Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm

REFERENCES

[1] Aczél, J.: Lectures on Functional Equations and their Applications, Academic Press, New York, 1966.Suche in Google Scholar

[2] Akella, P.: Structure of n-uninorms, Fuzzy Sets and Systems 158 (2007), 1631–1651.10.1016/j.fss.2007.02.015Suche in Google Scholar

[3] Drewniak, J.—Drygaś, P.—Rak, E.: Distributivity between uninorms and nullnorms, Fuzzy Sets and Systems 159 (2008), 1646–1657.10.1016/j.fss.2007.09.015Suche in Google Scholar

[4] Drygaś, P.—Qin, F.—Rak, E.: Left and right distributivity equations for semi-t-operators and uninorms, Fuzzy Sets and Systems 325 (2017), 21–34.10.1016/j.fss.2017.04.012Suche in Google Scholar

[5] Drygaś, P.—Rak, E.: Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems 291 (2016), 82–97.10.1016/j.fss.2015.02.014Suche in Google Scholar

[6] Fodor, J. C.— Yager, R. R—Rybalov, A.: Structure of uninorms, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 5 (1997), 411–427.10.1142/S0218488597000312Suche in Google Scholar

[7] Grabisch, M.—Marichal, J. L—Mesiar, R.—Pap, E.: Aggregations Functions, Cambridge University Press, New York, 2009.10.1017/CBO9781139644150Suche in Google Scholar

[8] Jočić, D.—štajner-Papuga, I.: Some implications of the restricted distributivity of aggregation operators with absorbing elements for utility theory, Fuzzy Sets and Systems 291 (2016), 54–65.10.1016/j.fss.2015.06.003Suche in Google Scholar

[9] JOčić, D.—štajner-Papuga, I.: Distributivity and conditional distributivity for T-uninorms, Information Sciences 424 (2018), 91–103.10.1016/j.ins.2017.09.065Suche in Google Scholar

[10] JOčić, D.—štajner-Papuga, I.: Distributivity equations for aggregation operations with annihilator over uninorms, Aequationes Math. 96 (2022), 677–699.10.1007/s00010-021-00844-4Suche in Google Scholar

[11] Klement, E. P.—Mesiar, R.—Pap, E.: Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000.10.1007/978-94-015-9540-7Suche in Google Scholar

[12] Li, G.—Liu, H.-W,—Su, Y.: On the conditional distributivity of nullnorms over uninorms, Information Sciences 317 (2015), 157–169.10.1016/j.ins.2015.04.040Suche in Google Scholar

[13] Mas, M.—Massanet, S.—Ruiz-Aguilera, D.—Torrens, J.: A survey on the existing classes of uninorms, J. Intell. Fuzzy Syst. 29 (2015), 1021–1037.10.3233/IFS-151728Suche in Google Scholar

[14] Mesiarová-Zemánková, A.: Characterization of uninorms with continuous underlying t-norm and t-conorm by means of an exended ordinal sum construction, Internat. J. Approx. Reason. 83 (2017), 176–192.10.1016/j.ijar.2017.01.007Suche in Google Scholar

[15] Mesiarová-Zemánková, A.: The n-uninorms with continuous underlying t-norms and t-conorms, Int. J. Gen. Syst. 50(1) (2021), 92–116.10.1080/03081079.2020.1863395Suche in Google Scholar

[16] Ruiz, D.—Torrens, J.: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm, IEEE Transactions on Fuzzy Systems 14(2) (2006), 180–190.10.1109/TFUZZ.2005.864087Suche in Google Scholar

[17] Ruiz-Aguilera, D.—Torrens, J.—De Baets, B.—Fodor, J. C.: Some remarks on the characterization of idempotent uninorms. In: Proceedings of the 13th IPMU Conference 2010 (E. Hullermeier, R. Kruse, F. Hoffmann, eds.), Lect. Notes Comput. Sci. 6178, Springer-Verlag, 2010, pp. 425–434.10.1007/978-3-642-14049-5_44Suche in Google Scholar

[18] Su, J.—Liu, H.-W—Ruiz-Aguilera, D.—Vicente Riera, J.—Torrens, J.: On the distributivity property for uninorms, Fuzzy Sets and Systems 287 (2016), 184–202.10.1016/j.fss.2015.06.023Suche in Google Scholar

[19] Su, J.—Liu, H.-W—Vicente Riera, J.—Ruiz-Aguilera, D.—Torrens, J.: The distributivity equation for uninorms revisited, Fuzzy Sets and Systems 334 (2018), 1–23.10.1016/j.fss.2016.11.015Suche in Google Scholar

[20] Su, Y.—Zong, W.—Liu, H.-W.: On distributivity equations for uninorms over semi-t-operators, Fuzzy Sets and Systems 299 (2016), 41–65.10.1016/j.fss.2015.08.001Suche in Google Scholar

[21] Sun, F.—Wang, X. P—Qu, X. B.: Uni-nullnorms and null-uninorms, J. Intell. Fuzzy Syst. 32 (2017), 1969–1981.10.3233/JIFS-161495Suche in Google Scholar

[22] Sun, F.—Wang, X. P—Qu, X. B.: Characterizations of uni-nullnorms with continuous Archimedean t-norms and t-conorms, Fuzzy Sets and Systems 334 (2018), 24–35.10.1016/j.fss.2017.03.001Suche in Google Scholar

[23] Sun, X. R.—Liu, H.-W.: The left (right) distributivity of semi-t-operators over 2-uninorms, Iran. J. Fuzzy Syst. 17(3) (2020), 103–116.Suche in Google Scholar

[24] Wang, G.—Qin, F.—Li, H.-W.: Distributivity and conditional distributivity for uni-nullnorms, Fuzzy Sets and Systems 372 (2019), 34–49.10.1016/j.fss.2018.08.008Suche in Google Scholar

[25] Wang, G.—Qin, F.—Li, H.-W.: Conditional distributivity for uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, J. Intell. Fuzzy Syst. 36 (2019), 2773–2785.10.3233/JIFS-181702Suche in Google Scholar

[26] Wang, J. M.—Liu, H.-W.: On the distributivity equation for uni-nullnorms, Kybernetika 55(1) (2019), 24–43.10.14736/kyb-2019-1-0024Suche in Google Scholar

[27] Yager, R. R.—Rybalov, A.: Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996), 111–120.10.1016/0165-0114(95)00133-6Suche in Google Scholar

[28] Zhang, F.-X.—Rak, E.—Bazan, J.: On the distributivity of continuous triangular norms and triangular conorms with respect to 2-uninorms, Fuzzy Sets and Systems 395 (2020), 168–177.10.1016/j.fss.2019.09.002Suche in Google Scholar

[29] Zhang, T.-H.—Qin, F.: On distributive laws between 2-uninorms and overlap (grouping) functions, Internat. J. Approx. Reason. 119 (2020), 353–372.10.1016/j.ijar.2020.01.008Suche in Google Scholar

[30] Zhang, T.-H.—Qin, F.—Li, W.-H.: On the distributivity equations between uni-nullnorms and overlap (grouping) functions, Fuzzy Sets and Systems 403 (2021), 56–67.10.1016/j.fss.2019.12.005Suche in Google Scholar