Migrativity of uninorms not internal on the boundary over continuous t-(co)norms

[1] E. A¸sıcı, On the migrativity property for uninorms and nullnorms, In: Medina, J., et al. Information Processing and
Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. Communications in Computer
and Information Science, 853, Springer, Cham, (2018), 319-328. https://doi.org/10.1007/978-3-319-91473-2_
28

[2] H. Bustince, J. Fernandez, R. Mesiar, J. Montero, R. Orduna, Overlap functions, Nonlinear Analysis, 72 (2010),
1488-1499. https://doi.org/10.1016/j.na.2009.08.033

[3] B. De Baets, Idempotent uninorms, European Journal of Operational Research, 118 (1999), 631-642. https://doi.
org/10.1016/S0377-2217(98)00325-7

[4] B. De Baets, J. Fodor, Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof,
Fuzzy Sets and Systems, 104 (1999), 133-136. https://doi.org/10.1016/S0165-0114(98)00265-6

[5] P. Dryga´s, Discussion of the structure of uninorms, Kybernetika, 41 (2005), 213-226.

[6] F. Durante, P. Sarkoci, A note on the convex combinations of triangular norms, Fuzzy Sets and Systems, 159
(2008), 77-80. https://doi.org/10.1016/j.fss.2007.07.005

[7] J. Fodor, B. De Baets, A single-point characterization of representable uninorms, Fuzzy Sets and Systems, 202
(2012), 89-99. https://doi.org/10.1016/j.fss.2011.12.001

[8] J. Fodor, I. J. Rudas, On continuous triangular norms that are migrative, Fuzzy Sets and Systems, 158 (2007),
1692-1697. https://doi.org/10.1016/j.fss.2007.02.020

[9] J. Fodor, I. J. Rudas, An extension of the migrative property for triangular norms, Fuzzy Sets and Systems, 168
(2011), 70-80. https://doi.org/10.1016/j.fss.2010.09.020

[10] J. Fodor, I. J. Rudas, Migrative t-norms with respect to continuous ordinal sums, Information Sciences, 181 (2011),
4860-4866. https://doi.org/10.1016/j.ins.2011.05.014

[11] J. Fodor, R. R. Yager, A. Rybalov, Structure of uninorms, International Journal of Uncertainty, Fuzziness and
Knowledge-Based Systems, 5 (1997), 411-427. https://doi.org/10.1142/S0218488597000312

[12] C. Y. Huang, F. Qin, Migrativity properties of uninorms over 2-uninorms, International Journal of Approximate
Reasoning, 139 (2021), 104-129. https://doi.org/10.1016/j.ijar.2021.09.008

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

[14] G. Li, H. W. Liu, On properties of uninorms locally internal on the boundary, Fuzzy Sets and Systems, 332 (2018),
116-128. https://doi.org/10.1016/j.fss.2017.07.014

[15] W. H. Li, F. Qin, New results on the migrativity properties for overlap (grouping) functions and uninorms, Iranian
Journal of Fuzzy Systems, 18 (2021), 111-128. https://doi.org/10.22111/IJFS.2021.6085

[16] W. H. Li, F. Qin, Migrativity equation for uninorms with continuous underlying operators, Fuzzy Sets and Systems,
414 (2021), 115-134. https://doi.org/10.1016/j.fss.2020.08.007

[17] W. H. Li, F. Qin, Y. Y. Zhao, A note on uninorms with continuous underlying operators, Fuzzy Sets and Systems,
386 (2020), 36-47. https://doi.org/10.1016/j.fss.2019.03.007

[18] X. F. Liang, W. Pedrycz, Logic-based fuzzy networks: A study in system modeling with triangular norms and
uninorms, Fuzzy Sets and Systems, 160 (2009), 3475-3502. https://doi.org/10.1016/j.fss.2009.04.014

[19] S. D. Liang, X. P. Wang, On the migrativity of 2-uninorms, Fuzzy Sets and Systems, 472 (2023), 108703. https:
//doi.org/10.1016/j.fss.2023.108703

[20] J. Mart´ın, G. Mayor, J. Torrens, On locally internal monotonic operations, Fuzzy Sets and Systems, 137 (2003),
27-42. https://doi.org/10.1016/S0165-0114(02)00430-X

[21] M. Mas, M. Monserrat, D. Ruiz, J. Torrens, An extension of the migrative property for uninorms, Information
Sciences, 246 (2013), 191-198. https://doi.org/10.1016/j.ins.2013.05.024

[22] M. Mas, M. Monserrat, D. Ruiz, J. Torrens, Migrative uninorms and nullnorms over t-norms and t-conorms, Fuzzy
Sets and Systems, 26 (2015), 20-32. https://doi.org/10.1016/j.fss.2014.05.012

[23] R. Mesiar, H. Bustince, J. Fernandez, On the α-migrativity of semicopulas, quasi-copulas, and copulas, Information
Sciences, 180 (2010), 1967-1976. https://doi.org/10.1016/j.ins.2010.01.024

[24] R. Mesiar, V. Nov´ak, Open problems from the 2nd international conference on fuzzy sets theory and its applications,
Fuzzy Sets and Systems, 81 (1996), 185-190. https://doi.org/10.1016/0165-0114(95)00209-X

