Expected Value of Function of Uncertain Variables

By Yuhan Liu, Minghu Ha. 2010

381 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7d27fe31fffca1a2c56d10734b1cf1e0e0d81ab2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Kai Yao
2. Yuhong Sheng
3. Yongchao Hou
4. Zixiong Peng
5. Xiaowei Chen
6. Baoding Liu
7. Yuan Gao
8. Yuanguo Zhu

Citations in the corpus

• Some formulas of variance of uncertain random variable (2014, background): “(Liu and Ha [9]) Let ξ1, ξ2, · · · , ξn be independent uncertain variables with uncertainty distributions 1, 2, · · · , n, respectively.”
• Uncertain Risk Analysis and Uncertain Reliability Analysis (2010, background): “In addition, Liu [8], Gao [3], You [15], Liu and Ha [13], and Peng and Iwamura [14] also made significant contributions to this research area.”
• Subadditivity of chance measure (2014, methodology): “For calculating the expected value by inverse uncertainty distribution, Liu and Ha [5] proved the following theorem.”
• A numerical method for solving uncertain differential equations (2013, background): “Many researchers have done some theoretical work such as [2–4, 9, 16, 19, 20].”
• Toward uncertain finance theory (2013, unknown): “(17) Then Liu and Ha [23] proved that the uncertain variable ξ = f (ξ1, ξ2, · · · , ξn) has an expected value”
• Method of moments for estimating uncertainty distributions (2014, background): “[12], Peng and Iwamura [13], and Liu and Ha [14].”
• Extreme values and integral of solution of uncertain differential equation (2013, unknown): “(Liu and Ha [31]) Let ξ1, ξ2, · · · , ξn be independent uncertain variables with uncertainty distributions 1, 2, · · · , n, respectively.”
• A Transportation Problem with Uncertain Costs and Random Supplies (2015, unknown): “Theorem 2 (Liu and Ha, 2010) Assume n,,, 21 are independent uncertain variables with regular uncertainty distributions n,,, 21 , respectively.”
• A type of uncertain differential equations with analytic solution (2013, background): “Liu and Ha [4] gave a formula to calculate the expected value of a function of multiple uncertain variables.”
• Uncertain Programming Model for Chinese Postman Problem with Uncertain Weights (2012, unknown): “It has been proved by Liu and Ha (2010) that the uncertain variable 1 2( , , , )nf x x x= Lξ has an expected value [ ] 1 1 1 1 1 1 10 ( ( ), , ( ), (1 ), , (1 )) .m m nE f dξ α α α α α − − − − += Φ Φ Φ − Φ −∫ L L We can calculated that the inverse distribution of the zigzag uncertain variable ( ),…”