Title:
|
Construction methods for uni-nullnorms and null-uninorms on bounded lattice (English) |
Author:
|
Ertuğrul, Ümit |
Author:
|
Kesicioğlu, M. Nesibe |
Author:
|
Karaçal, Funda |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
55 |
Issue:
|
6 |
Year:
|
2019 |
Pages:
|
994-1015 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice $L$ are given and a contruction method is presented. (English) |
Keyword:
|
uni-nullnorm |
Keyword:
|
bounded lattices |
Keyword:
|
uni-nullnorms |
Keyword:
|
null-norms |
Keyword:
|
uninorms |
Keyword:
|
nullnorms |
Keyword:
|
t-norms |
MSC:
|
03B52 |
MSC:
|
03E72 |
MSC:
|
03G10 |
idZBL:
|
Zbl 07217223 |
idMR:
|
MR4077141 |
DOI:
|
10.14736/kyb-2019-6-0994 |
. |
Date available:
|
2020-05-20T15:15:39Z |
Last updated:
|
2020-08-26 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148088 |
. |
Reference:
|
[1] P., Akella,: Structure of n-uninorms..Fuzzy Sets Systems 158 (2007), 1631-1651. MR 2341328, 10.1016/j.fss.2007.02.015 |
Reference:
|
[2] G., Birkhoff,: Lattice Theory. Third edition..Providence, 1967. MR 0227053, 10.1090/coll/025 |
Reference:
|
[3] S., Bodjanova,, M., Kalina,: Construction of uninorms on bounded lattices..IEEE 12th International Symposium on Intelligent Systems and Informatics (SISY) Book Series: International Symposium on Intelligent Systems and Informatics, 2014, pp. 61-66. 10.1109/sisy.2014.6923558 |
Reference:
|
[4] T., Calvo,, De, Baets, B., J., Fodor,: The functional equations of Frank and Alsina for uninorms and nullnorms..Fuzzy Sets Systems 120 (2001), 385-394. MR 1829256, 10.1016/s0165-0114(99)00125-6 |
Reference:
|
[5] D., Çaylı, G., Ü., Ertuğrul,, T., Köroğlu,, F., Karaçal,: Notes on locally internal uninorm on bounded lattice..Kybernetika 53 (2017), 5, 911-921. MR 3750111, 10.14736/kyb-2017-5-0911 |
Reference:
|
[6] D., Çaylı, G., F., Karaçal,: Construction of uninorms on bounded lattices..Kybernetika 53 (2017), 3, 394-417. MR 3684677, 10.14736/kyb-2017-3-0394 |
Reference:
|
[7] Ü., Ertuğrul,: Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms..Fuzzy Sets Systems 334 (2018), 94-109. MR 3742235, 10.1016/j.fss.2017.07.020 |
Reference:
|
[8] Ü., Ertuğrul,, N., Kesicioğlu, M., F., Karaçal,: Ordering based on uninorms..Inform. Sci. 330 (2016), 315-327. 10.1016/j.ins.2015.10.019 |
Reference:
|
[9] J., Fodor,, R., Yager, R., A., Rybalov,: Structure of uninorms..Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 4, 411-427. Zbl 1232.03015, MR 1471619, 10.1142/s0218488597000312 |
Reference:
|
[10] M., Grabisch,, J.-L., Marichal,, R., Mesiar,, E., Pap,: Aggregation Functions..Cambridge University Press, 2009. Zbl 1206.68299, MR 2538324, 10.1017/cbo9781139644150 |
Reference:
|
[11] F., Karaçal,, Ü., Ertuğrul,, R., Mesiar,: Characterization of uninorms on bounded lattices..Fuzzy Sets Systems 308 (2017), 54-71. MR 3579154, 10.1016/j.fss.2016.05.014 |
Reference:
|
[12] F., Karaçal,, A., İnce, M., R., Mesiar,: Nullnorms on bounded lattices..Inf. Sci. 325 (2015), 227-236. MR 3392300, 10.1016/j.ins.2015.06.052 |
Reference:
|
[13] F., Karaçal,, R., Mesiar,: Uninorms on bounded lattices..Fuzzy Sets Systems 261 (2015), 33-43. MR 3291484, 10.1016/j.fss.2014.05.001 |
Reference:
|
[14] N., Kesicioğlu, M.: Some notes on the partial orders induced by a uninorm and a nullnorm in a bounded lattice..Fuzzy Sets Systems 346 (2018), 55-71. MR 3812757, 10.1016/j.fss.2017.08.010 |
Reference:
|
[15] N., Kesicioğlu, M., Ü., Ertuğrul,, F., Karaçal,: Some notes on U-partial order..Kybernetika 55 (2019), 3, 518-530. MR 4015996, 10.14736/kyb-2019-3-0518 |
Reference:
|
[16] P., Klement, E., R., Mesiar,, E., Pap,: On Locally Internal Monotonic Operations..Kluwer Academic Publishers, Dordrecht 2000. |
Reference:
|
[17] M., Mas,, G., Mayor,, J., Torrens,: t-operators..Int. J. Uncertain. Fuzziness Knowl.-Based Systems 7 (1999), 31-50. Zbl 1005.03047, MR 1691482, 10.1142/s0218488599000039 |
Reference:
|
[18] M., Mas,, G., Mayor,, J., Torrens,: The distributivity condition for uninorms and t-operators..Fuzzy Sets Systems 128 (2002), 209-225. Zbl 1005.03047, MR 1908427, 10.1016/S0165-0114(01)00123-3 |
Reference:
|
[19] F., Sun,, P., Wang, X., B., Qu, X.: Uni-nullnorms and null-uninorms..J. Intell. Fuzzy Systems 32 (2017), 1969-1981. 10.3233/JIFS-161495 |
Reference:
|
[20] F., Sun,, P., Wang, X., B., Qu, X.: Characterizations of uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms..Fuzzy Sets Systems 334 (2018), 24-35. MR 3742230, 10.1016/j.fss.2017.03.001 |
Reference:
|
[21] Y.-M., Wang,, W.-H., Liu,: On the distributivity equation for uni-nullnorms..Kybernetika 55 (2019), 1, 24-43. MR 3935413, 10.14736/kyb-2019-1-0024 |
Reference:
|
[22] G., Wang,, F., Qin,, W.-H., Liu,: Distributivity and conditional distributivity for uni-nullnorms..Fuzzy Sets Systems 372 (2018), 34-49. MR 3961834, 10.1016/j.fss.2018.08.008 |
Reference:
|
[23] Y.-M., Wang,, H., Zhan,, H.-W., Liu,: Uni-nullnorms on bounded lattices..Fuzzy Sets Systems (2019). MR 4073382 |
Reference:
|
[24] R., Yager, R., A., Rybalov,: Uninorm aggregation operators..Fuzzy Sets Systems 80 (1996), 1, 111-120. Zbl 0871.04007, MR 1389951, 10.1016/0165-0114(95)00133-6 |
. |