Geodesic
Migrativity properties of 2-uninorms over semi-t-operators
Kybernetika, Tome 58 (2022) no. 3, pp. 354-375
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In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$.
In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$.
DOI : 10.14736/kyb-2022-3-0354
Classification : 03B52, 94D05
Keywords: 2-uninorms; uninorms; semi-t-operators; triangular norms; triangular conorms 
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Li-Jun, Ying; Feng, Qin. Migrativity properties of 2-uninorms over semi-t-operators. Kybernetika, Tome 58 (2022) no. 3, pp. 354-375. doi: 10.14736/kyb-2022-3-0354

[1] Alsina, C., Schweizer, B., Frank, M. J.: Associative Functions: Triangular Norms and Copulas. World Scientific, 2006. | MR

[2] Akella, P.: Structure of red $n$-uninorms. Fuzzy Sets Syst. 158 (2007), 1631-1651. | DOI | MR

[3] Baets, B. De: Idempotent uninorms. Eur. J. Oper. Res. 118 (1999), 631-642. | DOI | Zbl

[4] Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practioners. Springer-Verlag, Berlin-Heidelberg 2007.

[5] Bustince, H., Baets, B. De, Fernandez, J., Mesiar, R., Montero, J.: A generalization of the migrativity property of aggregation functions. Inf. Sci. 191 (2012), 76-85. | DOI | MR

[6] Calvo, T., Mayor, G., (Eds.), R. Mesiar: Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg, 2002. | MR | Zbl

[7] Durante, F., Sarkoci, P.: A note on the convex combination of triangular norms. Fuzzy Sets Syst. 159 (2008), 77-80. | DOI | MR

[8] Drygaś, P.: Distributivity between semi-t-operators and semi-nullnorms. Fuzzy Sets Syst. 264 (2015), 100-109. | DOI | MR

[9] Fodor, J. C., Yager, R. R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. | DOI | MR | Zbl

[10] Fodor, J. C., Rudas, I. J.: A extension of the migrative property for triangular norms. Fuzzy Sets Syst. 168 (2011), 70-80. | DOI | MR

[11] Hu, S. K., Li, Z. F.: The structure of continuous uninorms. Fuzzy Sets Syst. 124 (2001), 43-52. | DOI | MR

[12] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht 2000. | DOI | MR | Zbl

[13] Li, G., Liu, H. W., Fodor, J. C.: On almost equitable uninorms. Kybernetika. 51 (2015), 699-711. | DOI | MR

[14] Li, W. H., Qin, F.: Migrativity equation for uninorms with continuous underlying operators. Fuzzy Sets Syst. 414 (2021), 115-134. | DOI | MR

[15] Li, W. H., Qin, F., Zhao, Y. Y.: A note on uninorms with continuous underlying operators. Fuzzy Sets Syst. 386 (2020), 36-47. | DOI | MR

[16] Mesiar, R., Novák, V.: Open problems. Tatra Mt. Math. Publ. 6 (1995), 195-204. | MR

[17] Mesiar, R., Novák, V.: Open problems from the 2nd international conference on fuzzy sets theory and its applications. Fuzzy Sets Syst. 81 (1996), 185-190. | DOI | MR

[18] Mesiar, R., Bustince, H., Fernandez, J.: On the $\alpha$-migrivity of semicopulas, quasi-copulas and copulas. Inf. Sci. 180 (2010), 1967-1976. | DOI | MR

[19] Mesiarová-Zemánková, A.: Characterization of idempotent $n$-uninorms. Fuzzy Sets Syst. 427 (2022), 1-22. | DOI | MR

[20] Mesiarová-Zemánková, A.: Characterizing functions of $n$-uninorms with continuous underlying functions. IEEE Trans. Fuzzy Syst. 30 (2022), 5, 1239-1247. | DOI

[21] Mesiarová-Zemánková, A.: The $n$-uninorms with continuous underlying t-norms and t-conorms. Int. J. General Syst. 50 (2020), 92-116. | DOI | MR

[22] Mesiarová-Zemánková, A.: Characterization of $n$-uninorms with continuous underlying functions via $z$-ordinal sum construction. Int. J. Approx. Reason. 133 (2021), 60-79. | DOI | MR

[23] Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: An extension of the migrative property for uninorms. Inf. Sci. 246 (2013), 191-198. | DOI | MR

[24] Mas, M., Mayor, G., Torrens, J.: T-operators. Int. J. Uncertain. Fuzziness Knowl.-based Syst. 7 (1999), 31-50. | DOI | MR

[25] Mas, M., Mayor, G., Torrens, J.: The modularity condition for uninorms and t-operators. Fuzzy Sets Syst. 126 (2002), 207-218. | DOI | MR

[26] Mas, M., Monserat, M., Ruiz-Aguilera, D., Torrens, J.: Migrativity of uninorms over t-norms and t-conorms. In: Aggregation Functions in Theory and in Practise (H. Bustince, J. Fernandez, R. Mesiar and T. Calvo, eds.), Springer Berlin, Heidelberg, pp. 155-166, 2013. | DOI | MR

[27] Mas, M., Monserat, M., Ruiz-Aguilera, D., Torrens, J.: Migrativity uninorms and nullnorms over t-norms and t-conorms. Fuzzy Sets Syst. 261 (2015), 20-32. | DOI | MR

[28] Ouyang, Y., Fang, J. X.: Some results of weighted qusi-arithmetic mean of continuous triangular norms. Inf. Sci. 178 (2008), 4396-4402. | DOI | MR

[29] Ouyang, Y., Fang, J. X., Li, G. L.: On the convex combination of $T_D$ and continuous triangular norms. Inf. Sci. 178 (2007), 2945-2953. | DOI | MR

[30] Qin, F., Ruiz-Aguilera, D.: On the $\alpha$-migrativity of idempotent uninorms. Int. J. Uncertain. Fuzziness Knowl.-based Syst. 23 (2015), 105-115. | DOI | MR

[31] Ruiz, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40 (2004), 21-38. | MR | Zbl

[32] Su, Y., Zong, W., Liu, H. W., Xue, P.: Migrative property for uninorms and semi-t-operators. Inf. Sci. 325 (2015), 455-465. | DOI | MR

[33] Su, Y., Zong, W., Drygaś, P.: Properties of uninorms with the underlying operation given as ordinal sums. Fuzzy Sets Syst. 357 (2019), 47-57. | DOI | MR

[34] Wang, Y. M., Qin, F.: Distributivity for 2-uninorms over semi-uninorms. Int. J. Uncertain. Fuzziness Knowl.-based Syst. 25 (2017), 317-345. | DOI | MR

[35] Wang, Y. M., Zong, W. W., Zhan, H., Liu, H. W.: On migrative 2-uninorms and nullnorms. Int. J. Uncertain. Fuzziness Knowl.-based Syst. 27 (2019), 303-328. | DOI | MR

[36] Wang, Y. M., Liu, H. W.: On the distributivity equation for uni-nullnorms. Kybernetika 55 (2019), 24-43. | DOI | MR

[37] Zong, W. W., Su, Y., Liu, H. W., Baets, B. D.: On the structure of 2-uninorms. Inf. Sci. 467 (2018), 506-527. | DOI | MR

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