A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

Rahman, Sadikur; Shaikh, Ali Akbar; Ali, Irfan; Bhunia, Asoke Kumar; Fügenschuh, Armin

doi:10.3390/math9080908

Cited by 13 publications

(6 citation statements)

References 25 publications

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“…However, because of the lack of samples or knowledge, the interval and fuzzy types of uncertainty are hard to invite in reliability evaluation practice. Rahman et al [11] discussed the optimization problem with type-2 interval uncertainty and provided a theoretical framework. In countering the multiple uncertainties, the main challenge lies in the synthesis quantification method of these three types of uncertainty, i.e., the multisource uncertainty fusion.…”

Section: Introductionmentioning

confidence: 99%

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

Gao,

Sun,

et al. 2024

International Journal of Energy Research

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The reliability of a pressurized water reactor power plant’s control rod drive mechanism (CRDM) is affected by many factors, such as operation states, unit performance, and dynamic environments. Multiple sources of uncertainties, including random, interval, and fuzzy, exist when analyzing the reliability of CRDMs. Modeling reliability without considering the fusion of multisource uncertainties may result in model distortion and may not provide realistic assessment results. This paper proposes a multisource uncertainty fusion method powered by the margin-based variable transformation and the Bayesian network propagation. The interval and fuzzy variables are transformed into random variables to obtain the corresponding generalized probability density function of the CRDM’s feature parameters. After that, the CRDM’s reliability can be evaluated via probability quantization of the Bayesian network inference result through sampling algorithms. A magnetic-jack type CRDM case is presented to verify the proposed method, and the results show that this method can fuse three types of uncertainty variable in a unified way and effectively obtain reliability evaluation results.

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Section: Introductionmentioning

confidence: 99%

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

Gao,

Sun,

et al. 2024

International Journal of Energy Research

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“…Wang et al 42 proposed a Legendre polynomial expansion method combined with subinterval technique to optimize nonlinear interval uncertain problems. Rahman et al 43 proposed the concept of type-2 interval order relation and type-2 interval valued function. Tang et al 44 proposed interval sequence linear programing to solve nonlinear robust optimization problems.…”

Section: Introductionmentioning

confidence: 99%

An interval particle swarm optimization method for interval nonlinear uncertain optimization problems

Zheng

Xie

2023

Advances in Mechanical Engineering

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For nonlinear optimization problems involving interval variables or parameters, the interval possibility degree or interval order relation is conventionally adopted to convert them into a deterministic corresponding counterpart and then can be solved with linear programing approaches, through which computational resources and costs have been preserved to a certain extent. However, some information and computational accuracy will be discounted during the model transformation. In this paper, an interval optimization algorithm based on particle swarm optimization is proposed aiming to cut down the loss of useful information by means of straight optimization instead of model deterministic converting so as to enhance calculation accuracy with few growths of computing expenses. The proposed method firstly employs an interval satisfaction value to cope with the constraints. Consequently, the particle swarm optimization method is used to seek the optimum solution sets without the model deterministic converting. And a criterion based on the satisfaction value model of interval possibility degree plays the role in individual selecting out of the above solution sets. Finally, the effectiveness of the proposed method is verified by investigating four examples.

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“…In recent years, the field of biomedical (7) and clinical trials has paid more attention to optimal experimental designs for Poisson regression models. The dependence of design support points on unknown parameters of the Fisher information matrix is a significant difficulty in the building and evolution of design for generic nonlinear models (8)(9)(10) for non-linear optimal design. The best designs for generalized linear models can't be found without knowing the parameters (11,12) .…”

Section: Introductionmentioning

confidence: 99%

A – Optimal Design for Poisson Regression Model Using Square Root Link

Swetha,

David

2023

IJST

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Objective:The main objective of this study is to identify the optimal operating conditions by determining the point of least variation on response variables, crucial for various aspects of product quality such as yield or strength. Method: Newton-Raphson method is used and the solution to these formulas are obtained numerically using R-software. The parameters in the context of A-optimal designs is a necessary step i.e., θ = (α, β , µ). Findings: Our findings show that A-optimal designs outperform conventional design criteria in terms of lowering parameter estimate variance. Moreover, we illustrate how the A-optimal designs can lead to a more efficient allocation of resources statistical models, optimizing the use of time and resources while ensuring robust statistical conclusions. Novelty and Applications : In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focused on optimal experimental designs with concentration on D optimality. In this research, Poisson regression models were considered for A-optimization with square root link. This approach proves to be particularly valuable as it accounts for the model's dependence on unknown parameters, making it a useful technique for practical applications. Suggestions: This methodology is quite general and may be applied to find A-optimal designs for other models, like the Compound Poisson, Gamma and inverse Gaussian model, with log link or other types of optimal designs.

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A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations

Cited by 13 publications

References 25 publications

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

An interval particle swarm optimization method for interval nonlinear uncertain optimization problems

A – Optimal Design for Poisson Regression Model Using Square Root Link

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