Some construction methods of interval-valued implications on bounded lattices

[1] I. Aguil´o, V. K. Gupta, B. Jayaram, S. Massanet, J. V. Riera, N. R. Vemuri, Generating methods of some classes
of fuzzy implications obtained by unary functions and algebraic structures, Fuzzy Sets and Systems, 484 (2024),
108948. https://doi.org/10.1016/j.fss.2024.108948

[2] C. Alcaldea, A. Buruscob, R. Fuentes-Gonz´alez, A constructive method for the definition of interval-valued fuzzy
implication operators, Fuzzy Sets and Systems, 153(2) (2005), 211-227. https://doi.org/10.1016/j.fss.2005.
01.006

[3] M. Baczy´nski, B. Jayaram, Fuzzy implications, Studies in Fuzziness and Soft Computing, Heidelberg: Springer,
Berlin, 231 (2008). https://doi.org/10.1007/978-3-540-69082-5

[4] B. C. Bedregal, G. P. Dimuro, R. H. N. Santiago, R. H. S. Reiser, On interval fuzzy S-implications, Information
Sciences, 180(8) (2010), 1373-1389. https://doi.org/10.1016/j.ins.2009.11.035

[5] G. Birkhoff, Lattice theory, American Mathematical Society Colloquium Publishers, Providence, RI, 1967.

[6] H. Bustince, Interval-valued fuzzy sets in soft computing, International Journal of Computational Intelligence Systems,
3(2) (2010), 215-222. https://doi.org/10.1080/18756891.2010.9727692

[7] G. Deschrijver, A representation of t-norms in interval-valued L-fuzzy set theory, Fuzzy Sets and Systems, 159(13)
(2008), 1597-1618. https://doi.org/10.1016/j.fss.2007.09.017

[8] G. Deschrijver, Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory, Information
Sciences, 244 (2013), 48-59. https://doi.org/10.1016/j.ins.2013.04.033

[9] G. Deschrijver, C. Cornelis, Representability in interval-valued fuzzy set theory, International Journal of Uncertainty,
Fuzziness and Knowledge-Based Systems, 15(3) (2007), 345-361. https://doi.org/10.1142/S0218488507004716

[10] P. Dryga´s, Some class of uninorms in interval valued fuzzy set theory in intelligent systems’2014, Springer International Publishing, Cham, 322 (2015), 33-43. https://doi.org/10.1007/978-3-319-11313-5_4

[11] M. B. Gorza lczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets
and Systems, 21(1) (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5

[12] F. M. He, B. W. Fang, Characterizations for the alpha-cross-migrativity of continuous t-conorms over generated
implications, Iranian Journal of Fuzzy Systems, 21(1) (2024), 65-82. https://doi.org/10.22111/ijfs.2023.
44829.7899

[13] F. Kara¸cal, K. Karacair, Some implication operators on bounded lattices, International Journal of General Systems,
53(7-8) (2024), 898-927. https://doi.org/10.1080/03081079.2024.2335907

[14] F. Kara¸cal, M. N. Kesicio˘glu, ¨U. Ertu˘grul, The implications obtained by two given implications on bounded lattices,
International Journal of General Systems, 50(3) (2021), 281-299. https://doi.org/10.1080/03081079.
2021.1908279

[15] M. N. Kesicio˘glu, Construction methods for implications on bounded lattices, Kybernetika, 55(4) (2019), 641-667.
https://doi.org/10.14736/kyb-2019-4-0641

[16] M. N. Kesicio˘glu, ¨U. Ertu˘grul, F. Kara¸cal, Generalized convex combination of implications on bounded lattices,
Iranian Journal of Fuzzy Systems, 17(6) (2020), 75-91. https://doi.org/10.22111/ijfs.2020.5602

[17] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000. https:
//doi.org/10.1007/978-94-015-9540-7

[18] M. Mas, M. Monserrat, J. Torrens, The law of importation for discrete implications, Information Sciences, 179(24)
(2009), 4208-4218. https://doi.org/10.1016/j.ins.2009.08.028

[19] M. Mas, M. Monserrat, J. Torrens, E. Trillas, A survey on fuzzy implication functions, IEEE Transactions on Fuzzy
Systems, 15(6) (2007), 1107-1121. https://doi.org/10.1109/TFUZZ.2007.896304

[20] D. Maximov, V. I. Goncharenko, Y. S. Legovich, Multi-valued neural networks I a multi-valued associative memory,
Neural Computing and Applications, 33(16) (2021), 10189-10198. https://doi.org/10.48550/arXiv.2302.11909

[21] Z. Peng, X. Zhang, Study of the generalized hypothetical syllogism for some well known families of fuzzy implications
with respect to strict t-norm, Iranian Journal of Fuzzy Systems, 21(2) (2024), 181-200. https://doi.org/10.22111/
ijfs.2024.46361.8164

[22] J. V. Riera, J. Torrens, Residual implications on the set of discrete fuzzy numbers, Information Sciences, 247
(2013), 131-143. https://doi.org/10.1016/j.ins.2013.06.008

[23] A. Starkey, H. Hagras, S. Shakya, G. Owusu, A multi-objective genetic type-2 fuzzy logic based system for mobile
field workforce area optimization, Information Sciences, 329 (2016), 390-411. https://doi.org/10.1016/j.ins.
2015.09.014

[24] C. Y. Wang, L. Wan, Type-2 fuzzy implications and fuzzy-valued approximation reasoning, International Journal
of Approximate Reasoning, 102 (2018), 108-122. https://doi.org/10.1016/j.ijar.2018.08.004

[25] M. Wang, X. Zhang, H. Bustince, J. Fernandez, Construction methods of fuzzy implications on bounded posets,
International Journal of Approximate Reasoning, 164 (2024), 109064. https://doi.org/10.1016/j.ijar.2023.
109064