Uncertain random variables: a mixture of uncertainty and randomness

Liu, Yuhan

doi:10.1007/s00500-012-0935-0

Cited by 261 publications

(259 citation statements)

References 21 publications

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“…(see [1]): An uncertain random variable is a function ξ from a chance space (Γ, L, M) × (Ω, A, Pr) to the set of real numbers such that {ξ ∈ B} is an event in an event in L×A for any Borel set B of real numbers.…”

Section: Theorem 1 (Liumentioning

confidence: 99%

“…(Liu [1]): Let ξ be an uncertain random variable. Then its chance distribution is defined by Φ(x) = Ch{ξ ≤ x} (4) for any x ∈ ℜ.…”

Section: Theorem 1 (Liumentioning

confidence: 99%

“…Liu [1] introduced the uncertain random variable for modeling complex systems. In other words; uncertain random variable is improved to illustrate the phenomenon which mixes uncertainty with randomness.…”

Section: Introductionmentioning

confidence: 99%

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A simulation algorithm with uncertain random variables

Dalman

2018

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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Section: Theorem 1 (Liumentioning

confidence: 99%

“…(Liu [1]): Let ξ be an uncertain random variable. Then its chance distribution is defined by Φ(x) = Ch{ξ ≤ x} (4) for any x ∈ ℜ.…”

Section: Theorem 1 (Liumentioning

confidence: 99%

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A simulation algorithm with uncertain random variables

Dalman

2018

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…For example, we can continue to study the minimum weight dominating set problem and the maximum bi-section problem in uncertain environment within the axiomatic framework of uncertainty theory. In addition, the current work can be extended to the uncertain random environment [34,35] where uncertainty and randomness coexist in a system. What's more, the situation in which the decision-makers adopt the minimax regret criterion [32,36] to make the decisions in the uncertain multidimensional knapsack problem might be considered.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Multidimensional Knapsack Problem Based on Uncertain Measure

Rao

Chen

2017

Scientia Iranica

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Abstract. The researchers of classical multidimensional knapsack problem have always assumed that the weights, values, and capacities are constant values. However, in the real-life industrial engineering applications, the multidimensional knapsack problem often comes with uncertainty about a lack of information about these parameters. This paper investigates a constrained multidimensional knapsack problem under uncertain environment, in which the relevant parameters are assumed to be uncertain variables. Within the framework of uncertainty theory, two types of uncertain programming models with discount constraints are constructed for the problem with di erent decision criteria, including the expected value criterion and the critical value criterion. Taking full advantage of the operational law for uncertain variables, the proposed models can be transformed into their corresponding deterministic models. After theoretically investigating the properties of the models, we do some numerical experiments. The numerical results illustrate that the proposed models are feasible and e cient for solving the constrained multidimensional knapsack problem with uncertain parameters.

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“…Its theoretical system was recognized and accepted gradually by the majority of scholars and experts, and part of them have put themselves in studying this theory [2] [3]. At present, axiom system of the theory has been established on the whole, and its theoretical system has been extended to planning theory, risk analysis, reliability analysis, logical reasoning, differential equa-cluding embedded relation, self-compliance, long-term time, the openness of terms, and noted that the safeguards of Relational Contract implementation: value of future cooperation, reputation and relationship rules.…”

Section: Introductionmentioning

confidence: 99%

Supply Chain Commitment Contract Model Based on Uncertainty Theory under Uncertain Market Information

Cui¹,

Xiaolin²,

Lu³

2015

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Based on the uncertainty theory, market demand information updating as the background, we study the coordination and optimization problem of three-stage supply chain in this paper. In half a asymmetric market information, participants are risk neutral; under the situation of the manufacturers and wholesalers having twice pre-season decision-making opportunity, wholesalers can be replenished in the season; manufacturers join the lowest supply contract of commitment: manufacturers for exchanging the information that they cannot get directly from the market will promise wholesalers to have a season lowest supply in pre-season. According to this contract, we establish optimization models of manufacturers and wholesalers respectively, and get the optimal strategy of supply chain members by analyzing the supply chain system. Finally, by giving a numerical example and comparing the results with that under random circumstances, the result is reasonable.

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Uncertain random variables: a mixture of uncertainty and randomness

Cited by 261 publications

References 21 publications

A simulation algorithm with uncertain random variables

A simulation algorithm with uncertain random variables

Multidimensional Knapsack Problem Based on Uncertain Measure

Supply Chain Commitment Contract Model Based on Uncertainty Theory under Uncertain Market Information

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