An order induced by nullnorms and its properties

Abstract In this paper, an order induced by nullnorms on bounded lattices is given and discussed. We define the set of incomparable elements with respect to the order induced by a nullnorm. Also, by defining such an order, an equivalence relation on the class of nullnorms is defined and this equivalence is deeply investigated.

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

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

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

[4]  Funda Karaçal,et al.  Distributive and infinitely-distributive t-norms on complete lattices , 2005, Fuzzy Sets Syst..

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

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

[7]  Radko Mesiar,et al.  Nullnorms on bounded lattices , 2015, Inf. Sci..

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

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

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

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

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

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

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

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

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

[17]  Pawel Drygas,et al.  A characterization of idempotent nullnorms , 2004, Fuzzy Sets Syst..

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

[19]  Radko Mesiar,et al.  Order-equivalent triangular norms , 2015, Fuzzy Sets Syst..

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

[21]  Huawen Liu,et al.  On the distributivity of uninorms over nullnorms , 2013, Fuzzy Sets Syst..

[22]  Joan Torrens,et al.  t-Operators , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

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

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