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Li, Z., Su, Y.. (1402). On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms. نشریه علمی دانشگاه سیستان و بلوچستان, 20(2), 161-166. doi: 10.22111/ijfs.2023.7563
Z. Li; Y. Su. "On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms". نشریه علمی دانشگاه سیستان و بلوچستان, 20, 2, 1402, 161-166. doi: 10.22111/ijfs.2023.7563
Li, Z., Su, Y.. (1402). 'On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms', نشریه علمی دانشگاه سیستان و بلوچستان, 20(2), pp. 161-166. doi: 10.22111/ijfs.2023.7563
Li, Z., Su, Y.. On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms. نشریه علمی دانشگاه سیستان و بلوچستان, 1402; 20(2): 161-166. doi: 10.22111/ijfs.2023.7563

On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms

Iranian Journal of Fuzzy Systems
دوره 20، شماره 2، خرداد و تیر 2023، صفحه 161-166    اصل مقاله (143.03 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7563
نویسندگان
Z. Li1؛ Y. Su* 2
1School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China
2School of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China
چکیده
This paper focuses on the topic of ordinal sums of semigroups in the sense of A. H. Clifford - a method for constructing a new semigroup from a given system of semigroups indexed by a linearly ordered index set. We completely describe the linearly ordered index set for an ordinal sum of semigroups yielding a uninorm.
کلیدواژه‌ها
Uninorm؛ ordinal sum؛ order
مراجع
[1] G. Birkhoff, Lattice theory, American Mathematical Society Colloquium Publications, 1940.

[2] A. Clifford, Naturally totally ordered commutative semigroups, American Journal of Mathematics, 76 (1954), 631-646.

[3] A. Climescu, Sur l’´equation fonctionelle de l’associativit´e, Bulletin of Ecole Polytechnic Institute of Jassy, ´ 1 (1946), 211-224.

[4] S. Jenei, Structure of left-continuous triangular norms with strong induced negations (II). Rotation-annihilation construction, Journal of Applied Non-Classical Logics, 11 (2001), 351-366.

[5] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.

[6] E. P. Klement, R. Mesiar, E. Pap, Triangular norms as ordinal sums of semigroups in the sense of A. H. Clifford, Semigroup Forum, 65 (2002), 71-82.

[7] M. Mas, S. Massanet, D. Ruiz-Aguilera, J. Torrens, A survey on the existing classes of uninorms, Journal of Intelligent and Fuzzy Systems, 29 (2015), 1021-1037.

[8] A. Mesiarov´a-Zem´ankov´a, Ordinal sum construction for uninorms and generalized uninorms, International Journal of Approximate Reasoning, 76 (2016), 1-17.

[9] A. Mesiarov´a-Zem´ankov´a, R. Mesiar, Y. Su, Ordinal sum constructions for aggregation functions on the real unit interval, Iranian Journal of Fuzzy Systems, 19(1) (2022), 83-96.

[10] Y. Su, F. Qin, B. Zhao, On the inner structure of uninorms with continuous underlying operators, Fuzzy Sets and Systems, 403 (2021), 1-9.

[11] Y. Su, W. Zong, A. Mesiarov´a-Zem´ankov´a, Constructing uninorms via ordinal sums in the sense of A. H. Clifford, Semigroup Forum, 105 (2022), 328-344.

[12] R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80(1) (1996), 111-120.

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