اخبار و اعلانات
آمار
| تعداد نشریات | 30 |
| تعداد شمارهها | 690 |
| تعداد مقالات | 6,765 |
| تعداد مشاهده مقاله | 10,998,823 |
| تعداد دریافت فایل اصل مقاله | 7,409,789 |
A note on the ordinal sum of triangular norms on bounded lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 4، مهر و آبان 2023، صفحه 75-80 اصل مقاله (137.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.41885.7279 | ||
| نویسندگان | ||
| Tingsu Y Yan؛ Yao Y Ouyang* | ||
| Faculty of Science, Huzhou University | ||
| چکیده | ||
| The ordinal sum construction is an important way to generate new triangular norms (t-norms for short) on real unit interval from existing ones. Saminger extended the ordinal sum construction of t-norms to bounded lattices in a direct way and proved that, except for very special cases the ordinal sum of t-norms on bounded lattices may be not a t-norm. To ensure the ordinal sum of t-norms is always a t-norm, several modified ordinal sum of t-norms have been developed. This note reviews several such constructions. As a byproduct, we point out that some recent results concerning ordinal sum of t-norms by A\c{s}ici can be seen as corollaries of these construction. | ||
| کلیدواژهها | ||
| Bounded lattices؛ Triangular norms؛ Ordinal sum | ||
| مراجع | ||
|
[1] E. Asici, On the constructions of t-norms and t-conorms on some special classes of bonded lattices, Kybernetika, 57(2021), 352-371.
[2] E. Asici, Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices, Iranian Journal of Fuzzy Systems, 19 (2022), 125-140.
[3] E. Asici, Some further results about t-norms and t-conorms on some special classes of bounded lattices, International Journal of General Systems, 51(4) (2022), 334-351. DOI:10.1080/03081079.2022.2028783.
[4] G. Birkhoff , Lattice theory, American Mathematical Society Colloquium Publications, 25, 1940.
[5] A. H. Cli ord, Naturally totally ordered commutative semigroups, American Journal of Mathematics, 76 (1954), 631-646.
[6] G. De Cooman, E. E. Kerre, Order norms on bounded partially ordered sets, The Journal of Fuzzy Mathematics, 2 (1994), 281-310.
[7] A. Dvorak, M. Holcapek, New construction of an ordinal sum of t-norms and t-conorms on bounded lattices, Infor-mation Sciences, 515 (2020), 116-131.
[8] F. Esteva, L. Godo, Monoidal t-norm based logic: Towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, 124 (2001), 271-288.
[9] F. Karacal, M. A. _Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
[10] F. Karacal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
[11] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.
[12] C. M. Ling, Representation of associative functions, Publicationes Mathematicae Debrecen, 12 (1965), 189-212.
[13] Y. Ouyang, H. P. Zhang, Constructing uninorms via closure operators on a bounded lattice, Fuzzy Sets and Systems, 395 (2020), 93-106.
[14] Y. Ouyang, H. P. Zhang, B. De Baets, Ordinal sums of triangular norms on a bounded lattice, Fuzzy Sets and Systems, 408 (2021), 1-12.
[15] Y. Ouyang, H. P. Zhang, Z. Wang, B. De Baets, On triangular norms representable as ordinal sums based on interior operators on a bounded meet semilattice, Fuzzy Sets and Systems, 439 (2022), 89-101.
[16] S. Saminger-Platz, On ordinal sums of triangular norms on bounded lattices, Fuzzy Sets and Systems, 157 (2006), 1403-1416.
[17] S. Saminger-Platz, E. P. Klement, R. Mesiar, On extensions of triangular norms on bounded lattices, Indagationes Mathematicae, 19 (2008), 135-150. | ||
|
آمار تعداد مشاهده مقاله: 191 تعداد دریافت فایل اصل مقاله: 279 |
||