Law of Large Numbers for Uncertain Random Variables

@article{Yao2016LawOL,
  title={Law of Large Numbers for Uncertain Random Variables},
  author={Kai Yao and Jinwu Gao},
  journal={IEEE Transactions on Fuzzy Systems},
  year={2016},
  volume={24},
  pages={615-621}
}
  • K. Yao, Jinwu Gao
  • Published 1 June 2016
  • Mathematics
  • IEEE Transactions on Fuzzy Systems
The law of large numbers in probability theory states that the average of random variables converges to its expected value in some sense under some conditions. Sometimes, random factors and human uncertainty exist simultaneously in complex systems, and a concept of uncertain random variable has been proposed to study this type of complex systems. This paper aims to provide a law of large numbers for uncertain random variables, which states that the average of uncertain random variables… 
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References

SHOWING 1-10 OF 41 REFERENCES
Uncertain random variables: a mixture of uncertainty and randomness
TLDR
To measure uncertain random events, this paper combines probability measure and uncertain measure into a chance measure and based on the tool of chance measure, the concepts of chance distribution, expected value and variance of uncertain random variable are proposed.
Uncertain random programming with applications
  • Yuhan Liu
  • Mathematics, Computer Science
    Fuzzy Optim. Decis. Mak.
  • 2013
TLDR
An operational law of uncertain random variables is presented, and an expected value formula is shown by using probability and uncertainty distributions.
Expected Value of Function of Uncertain Variables
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty…
The strong law of large numbers for fuzzy random variables
Risk Index in Uncertain Random Risk Analysis
TLDR
A concept of risk index is proposed to quantify the risk of an uncertain random system, and a risk index theorem is proved in order to calculate the risk index and is applied to series systems, parallel systems and standby systems.
Multi-objective optimization in uncertain random environments
TLDR
A class of uncertain random optimization is suggested for decision systems in this paper, called the uncertain random multi-objective programming, which involves some notions of the Pareto solutions and the compromise solutions as well as two compromise models.
A strong law of large numbers for fuzzy random variables
Uncertain Random Alternating Renewal Process With Application to Interval Availability
TLDR
An alternating renewal theorem is proved, which gives the limit chance distribution of the interval availability of the uncertain random alternating renewal system.
Uncertain random logic and uncertain random entailment
TLDR
An uncertain random logic to deal with complex knowledge containing random factors and human uncertainty simultaneously, and derives a formula to calculate the truth value of an uncertain random proposition.
Law of large numbers for non-elliptic random walks in dynamic random environments
In this paper we prove a law of large numbers for a general class of Z d -valued random walks in dynamic random environments, including examples that are non-elliptic. We assume that the random…
...
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