This paper introduces noncommutative symmetric difference operators for fuzzy logics. Structures and properties of these operators are investigated. Finally, pseudo-quasi-metric and pseudo-metric are constructed on [0,1] based on the noncommutative symmetric differences.
HájekP., Fuzzy logics with noncommutative conjuctions, Journal of Logic and Computation13(4) (2003), 469–479.
15.
HájekP., Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, The Netherlands, 1998.
16.
HuB., BiL., LiS. and DaiS., Asymmetric equivalences in fuzzy logic, Symmetry9(10) (2017), 224.
17.
JiangH., ZhanJ. and ChenD., Covering based variable precision (I,T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems. doi:10.1109/TFUZZ.2018.2883023.
18.
KawaguchiM.F. and MiyakoshiM., Composite fuzzy relational equations with non-commutative conjunctions, Information Sciences110 (1998), 113–125.
19.
KlementE.P., MesiarR., PapE., Triangular Norms, Kluwer, Dordrecht, The Netherlands, 2000.
20.
LiebscherE., Construction of asymmetric multivariate copulas, J Multivar Anal99(10) (2008), 2234–2250.
21.
MegillN.D. and PavičićM., Equivalencies, identities, symmetric differences, and congruencies in orthomodular lattices, Int J Theor Phys42(12) (2003), 2797–2805.
22.
ShenZ. and ZhangD., Symmetric difference operators on fuzzy sets, Fuzzy Sets Syst308 (2017), 1–26.
23.
WuS., Construction of asymmetric copulas and its application in two-dimensional reliability modelling, Eur J Oper Res238 (2014), 476–485.
24.
ZhanJ., SunB. and AlcantudJ.C.R., Covering based multigranulation (I, T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences476 (2019), 290–318.
25.
ZhangL., ZhanJ. and XuZ., Covering-based generalize, IF rough sets with applications to multi-attribute decisionmaking, Information Sciences478 (2019), 275–302.