Distributivity equation has been widely studied involving different classes of logical connectives or aggregation operators, such as implications, uninorms, t-operators and their generalizations. In this paper, we follow on these works by investigating the distributivity for uninorms and Mayor’s aggregation operators.
AczélJ.Lectures on Functional Equations and Their Applications, Acad Press, New York, 1966.
2.
AlsinaC., MayorG., TomásM.S. and TorrensJ., Subdistributive De Morgan triplets, Serdica19 (1993), 258–266.
3.
AlsinaC. and TrillasE., On almost distributive Lukasiewicz triplets, Fuzzy Sets Syst50 (1992), 175–178.
4.
BaczyńskiM. and JayaramB., On the distributivity of fuzzy implications over nilpotent or strict triangular conorms, IEEE Trans Fuzzy Syst17 (2009), 590–603.
5.
BaczyńskiM., On the distributivity of fuzzy implications over continuous and Archimedean triangular conorms, Fuzzy Sets Syst161 (2010), 1406–1419.
6.
BalasubramaniamJ. and JaganC., Mohan Rao, On the distributivity of implication operators over T- and S-norms, IEEE Trans Fuzzy Syst12 (2004), 194–198.
7.
CarbonellM., MasM., SunerJ. and TorrensJ., On the distributivity and modularity in De Morgan triplets, Int J Uncertain Fuzziness Knowl-Based Syst4(4) (1996), 351–368.
8.
DrygaśP., Distributivity between semi-t-operators and inullnorms, Fuzzy Sets Syst264 (2015), 100–109.
9.
FodorJ., YagerR.R. and RybalovA., Structure of uninorms, Int J Uncertain Fuzziness Knowl-Based Syst5(4) (1997), 411–427.
10.
FodorJ. and RudasI.J., On continuous triangular norms that are migrative, Fuzzy Sets Syst158 (2007), 1692–1697.
11.
Suárez GarciaF. and Gil ÁlvarezP., Two families of fuzzy integrals, Fuzzy Sets Syst18 (1986), 67–81.
12.
HuS.H. and LiZ.F., The structure of continuous uninorms, Fuzzy Sets Syst124(1) (2001), 43–52.
13.
JočićD. and Štajner-PapugaI., Distributivity equations and Mayor’s aggregation operators, Knowledge Based Syst52 (2013), 194–200.
LiuH., Semi-uninorms and implications on a complete lattice, Fuzzy Sets Syst191 (2012), 72–82.
16.
LiuH., Distributivity and conditional distributivity of semiuninorms over continuous t-conorms and t-norms, Fuzzy Sets Syst268 (2015), 27–43.
17.
MayorG., Contribuciòa l’estudi dels models matemàtics per a la lògica de la vaguetat, Universitat de les Illes Balears, (Ph. D. thesis), (1984).
18.
MasM., MayorG. and TorrensJ., The distributivity condition for uninorms and t-operators, Fuzzy Sets and Systems128 (2002), 209–225.
19.
MartinJ., MayorG. and TorrensJ., On locally internal monotonic operations, Fuzzy Sets Syst137(1) (2003) 27–42.
20.
QinF. and YangL., Distributive equations of implications based on nilpotent triangular norms, Int J Approx Reasoning51 (2010), 984–992.
21.
QinF. and WangY.-M., Distributivity between semi-toperators and Mayor’s aggregation operators, Inf Sci346-347 (2016), 6–16.
22.
Ruiz-AguileraD. and TorrensJ., Distributivity of strong implications over conjunctive and disjunctive uninorms, Kybernetika42 (2006), 319–336.
23.
Ruiz-AguileraD. and TorrensJ., Distributivity of residual implications over conjunctive and disjunctive uninorms, Fuzzy Sets Syst158 (2007), 23–37.
24.
RuizD. and TorrensJ., Distributive idempotent uninorms, Int J Uncertain Fuzziness Knowl-Based Syst11 (2003), 413–428.
25.
RuizD. and TorrensJ., Distributivity and conditional distributivity of a uninorm and a continuous t-conorm, IEEE Trans Fuzzy Syst14(2) (2006), 180–190.
26.
Ruiz-AguileraD., TorrensJ., De BaetsB. and FodorJ., Some remarks on the characterization of idempotent uninorms, in: HullermeirE., KruseR., HoffmannF. (Eds.), IPMU 2010. IN:LNAI, vol 6178, Springer-Verlag, Berlin. Hendelberg. 2010. pp. 425–434.
27.
SuY., ZongW., LiuH. and XueP., The distributivity equations for semi-t-operators over uninorms, Fuzzy Sets Syst287 (2016), 172–183.
28.
SuY., ZongW. and LiuH., On distributivity equations for uninorms over semi-t-operators, Fuzzy Sets Syst299 (2016) 41–65.
29.
SuY., LiuH., Ruiz-AguileraD., RieraJ.V. and TorrensJ., On the distributivity property for uninorms, Fuzzy Sets Syst287 (2016), 184–202.
30.
SuY., LiuH., RieraJ.V., Ruiz-AguileraD. and TorrensJ., The distributivity equation for uninorms revisited, Fuzzy Sets Syst334 (2018), 1–23.
