Uncertain Programming in Preliminary Design of Technical Systems with Uncertain Parameters

Veresnikov, Georgy; Pankova, L.A.; Pronina, Valeriya

doi:10.1016/j.procs.2017.01.007

Cited by 11 publications

(6 citation statements)

References 6 publications

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“…The existing uncertain optimization solutions are the special cases of the proposed NN-NP optimization solutions. Furthermore, the existing uncertain optimization methods in [1][2][3][4][5][6] cannot express and solve the NN-NP problems from this study. Obviously, the optimal solutions in the NN-NP problems are intervals corresponding to different specific ranges of the indeterminacy I ∈ [I L , I U ] and show the flexibility and rationality under indeterminate/NN environments, which is the main advantage of the proposed NN-NP methods.…”

Section: Examplementioning

confidence: 92%

“…If I ∈ [1,2] is considered as a possible interval range, then d 2 F(x * , I)/dx 2 > 0, and x * = 0 is the optimal solution for the minimum F(x * , I). Thus, the minimum value of the NN objective function is F(x * , I) = [5,10], which, in this case, is a possible interval range, but not always. Specifically if I = 1 (crisp value), then F(x * , I) = 5.…”

Section: One-dimension Unconstrained Nn Nonlinear Optimizationmentioning

confidence: 98%

“…By solving these equations, we can obtain the results of x 1 = µ/(2I), x 2 = µ/4, and µ = 4I 2 /(2 + I) (µ = 0 yields an infeasible solution for I > 0). Hence, the NN optimal solution is obtained by the results of Compared with existing uncertain optimization methods [1][2][3][4][5][6], the proposed NN-NP methods can obtain ranges of optimal solutions (usually NN solutions but not always) rather than the crisp optimal solutions of previous uncertain optimization methods [1][2][3][4][5][6], which are not really meaningful in indeterminate programming of indeterminate solutions in real situations [23,24]. The existing uncertain optimization solutions are the special cases of the proposed NN-NP optimization solutions.…”

Section: Examplementioning

confidence: 99%

“…However, uncertainty also exists in real problems. Hence, many researchers have proposed uncertain optimization methods, such as approaches using fuzzy and stochastic logics, interval numbers, or uncertain variables [1][2][3][4][5][6]. Uncertain programming has been widely applied in engineering, management, and design problems.…”

Section: Introductionmentioning

confidence: 99%

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Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments

Cui

2018

Axioms

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In practical situations, we often have to handle programming problems involving indeterminate information. Building on the concepts of indeterminacy I and neutrosophic number (NN) (z = p + qI for p, q ∈ R), this paper introduces some basic operations of NNs and concepts of NN nonlinear functions and inequalities. These functions and/or inequalities contain indeterminacy I and naturally lead to a formulation of NN nonlinear programming (NN-NP). These techniques include NN nonlinear optimization models for unconstrained and constrained problems and their general solution methods. Additionally, numerical examples are provided to show the effectiveness of the proposed NN-NP methods. It is obvious that the NN-NP problems usually yield NN optimal solutions, but not always. The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations.

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Section: Examplementioning

confidence: 92%

Section: One-dimension Unconstrained Nn Nonlinear Optimizationmentioning

confidence: 98%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments

Cui

2018

Axioms

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“…For example, Dalman [25] considers an uncertain multi-objective multi-item solid transportation problem. Veresnikov et al [26] designs an uncertain technical systems. In particular, Zhang and Peng [27] study an uncertain assignment problem in which coefficients are uncertain variables.…”

Section: Introductionmentioning

confidence: 99%

Uncertain random assignment problem

Ding

Zeng

2018

Applied Mathematical Modelling

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This paper proposes an uncertain random assignment problem in which random variables coexist with uncertain variables. Critical values of uncertain random variables are used to rank uncertain random variables. An uncertain random simulation algorithm is developed in order to obtain chance distributions and critical values of uncertain random variables. An α-optimistic model is presented. A combined optimization approach is designed to solve the α-optimistic model. This approach incorporates uncertain random simulation into branch and bound algorithm. Finally, an example application of the approach is presented.

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Neutrosophic linear programming using possibilistic mean

Khatter

2020

Soft Comput

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Uncertain Programming in Preliminary Design of Technical Systems with Uncertain Parameters

Cited by 11 publications

References 6 publications

Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments

Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments

Uncertain random assignment problem

Neutrosophic linear programming using possibilistic mean

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