Complex uncertain variables are measurable functions from uncertainty spaces to the set of complex numbers and are used to model complex uncertain quantities. In this paper, we investigate Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences. For studying these theorems, we introduce two concepts: strongly order continuous and regular. And as far as we know, our results are new.
ChenX. and LiuB., Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making9(1) (2010), 69–81.
2.
ChenX., NingY. and WangX., Convergence of complex uncertain sequences, Journal of Intelligent and Fuzzy Systems30(6) (2016), 3357–3366.
3.
GaoY., Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition, Journal of Uncertain Systems6(3) (2012), 223–232.
4.
GaoY., Uncertain inference control for balancing inverted pendulum, Fuzzy Optimization and Decision Making11(4) (2012), 481–492.
LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems2(1) (2008), 3–16.
7.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
8.
LiuB., Theory and Practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin, 2009.
9.
LiuB., Uncertain set theory and uncertain inference rule with application to uncertain control, Journal of Uncertain Systems4(2) (2010), 83–98.
10.
LiuB., Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Systems4(3) (2010), 163–170.
11.
LiuB., Uncertainty Theory: A Branch of Mathematics for Modelling Human Uncertainty, Springer-Verlag, Berlin, 2011.
12.
LiuB. and ChenX., Uncertain multiobjective programming and uncertain goal programming, Journal of Uncertainty Analysis and Applications3 (2015), Article 10.
13.
LiuY., An analytic method for solving uncertain differential equations, Journal of Uncertain Systems6(4) (2012), 244–249.
14.
PengJ. and YaoK., A new option pricing model for stocks in uncertainty markets, International Journal of Operations Research8(2) (2011), 18–26.
RoydenH.L., Real Analysis, Macmillan, New York, 1988.
17.
SunJ. and ChenX., Asian option pricing formula for uncertain financial market, Journal of Uncertainty Analysis and Applications3 (2015), Article 11.
18.
TripathyB.C. and NathP.K., Statistical convergence of complex uncertain sequences, New Mathematics and Natural Computation13(3) (2017), 359–374.
19.
YaoK., Extreme values and integral of solution of uncertain differential equation, Journal of Uncertainty Analysis and Applications1 (2013), Article 2.
20.
YaoK. and ChenX., A numerical method for solving uncertain differential equations, Journal of Intelligent and Fuzzy Systems25(3) (2013), 825–832.
21.
YouC., On the convergence of uncertain sequences, Mathematical and Computer Modelling49(3-4) (2009), 482–487.
22.
YuX., A stock model with jumps for uncertain markets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems20(3) (2012), 421–432.