[25] A. Mesiarov´a-Zem´ankov´a, Uninorms continuous on [0, e[2∪]e, 1]2, Information Sciences, 393 (2017), 130-143.
https://doi.org/10.1016/j.ins.2017.02.006

[26] A. Mesiarov´a-Zem´ankov´a, Characterization of uninorms with continuous underlying t-norm and t-conorm by means of the ordinal sum construction, International Journal of Approximate Reasoning, 83 (2017), 176-192. https:
//doi.org/10.1016/j.ijar.2017.01.007

[27] Y. Ouyang, J. X. Fang, G. L. Li, On the convex combination of TD and continuous triangular norms, Information
Sciences, 177 (2007), 2945-2953. https://doi.org/10.1016/j.ins.2007.01.023

[28] J. S. Qiao, B. Q. Hu, On the migrativity of uninorms and nullnorms over overlap and grouping functions, Fuzzy
Sets and Systems, 346 (2018), 1-54. https://doi.org/10.1016/j.fss.2017.11.012

[29] F. Qin, L. Fu, A characterization of uninorms not internal on the boundary, Fuzzy Sets and Systems, 469 (2023),
108641. https://doi.org/10.1016/j.fss.2023.108641

[30] F. Qin, D. Ruiz-Aguilera, On the α-Migrativity of idempotent uninorms, International Journal of Uncertainty,
Fuzziness and Knowledge-Based Systems, 23 (2015), 105-115. https://doi.org/10.1142/S0218488515500051

[31] B. Roy, Decision science or decision-aid science, European Journal of Operational Research, 66 (1993), 184-203.
https://doi.org/10.1016/0377-2217(93)90312-B

[32] D. Ruiz, J. Torrens, Distributivity and conditional distributivity of a uninorm and a continuous t-conorm, IEEE
Transactions on Fuzzy Systems, 14(2) (2006), 180-190. https://doi.org/10.1109/TFUZZ.2005.864087

[33] Y. Su, H. W. Liu, J. V. Riera, D. Ruiz, J. Torrens, The migrativity equation for uninorms revisited, Fuzzy Sets
and Systems, 323 (2017), 56-78. https://doi.org/10.1016/j.fss.2017.03.003

[34] Y. Su, W. W. Zong, H. W. Liu, A note on “An extension of the migrative property for uninorms”, Information
Sciences, 281 (2014), 334-337. https://doi.org/10.1016/j.ins.2014.05.038

[35] Y. Su, W. W. Zong, H. W. Liu, Migrativity property for uninorms, Fuzzy Sets and Systems, 287 (2016), 213-226.
https://doi.org/10.1016/j.fss.2015.05.018

[36] Y. Su, W. W. Zong, H. W. Liu, P. J. Xue, Migrativity property for uninorms and semi t-operators, Information
Sciences, 325 (2015), 455-465. https://doi.org/10.1016/j.ins.2015.07.030

[37] Y. Su, W. W. Zong, H. W. Liu, F. X. Zhang, On migrativity property for uninorms, Information Sciences, 300
(2015), 114-123. https://doi.org/10.1016/j.ins.2014.12.027

[38] F. Sun, X. B. Qu, A common characterization for migrative uni-nullnorms, Information Sciences, 546 (2021),
627-632. https://doi.org/10.1016/j.ins.2020.08.108

[39] F. Sun, X. B. Qu, L. Zhu, On the migrativity of uni-nullnorms, Journal of Intelligent and Fuzzy Systems, 37
(2019), 5269-5279. https://doi.org/10.3233/JIFS-190377

[40] Y. M. Wang, H. W. Liu, Migrativity equations and Mayor’s aggregation operators, Iranian Journal of Fuzzy Systems,
16 (2019), 41-53. https://doi.org/10.22111/IJFS.2019.4780

[41] L. M. Wu, Y. Ouyang, On the migrativity of triangular subnorms, Fuzzy Sets and Systems, 226 (2013), 89-98.
https://doi.org/10.1016/j.fss.2012.12.013

[42] A. F. Xie, Structure of uninorms not locally internal on the boundary, Fuzzy Sets and Systems, 433 (2022), 176-193.
https://doi.org/10.1016/j.fss.2021.08.004

[43] R. R. Yager, Uninorms in fuzzy systems modeling, Fuzzy Sets and Systems, 122 (2001), 167-175. https://doi.
org/10.1016/S0165-0114(00)00027-0

[44] R. R. Yager, Defending against strategic manipulation in uninorm-based multi-agent decision making, European
Journal of Operational Research, 141 (2002), 217-232. https://doi.org/10.1016/S0377-2217(01)00267-3

[45] R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120. https:
//doi.org/10.1016/0165-0114(95)00133-6

[46] H. J. Zhou, X. X. Yan, Migrativity properties of overlap functions over uninorms, Fuzzy Sets and Systems, 403
(2021), 10-37. https://doi.org/10.1016/j.fss.2019.11.011

[47] K. Y. Zhu, J. R. Wang, Y. W. Yang, Migrative uninorms and nullnorms over t-norms and t-conorms revisited,
Fuzzy Sets and Systems, 423 (2021), 74-88. https://doi.org/10.1016/j.fss.2020.10.009

[48] W. W. Zong, Y. Su, H. W. Liu, Migrative property for nullnorms, International Journal of Uncertainty, Fuzziness
and Knowledge-Based Systems, 22 (2014), 749-759. https://doi.org/10.1142/S021848851450038x