اخبار و اعلانات
آمار
| تعداد نشریات | 27 |
| تعداد شماره‌ها | 612 |
| تعداد مقالات | 6,232 |
| تعداد مشاهده مقاله | 9,353,206 |
| تعداد دریافت فایل اصل مقاله | 6,105,053 |
A new extension of a triangular norm on a subinterval $[0,\alpha]$ via an interior operator to the underlying entire bounded lattice | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 3، مرداد و شهریور 2023، صفحه 95-113 اصل مقاله (236.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7641 | ||
| نویسندگان | ||
| B. Wu؛ H. Zhou* | ||
| Institute of Mathematics, Shaanxi Normal University, Xi'an, China | ||
| چکیده | ||
| As a proper generalization of the ordinal sum t-norm construction on bounded lattices proposed in [E. A\c{s}{\i}c{\i}, R. Mesiar, New constructions of triangular norms and triangular conorms on an arbitrary bounded lattice, International Journal of General Systems, {\bf 49}(2) (2020), 143-160], the present paper studies a new extension of a triangular norm on a subinterval $[0,\alpha]$ via an interior operator to the underlying entire bounded lattice, where the necessary and sufficient conditions under which the constructed operation is again a t-norm are given. By comparing the graphic structures of two t-norms on a common bounded lattice which are constructed in different ways, it is shown that the new method in this paper is essentially different from the ones existing in the literature. As an end, this new construction is generalized to construct ordinal sums of finitely many t-norms by recursion on bounded lattices. The dual results for ordinal sum construction of t-conorms via closure operators on bounded lattices are also presented. | ||
| کلیدواژه‌ها | ||
| Triangular norm؛ ordinal sum؛ bounded lattice؛ interior operator | ||
| مراجع | ||
|
[1] C. Alsina, M. J. Frank, B. Schweizer, Associative functions: Triangular norms and copulas, World Scientific Publishing Company, Singapore, (2006), 23-98.
[2] E. A¸sıcı, Some methods to construct t-norms and t-conorms on bounded lattices, Journal of Intelligent and Fuzzy Systems, 40(6) (2021), 10877-10892. [3] E. A¸sıcı, On generating t-norms (t-conorms) on some special classes of bounded lattices, International Journal of Fuzzy Logic and Intelligent Systems, 22(1) (2022), 48-58. [4] E. A¸sıcı, F. Kara¸cal, On the t-partial order and properties, Information Sciences, 267 (2014), 323-333.
[5] E. A¸sıcı, R. Mesiar, Alternative approaches to obtain t-norms and t-conorms on bounded lattices, Iranian Journal of Fuzzy Systems, 17(4) (2020), 121-138. [6] E. A¸sıcı, R. Mesiar, New consrtuctions of triangular norms and triangular conorms on an arbitrary bounded lattice, International Journal of General Systems, 49(2) (2020), 143-160. [7] E. A¸sıcı, R. Mesiar, On the construction of uninorms on bounded lattices, Fuzzy Sets and Systems, 408 (2021), 65-85. [8] E. A¸sıcı, R. Mesiar, Some construction approaches for t-norms and t-conorms on bounded lattices, Aequationes Mathematicae, 96(5) (2022), 955-979. [9] G. Birkhoff, Lattice theory, 3rd ed, American Mathematical Society Colloquium Publishers, Providence, (1967), 1-158.
[10] G. D. C¸ aylı, A characterization of uninorms on bounded lattices by means of triangular norms and triangular conorms, International Journal of General Systems, 47(8) (2018), 772-793. [11] G. D. C¸ aylı, On a new class of t-norms and t-conorms on bounded lattices, Fuzzy Sets and Systems, 332 (2018), 129-143. [12] G. D. C¸ aylı, Some methods to obtain t-norms and t-conorms on bounded lattices, Kybernetika, 55(2) (2019), 273-294. [13] G. D. C¸ aylı, Construction of nullnorms on some special classes of bounded lattices, International Journal of Approximate Reasoning, 134 (2021), 111-128.
