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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.
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[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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