sets and Systems 40 1991 143 202
26. R.E. Moore, R.B. Kearfott, and M.J. Cloud Introduction to interval analysis 2009 SIAM Philadelpha
27. E.E. Kerre Fuzzy sets and approximate reasoning 1999 Xi'an Jiaotong University Press Xi'an
28. B.M. Acióly, and B.C. Bedregal A quasi-metric topology compatible with inclusion-monotonicity property on interval space Reliable Computing 3 3 1997 305 313 (Pubitemid 127506435)