[14] G. D. C¸ aylı, New construction approaches of uninorms on bounded lattices, International Journal of General Systems, 50(2) (2021), 139-158.
[15] Y. Dan, B. Q. Hu, J. Qiao, New construction of t-norms and t-conorms on bounded lattices, Fuzzy Sets and Systems, 395 (2020), 40-70. [16] Y. Dan, B. Q. Hu, J. Qiao, New constructions of uninorms on bounded lattices, International Journal of Approximate Reasoning, 110 (2019), 185-209.
[17] B. De Baets, R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems, 104(1) (1999), 61-75.
[18] A. Dvo˘r´ak, M. Hol˘capk, New construction of an ordinal sum of t-norms and t-conorms on bounded lattices, Information Sciences, 515 (2020), 116-131.
[19] U. Ertu˘grul, F. Kara¸cal, R. Mesiar, ¨ Modified ordinal sums of triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30(7) (2015), 807-817. [20] U. Ertu˘grul, M. N. Kesicio˘glu, F. Kara¸cal, ¨ Some new construction methods for t-norms on bounded lattices, International Journal of General Systems, 48(7) (2019), 775-791.
[21] U. Ertu˘grul, M. Ye¸silyurt, ¨ Ordinal sums of triangular norms on bounded lattices, Information Sciences, 517 (2020), 198-216. [22] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18 (1967), 145-174.
[23] J. A. Goguen, Concept representation in nature and artificial languages: Axioms, extensions and applications for fuzzy sets, International Journal of Man-Machine Studies, 6(5) (1974), 513-561. [24] F. Kara¸cal, U. Ertu˘grul, M. N. Kesicio˘glu, ¨ A construction method for t-norms on bounded lattices, Advances in Intelligent Systems and Computing, 981 (2019), 205-211. [25] F. Kara¸cal, U. Ertu˘grul, R. Mesiar, ¨ Characterization of uninorms on bounded lattices, Fuzzy Sets and Systems, 308 (2017), 54-71. [26] E. P. Klement, R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular norms, Elsevier, Amsterdam, (2005), 53-274. [27] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, (2000), 3-140, 215-228. [28] G. J. Klir, B. Yuan, Fuzzy sets and fuzzy logic, theory and application, Prentice Hall PTR, Upper Saddle River, (1995), 50-93. [29] J. Medina, Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices, Fuzzy Sets and Systems, 202 (2012), 75-88. [30] K. Menger, Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America, South Bend, America, December, 1942. [31] Y. Ouyang, H. P. Zhang, Constructing uninorms via closure operators on a bounded lattice, Fuzzy Sets and Systems, 395 (2020), 93-106. [32] 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. [33] Y. Ouyang, H. P. Zhang, Z. D. 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. [34] S. Saminger-Platz, On ordinal sums of triangular norms on bounded lattices, Fuzzy Sets and Systems, 157(10) (2006), 1403-1416. [35] S. Saminger, E. P. Klement, R. Mesiar, On extensions of triangular norms on bounded lattices, Indagationes Mathematicae, 19(1) (2008), 135-150. [36] B. Schweizer, A. Sklar, Probabilistic metric spaces, North-Holland, New York, (1983), 78-105.
[37] X. R. Sun, H. W. Liu, On the constructions of t-norms on bounded lattices, Information Sciences, 575 (2021), 173-184. [38] X. R. Sun, H. W. Liu, Further characterization of uninorms on bounded lattices, Fuzzy Sets and Systems, 427 (2022), 96-108. [39] D. Zhang, Triangular norms on partially ordered sets, Fuzzy Sets and Systems, 153(2) (2005), 195-209.
[40] H. P. Zhang, Y. Ouyang, B. De Baets, Constructions of uni-nullnorms and null-uninorms on a bounded lattice, Fuzzy Sets and Systems, 403 (2021), 78-87. | ||
|
آمار تعداد مشاهده مقاله: 33 تعداد دریافت فایل اصل مقاله: 57 |
||