This paper aims at putting forward several types of convergence concepts of complex uncertain random sequences. The relations among convergence concepts are derived by some limit theorems. In addition, for illustrating of convergence theorems, lots of examples are derived. Finally, a lot of counterexamples about relationships between convergence concepts are stated.
AhmadzadeH., ShengY.H. and HassantabarF., Some results of moments of uncertain random variables, Iranian Journal of Fuzzy Systems14(2) (2017), 1–21.
2.
AhmadzadeH., ShengY. and EsfahaniM., On the convergence of uncertain random sequences, Fuzzy Optimization and Decision Making16(2) (2016), 205–220.
3.
ChenX.M., NingY.F. and WangX., Formulas to calcu late the variance and Pseudo-variance of complex uncertain variable, http://orsc.edu.cn/online/150720.pdf.
4.
ChenX.M., NingY.F. and WangX., Convergence of complex uncertain sequences, to be published, Journal of Intelligent and Fuzzy Systems, to be published.
5.
GaoR. and RalescuD.A., Convergence in distribution for uncertain random variables, IEEE Transactions on Fuzzy Systems,. DOI: 10.1109/TFUZZ.2017.2724021.
6.
GaoR., SunY. and RalescuD.A., Order statistics of uncertain random variables with application to k-out-of-n system, Fuzzy Optimization and Decision Making16(2) (2017), 159–181.
7.
GaoR. and ShengY.H., Law of large numbers for uncertain random variables with different chance distributions, Journal of Intelligent and Fuzzy Systems31(3) (2016), 1227–1234.
8.
GaoR., ZhangZ., AhmadazdeH. and RalescuD.A., Complex uncertain random variables, Soft Computing, DOI: 10.1007/s00500-017-2717-1.
9.
GaoR. and YaoK., Importance index of components in uncertain random systems, Knowledge-Based Systems109 (2016), 208–217.
10.
GuoH.Y. and WangX.S., Variance of uncertain random variables,Article, Journal of Uncertainty Analysis and Applications2 (2014), 6.
11.
HouY., Subadditivity of chance measure,Article, Journal of Uncertainty Analysis and Applications2 (2014), 14.
12.
KumarT. and BajajR.K., On Complex intuitionistic fuzzy soft Sets with distance measures and entropies,Article, Journal of Mathematics2014 (2014), 972198.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
15.
LiuB., Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty2010. Springer-Verlag, Berlin.
16.
LiuB., Toward uncertain finance theory, Journal of Uncertainty Analysis and Applications1 (2013), Article 1.
17.
LiuB., Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Systems4(3) (2010), 163–170.
18.
LiuY.H., Uncertain random variables: A mixture of uncertainty and randomness, Soft Computing17(4) (2013), 625–634.
19.
LiuY.H., Uncertain random programming with applications, Fuzzy Optimization and Decision Making12(2) (2013), 153–169.
20.
LiuY.H. and RalescuD.A., Risk index in uncertain random risk analysis, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems22(4) (2014), 491–504.
21.
MaX., ZhanJ., AliM.I. and MehmoodN., A survey of decision making methods based on two classes of hybrid soft set models, Artificial Intelligence Review49(4) (2018) 511–529.
RamotD., MiloR., FriedmanM. and KandelA., Complex fuzzy sets, IEEE Transactions on Fuzzy Systems10(2) (2002), 171–186.
24.
SelvachandranG., MajiP.K., AbedI.E. and SallehA.R., Relations between complex vague soft sets, Applied Soft Computing47 (2016), 438–448.
25.
WangX., ChenD., AhmadzadeH. and GaoR., Some limit theorems on uncertain random sequences, Journal of Intelligent and Fuzzy Systems34(1) (2018), 507–515.
26.
ZhanJ. and AlcantudJ.C.R., Alcantud, A novel type of soft rough covering and its application to multicriteria group decision making, ArtificialIntelligenceReview (2018), 10.1007/s10462-018-9617-3.
27.
ZhanJ. and AlcantudJ.C.R., A survey of parameter reduction of soft sets and corresponding algorithms, Artificial Intelligence Review (2018), DOI: 10.1007/s10462-017-9592-0.