An equivalence relation based on the U-partial order

Abstract In this paper, an equivalence relation on the class of uninorms induced by the U-partial order is discussed. Defining the set of all incomparable elements w.r.t. the U-partial order, this set is deeply investigated and some relations with the sets of all incomparable elements w.r.t. the orders induced by the corresponding underlying t-norm and t-conorm are presented. Also, the set of all incomparable elements with a fixed element w.r.t. the U-partial order is defined and studied in detail.

[1]  Didier Dubois,et al.  A review of fuzzy set aggregation connectives , 1985, Inf. Sci..

[2]  M. Kesicioglu,et al.  On the property of T-distributivity , 2013 .

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

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

[5]  Funda Karaçal,et al.  On the direct decomposability of strong negations and S-implication operators on product lattices , 2006, Inf. Sci..

[6]  Bernard De Baets,et al.  A single-point characterization of representable uninorms , 2012, Fuzzy Sets Syst..

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

[8]  R. Mesiar,et al.  Aggregation Functions: Aggregation on ordinal scales , 2009 .

[9]  Zhudeng Wang,et al.  Residual coimplicators of left and right uninorms on a complete lattice , 2009, Fuzzy Sets Syst..

[10]  Ma Zherui,et al.  Logical operators on complete lattices , 1991, Inf. Sci..

[11]  Dana Hlinená,et al.  Pre-orders and Orders Generated by Conjunctive Uninorms , 2014, IPMU.

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

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

[14]  Radko Mesiar,et al.  Modified Ordinal Sums of Triangular Norms and Triangular Conorms on Bounded Lattices , 2015, Int. J. Intell. Syst..

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

[16]  Michal Baczynski,et al.  Fuzzy Implications , 2008, Studies in Fuzziness and Soft Computing.

[17]  Radko Mesiar,et al.  Ordering based on implications , 2014, Inf. Sci..

[18]  Zhudeng Wang,et al.  Residual operations of left and right uninorms on a complete lattice , 2009, Fuzzy Sets Syst..

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