The cross-migrativity equation with respect to semi-t-operators

	The cross-migrativity equation with respect to semi-t-operators
Iranian Journal of Fuzzy Systems
مقاله 3، دوره 18، شماره 1، فروردین و اردیبهشت 2021، صفحه 17-33 اصل مقاله (386.33 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2021.5869
نویسندگان
Y. Y. Zhao^* ¹؛ F. Qin²
¹School of Mathematics, Shandong University, 250100 Jinan, PR China
²College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China
چکیده
The cross-migrativity has been investigated for families of certain aggregation operators, such as t-norms, t-subnorms and uninorms. In this paper, we aim to study the cross-migrativity property for semi-t-operators, which are generalizations of t-operators by omitting commutativity. Specifically, we give all solutions of the cross-migrativity equation for all possible combinations of semi-t-operators. Moreover, it is shown that if a semi-t-operator F is alpha-cross-migrative over another semi-t-operator G, then G must be a semi-nullnorm except one case. Finally, it is pointed out that the cross-migrativity property between two semi-t-operators is always determined by their underlying operators except a few cases.
کلیدواژه‌ها
Fuzzy connectives؛ cross-migrativity؛ semi-t-operators؛ semi-nullnorms

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