[1] M. Baczynski and B. Jayaram, Fuzzy Implications, Studies in Fuzziness and Soft Computing,
Springer, Berlin, 231 (2008).
[2] M. Baczynski and B. Jayaram, (S;N)- and R-implications: A state-of-the-art survey, Fuzzy
Sets Syst., 159 (2008), 1836{1859.
[3] M. Baczynski and B. Jayaram, On the characterization of (S;N)-implications, Fuzzy Sets
Syst., 158 (2007), 1713{1737.
[4] B. C. Bedregal, H. S. Santos and R. Callejas-Bedregal, T-norms on bounded lattices: t-norm
morphisms and operators, in: IEEE International Conference on Fuzzy Systems, (2006),
22{28.
[5] B. C. Bedregal, G. Beliakov, H. Bustince, J. Fernandez, A. Pradera and R. Reiser, Advances in
fuzzy implication functions, in: M. Baczynski, et al.(Eds.), (S;N)-Implications on Bounded
Lattices, Studies in Fuzziness and Soft Computing, Springer, Berlin, 300(3) (2013), 769{777.
[6] B. C. Bedregal and A. Takahashi, The best interval representations of t-norms and automor-
phisms, Fuzzy Sets Syst., 157 (2006), 3220{3230.
[7] G. Birkho , Lattice Theory, American Mathematical Society, Providence, RI, 1973.
[8] G. Chen and T. T. Pham, Fuzzy Sets, Fuzzy Logic and Fuzzy Control Systems, CRC Press,
Boca Raton, 2001.
[9] A. Cruz, B. Bedregal and R. Santiago, On the Boolean-like law I(x; I(y; x)) = 1, International
Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(2) (2014), 205{215.
[10] C. G. Da Costa, B. R. C. Bedregal and A. D. Doria Neto, Relating De Morgan triples with
Atanassov's intuitionistic De Morgan triples via automorphisms, Int. J. Approx. Reason.,
52(4) (2011), 473{487.
[11] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd ed., Cambridge
University Press, Cambridge, 2002.
[12] J. Fodor, On fuzzy implication operators, Fuzzy Sets Syst., 42 (1991), 293{300.
[13] Y. L. Han, Study on the extension method of fuzzy implications on generalized sublattices,
Journal of North China Institute of Science and Technology, 12(3) (2015), 111{115.
[14] A. K. Hans-Peter and L. B. Shapiro, On simultaneous extension of continuous partial func-
tions, Proc. Am. Math. Soc., 125(6) (1997), 1853{1859.
[15] K. Horiuchi and H. Murakami, Extension of the concept of mappings using fuzzy sets, Fuzzy
Sets Syst., 56 (1) (1993), 79{88.
[16] B. Jayaram, On the law of importation (x^y)!z(x!(y!z)) in fuzzy logic, IEEE Trans-
actions on Fuzzy Systems, 16(1) (2008), 130{144.
[17] S. Kasahara, A remark on the contraction principle, Proc. Jpn. Acad., 44(1) (1968), 1009{
1012.
[18] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers,
Dordrecht, 2000.
[19] H. W. Liu, Semi-uninorms and implications on a complete lattice, Fuzzy Sets Syst., 191
(2012), 72{82.
[20] S. Massanet and J. Torrens, The law of importation versus the exchange principle on fuzzy
implications, Fuzzy Sets Syst., 168 (2011), 47{69.
[21] E. S. Palmeira, B. C. Bedregal, R. Mesiar and J. Fernandez, A new way to extend t-norms,
t-conorms and negations, Fuzzy Sets Syst., 240 (2014), 1{21.
[22] E. S. Palmeira, B. C. Bedregal, J. Fernandez and A. Jurio, On the extension of lattice valued
implications via retractions, Fuzzy Sets Syst., 240 (2014), 66{85.
[23] E. S. Palmeira and B. C. Bedregal, Extension of fuzzy logic operators defi ned on bounded
lattices via retractions, Comput. Math. Appl., 63 (2012), 1026{1038.
[24] S. Saminger-Platz, E. P. Klement and R. Mesiar, On extension of triangular norms on
bounded lattices, Indag. Math., 19(1) (2008), 135{150.
[25] Y. Shi, D. Ruan and E. E. Kerre, On the characterizations of fuzzy implications satisfying
I(x; y) = I(x; I(x; y)), Information Sci., 177 (2007), 2954{2970.
[26] Y. Su and Z. Wang, Pseudo-uninorms and coimplications on a complete lattice, Fuzzy Sets
Syst., 224 (2013), 53{62.
[27] Z. D. Wang and Y. D. Yu, Pseudo t-norms and implication operators on a complete Brouw-
erian lattice, Fuzzy Sets Syst., 132 (2002), 113{124.
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