Quadratic and nonlinear programming problems solving and analysis in fully fuzzy environment

Gabr, Walaa Ibrahim

doi:10.1016/j.aej.2015.03.020

Cited by 11 publications

(6 citation statements)

References 11 publications

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“…Currently, along with the progress made during the recent decades in the area of computed systems, as well as supplying powerful software and hardware, fuzzy nonlinear programming methods are considered as one of the promising approaches for application in various fields, namely, in the form of systems assisting decision-making in different managerial and industrial fields [7]. Some of the managerial and decision-making applications related to these methods are shown in the recent studies of the optimization of performance timing in production lines [25], selectivity in the problems concerning warehousing and production [29], and the applied studies of the reliability theory [21].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, fuzzy theory provides an intuitive and quantitative tool that is suitable for solving real-world problems that have an acceptable range of ambiguity [3][4][5]. Fuzzy theory and grey systems can convert most unclear and ambiguous concepts, variables, and systems in such a way that it becomes possible to reason, deduce, control, study, and make decisions using them [4,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…The fuzzy set theory has so far been applied to solve problems in different fields such as control theory and operations research, mathematical modelling and its application in industries [7]. However, the concept of mathematical programming by fuzzy methods, in the general sense, was first presented by Tanaka et al in 1973, and formulating optimization problems through fuzzy linear programming models was presented for the first time by Zimmermann in 1978 [9].…”

Section: Introductionmentioning

confidence: 99%

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Application of Non-Linear Modelling with Uncertain Resource Limitations in the Optimization of Manufacturing and Production Dimensions Based on A Fuzzy Approach

Taghizadeh

Hajipirlu

2023

Preprint

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Currently, with regard to the increasing complexities in the industrial and organizational environments, the mathematical programming methods of the creation type used in the past do not meet the demands of the decision-makers of technical and managerial fields. As a result, making use of a combination of mathematical programming models and fuzzy set theory has led to creating further flexible methods and producing more reliable results for optimization problems. Thus, the main objective of applying the methods is to use the limited uncertainties in the decision-making model through the use of fuzzy logic. In the present article, a practical managerial case has been chosen to investigate how to obtain the optimum value for nonlinear programming problems using fuzzy techniques in models with uncertain resource constraints in the optimization of manufacturing and production dimensions. The modelling for this problem has led to creating a fuzzy nonlinear programming model and converting and solving it in the form of a particular model. Considering the findings of the optimum dimensions resulting from solving the converted fuzzy model in the manufacturing and production of a tool box ordered with the required constraints and conditions, it is clearly shown that the uncertain resource constraints have been suitably reflected in solving the problem, and the optimum solution has been obtained.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Non-Linear Modelling with Uncertain Resource Limitations in the Optimization of Manufacturing and Production Dimensions Based on A Fuzzy Approach

Taghizadeh

Hajipirlu

2023

Preprint

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“…For allocating resources, the quadratic programming problem, which has an objective function in the quadratic form and subject to a set of constraints, is employed. Consequently, a quantitative decision could be made by referring to the optimal solution obtained from solving the quadratic programming problem, especially with the fuzzy parameters [8,9,10]. Also, the computational techniques for solving the quadratic programming problem under the probabilistic environment [11] and the related robust solution [12] are actively studied.…”

Section: Introductionmentioning

confidence: 99%

Unconstrained Quadratic Programming Problem with Uncertain Parameters

Kek¹,

Lim²,

Ooi³

2021

GJRE

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In this paper, an unconstrained quadratic programming problem with uncertain parameters is discussed. For this purpose, the basic idea of optimizing the unconstrained quadratic programming problem is introduced. The solution method of solving linear equations could be applied to obtain the optimal solution for this kind of problem. Later, the theoretical work on the optimization of the unconstrained quadratic programming problem is presented. By this, the model parameters, which are unknown values, are considered. In this uncertain situation, it is assumed that these parameters are normally distributed; then, the simulation on these uncertain parameters are performed, so the quadratic programming problem without constraints could be solved iteratively by using the gradient-based optimization approach. For illustration, an example of this problem is studied. The computation procedure is expressed, and the result obtained shows the optimal solution in the uncertain environment. In conclusion, the unconstrained quadratic programming problem, which has uncertain parameters, could be solved successfully.

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“…Also, there are a number of researchers who have developed and presented new methods in this field of FFLP such as [25][26][27][28][29][30][31][32]. For the fully fuzzy non-linear programming problems, Walaa Ibrahim Gabr [33] presents a comprehensive methodology for solving and analyzing Quadratic and non-linear programming problems in fully fuzzy environment. It should be noted that all these works are considered in the case of onesingle-level FFLP.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2016

ORAJ

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This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFN s ). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this

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Quadratic and nonlinear programming problems solving and analysis in fully fuzzy environment

Cited by 11 publications

References 11 publications

Application of Non-Linear Modelling with Uncertain Resource Limitations in the Optimization of Manufacturing and Production Dimensions Based on A Fuzzy Approach

Application of Non-Linear Modelling with Uncertain Resource Limitations in the Optimization of Manufacturing and Production Dimensions Based on A Fuzzy Approach

Unconstrained Quadratic Programming Problem with Uncertain Parameters

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