On distributive laws between 2-uninorms and overlap (grouping) functions

Abstract Since Aczel studied the distributive law between two operations, the distributive laws among different binary aggregation functions become an interesting and vast research field. This paper is mainly devoted to solving the distributivity equations between 2-uninorms and overlap(grouping) functions, which are two classes of special aggregation functions found to possess wide applications in image processing, decision making, classification and fuzzy detection problems. We obtain the sufficient and necessary conditions of the distributivity equations between five classes of basic 2-uninorms and overlap(grouping) functions.

[1]  Ronald R. Yager,et al.  Uninorm aggregation operators , 1996, Fuzzy Sets Syst..

[2]  Bao Qing Hu,et al.  On multiplicative generators of overlap and grouping functions , 2018, Fuzzy Sets Syst..

[3]  Bao Qing Hu,et al.  On interval additive generators of interval overlap functions and interval grouping functions , 2017, Fuzzy Sets Syst..

[4]  Feng Sun,et al.  Characterizations of uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms , 2018, Fuzzy Sets Syst..

[5]  Ronald R. Yager,et al.  Structure of Uninorms , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Humberto Bustince,et al.  Some properties of overlap and grouping functions and their application to image thresholding , 2013, Fuzzy Sets Syst..

[7]  Francisco Herrera,et al.  Enhancing Multiclass Classification in FARC-HD Fuzzy Classifier: On the Synergy Between $n$-Dimensional Overlap Functions and Decomposition Strategies , 2015, IEEE Transactions on Fuzzy Systems.

[8]  Hang Zhan,et al.  Uni-nullnorms on bounded lattices , 2020, Fuzzy Sets Syst..

[9]  Joan Torrens,et al.  A characterization of a class of uninorms with continuous underlying operators , 2016, Fuzzy Sets Syst..

[10]  Eyke Hüllermeier,et al.  Grouping, Overlap, and Generalized Bientropic Functions for Fuzzy Modeling of Pairwise Comparisons , 2012, IEEE Transactions on Fuzzy Systems.

[11]  Daniel Ruiz,et al.  Distributivity and conditional distributivity of a uninorm and a continuous t-conorm , 2006, IEEE Transactions on Fuzzy Systems.

[12]  Humberto Bustince,et al.  On additive generators of overlap functions , 2016, Fuzzy Sets Syst..

[13]  Qin Feng.  Uninorm solutions and (or) nullnorm solutions to the modularity condition equations , 2004, Fuzzy Sets Syst..

[14]  Feng Qin,et al.  On the distributivity equations between uni-nullnorms and overlap (grouping) functions , 2021, Fuzzy Sets Syst..

[15]  Prabhakar Akella,et al.  Structure of n-uninorms , 2007, Fuzzy Sets Syst..

[16]  Bernard De Baets,et al.  On the structure of 2-uninorms , 2018, Inf. Sci..

[17]  Graçaliz Pereira Dimuro,et al.  On residual implications derived from overlap functions , 2015, Inf. Sci..

[18]  Bao Qing Hu,et al.  On interval (G, N)-implications and (O, G, N)-implications derived from interval overlap and grouping functions , 2018, Int. J. Approx. Reason..

[19]  Bao Qing Hu,et al.  On the migrativity of uninorms and nullnorms over overlap and grouping functions , 2017, Fuzzy Sets Syst..

[20]  Qin Feng,et al.  The distributive equations for idempotent uninorms and nullnorms , 2005, Fuzzy Sets Syst..

[21]  Humberto Bustince,et al.  Overlap Index, Overlap Functions and Migrativity , 2009, IFSA/EUSFLAT Conf..

[22]  Feng Qin,et al.  Distributivity between semi-uninorms and semi-t-operators , 2016, Fuzzy Sets Syst..

[23]  Ewa Rak,et al.  The distributivity property of increasing binary operations , 2013, Fuzzy Sets Syst..

[24]  Feng Qin,et al.  Distributivity and conditional distributivity for uni-nullnorms , 2019, Fuzzy Sets Syst..

[25]  Huawen Liu,et al.  Distributivity and conditional distributivity of semi-uninorms over continuous t-conorms and t-norms , 2015, Fuzzy Sets Syst..

[26]  Junsheng Qiao,et al.  On Distributive Laws of Uninorms Over Overlap and Grouping Functions , 2019, IEEE Transactions on Fuzzy Systems.

[27]  Bao Qing Hu,et al.  The distributive laws of fuzzy implications over overlap and grouping functions , 2018, Inf. Sci..

[28]  Humberto Bustince,et al.  A generalization of the migrativity property of aggregation functions , 2012, Inf. Sci..

[29]  Feng Sun,et al.  Uni-nullnorms and null-uninorms , 2017, J. Intell. Fuzzy Syst..

[30]  Bernard De Baets,et al.  The functional equations of Frank and Alsina for uninorms and nullnorms , 2001, Fuzzy Sets Syst..

[31]  M. Mas,et al.  Migrative uninorms and nullnorms over t-norms and t-conorms , 2015, Fuzzy Sets Syst..

[32]  Feng Qin,et al.  Distributivity between semi-t-operators and Mayor's aggregation operators , 2016, Inf. Sci..

[33]  Bao Qing Hu,et al.  On generalized migrativity property for overlap functions , 2019, Fuzzy Sets Syst..

[34]  Benjamín R. C. Bedregal,et al.  Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties , 2014, Fuzzy Sets Syst..

[35]  Huawen Liu,et al.  Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t-conorm , 2016, Fuzzy Sets Syst..

[36]  Ewa Rak,et al.  Distributivity equation in the class of 2-uninorms , 2016, Fuzzy Sets Syst..