Previous |  Up |  Next

Article

Title: Notes on locally internal uninorm on bounded lattices (English)
Author: Çaylı, Gül Deniz
Author: Ertuğrul, Ümit
Author: Köroğlu, Tuncay
Author: Karaçal, Funda
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 53
Issue: 5
Year: 2017
Pages: 911-921
Summary lang: English
.
Category: math
.
Summary: In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm. (English)
Keyword: bounded lattice
Keyword: uninorm
Keyword: idempotent uninorm
Keyword: locally internal
MSC: 03B52
MSC: 03E72
MSC: 06B20
idZBL: Zbl 06861632
idMR: MR3750111
DOI: 10.14736/kyb-2017-5-0911
.
Date available: 2018-02-26T11:51:50Z
Last updated: 2018-05-25
Stable URL: http://hdl.handle.net/10338.dmlcz/147101
.
Reference: [1] Aşıcı, E., Karaçal, F.: Incomparability with respect to the triangular order..Kybernetika 52 (2016), 15-27. MR 3482608, 10.14736/kyb-2016-1-0015
Reference: [2] Birkhoff, G.: Lattice Theory..American Mathematical Society Colloquium Publ., Providence 1967. Zbl 0537.06001, MR 0227053, 10.1090/coll/025
Reference: [3] Baets, B. De: Idempotent uninorms..European J. Oper. Res. 118 (1999), 631-642. Zbl 1178.03070, 10.1016/s0377-2217(98)00325-7
Reference: [4] Baets, B. De, Fodor, J.: A single-point characterization of representable uninorms..Fuzzy Sets Syst. 202 (2012), 89-99. MR 2934788, 10.1016/j.fss.2011.12.001
Reference: [5] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices..Inform. Sci. 367-368 (2016), 221-231. MR 3684677, 10.1016/j.ins.2016.05.036
Reference: [6] Çaylı, G. D., Drygaś, P.: Some properties of idempotent uninorms on bounded lattices..Inform. Sci. 422 (2018), 352-363. MR 3709474, 10.1016/j.ins.2017.09.018
Reference: [7] Drewniak, J., Drygaś, P.: On a class of uninorms..Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10 (2002), 5-10. MR 1962665, 10.1142/s021848850200179x
Reference: [8] Drygaś, P.: On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums..Fuzzy Sets Syst. 161 (2010), 149-157. Zbl 1191.03039, MR 2566236, 10.1016/j.fss.2009.09.017
Reference: [9] Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of uninorms locally internal in $A(e)$ with continuous underlying operators..Fuzzy Sets Syst. 287 (2016), 137-153. MR 3447023, 10.1016/j.fss.2009.09.017
Reference: [10] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms..Inform. Sci. 330 (2016), 315-327. 10.1016/j.ins.2015.10.019
Reference: [11] Fodor, J., Yager, R. R., Rybalov, A.: Structure of uninorms..Int. J. Uncertain Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. Zbl 1232.03015, MR 1471619, 10.1142/s0218488597000312
Reference: [12] Kesicioğlu, M. N., Mesiar, R.: Ordering based on implications..Fuzzy Sets Syst. 276 (2014), 377-386. MR 3206505, 10.1016/j.ins.2013.12.047
Reference: [13] Kesicioğlu, M. N., Ertuğrul, Ü., Karaçal, F.: An equivalence relation based on the U-partial order..Inform. Sci. 411 (2017), 39-51. MR 3659313, 10.1016/j.ins.2017.05.020
Reference: [14] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices..Fuzzy Sets Syst. 261 (2015), 33-43. MR 3291484, 10.1016/j.fss.2014.05.001
Reference: [15] Karaçal, F., Ertuğrul, Ü., Mesiar, R.: Characterization of uninorms on bounded lattices..Fuzzy Sets Syst. 308 (2017), 54-71. MR 3579154, 10.1016/j.fss.2016.05.014
Reference: [16] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms..Dordrecht, Kluwer Acad. Publ., 2000. Zbl 1087.20041, MR 1790096, 10.1007/978-94-015-9540-7
Reference: [17] Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations..Fuzzy Sets Syst. 137 (2003), 27-42. Zbl 1022.03038, MR 1992696, 10.1016/s0165-0114(02)00430-x
Reference: [18] Mesiarová-Zemánková, A.: Multi-polar t-conorms and uninorms..Inform. Sci. 301 (2015), 227-240. MR 3311790, 10.1016/j.ins.2014.12.060
Reference: [19] Yager, R. R.: Uninorms in fuzzy system modeling..Fuzzy Sets Syst. 122 (2001), 167-175. MR 1839955, 10.1016/s0165-0114(00)00027-0
Reference: [20] Yager, R. R.: Defending against strategic manipulation in uninorm-based multi-agent decision making..European J. Oper. Res. 141 (2002), 217-232. Zbl 0998.90046, MR 1925395, 10.1016/s0377-2217(01)00267-3
Reference: [21] Yager, R. R., Rybalov, A.: Uninorms aggregation operators..Fuzzy Sets Syst. 80 (1996), 111-120. MR 1389951, 10.1016/0165-0114(95)00133-6
.

Files

Files Size Format View
Kybernetika_53-2017-5_11.pdf 320.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo