Some Remarks on an Order Induced by Uninorms

Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper is mainly devoted to defining and investigating the set of incomparable elements with respect to the order induced by a uninorm. Also, by defining such an order, an equivalence relation on the class of uninorms is defined and this equivalence is deeply investigated.

[1]  Funda Karaçal,et al.  Some notes on T-partial order , 2013 .

[2]  S. Gottwald A Treatise on Many-Valued Logics , 2001 .

[3]  Joan Torrens,et al.  On locally internal monotonic operations , 2003, Fuzzy Sets Syst..

[4]  Witold Pedrycz,et al.  Logic-based fuzzy networks: A study in system modeling with triangular norms and uninorms , 2009, Fuzzy Sets Syst..

[5]  R. Yager Aggregation operators and fuzzy systems modeling , 1994 .

[6]  Radko Mesiar,et al.  Uninorms on bounded lattices , 2015, Fuzzy Sets Syst..

[7]  Radko Mesiar,et al.  Triangular norms on the real unit square , 1999, EUSFLAT-ESTYLF Joint Conf..

[8]  Gül Deniz Çayli,et al.  On a new class of t-norms and t-conorms on bounded lattices , 2018, Fuzzy Sets Syst..

[9]  Andrea Mesiarová-Zemánková,et al.  Cancellativity properties for t-norms and t-subnorms , 2009, Inf. Sci..

[10]  Józef Drewniak,et al.  Distributivity between uninorms and nullnorms , 2008, Fuzzy Sets Syst..

[11]  Radko Mesiar,et al.  Triangular norms on product lattices , 1999, Fuzzy Sets Syst..

[12]  Emel Asici An order induced by nullnorms and its properties , 2017, Fuzzy Sets Syst..

[13]  Susanne Saminger,et al.  On ordinal sums of triangular norms on bounded lattices , 2006 .

[14]  Funda Karaçal,et al.  Incomparability with respect to the triangular order , 2016, Kybernetika.

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

[16]  Funda Karaçal,et al.  On the T-partial order and properties , 2014, Inf. Sci..

[17]  H. Mitsch,et al.  A natural partial order for semigroups , 1986 .

[18]  Gaspar Mayor,et al.  Discrete t-norms and operations on extended multisets , 2008, Fuzzy Sets Syst..

[19]  Radko Mesiar,et al.  On a new class of uninorms on bounded lattices , 2016, Inf. Sci..

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

[21]  Funda Karaçal,et al.  Ordering based on uninorms , 2016, Inf. Sci..

[22]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[23]  R. Mesiar,et al.  ”Aggregation Functions”, Cambridge University Press , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[24]  Ronald R. Yager,et al.  Uninorms in fuzzy systems modeling , 2001, Fuzzy Sets Syst..

[25]  Funda Karaçal,et al.  Construction of uninorms on bounded lattices , 2017, Kybernetika.

[26]  R. P. Dilworth Review: G. Birkhoff, Lattice theory , 1950 .

[27]  Funda Karaçal,et al.  A t-partial order obtained from t-norms , 2011, Kybernetika.

[28]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[29]  Joan Torrens,et al.  The distributivity condition for uninorms and t-operators , 2002, Fuzzy Sets Syst..

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

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