QUADRATIC PROGRAMMING WITH FUZZY PARAMETERS: AN EXTENSION PRINCIPLE APPROACH

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NASERI S.H.; TALESHIAN F.; TAGHINEZHAD N.A.; KHALILI F.

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Journal: Journal of Operational Research in its Applications Year:2013 | Volume:9 | Issue:4 (35) Page(s): 9-25

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Information Journal Paper

Title

QUADRATIC PROGRAMMING WITH FUZZY PARAMETERS: AN EXTENSION PRINCIPLE APPROACH

Author(s)

NASERI S.H. | TALESHIAN F. | TAGHINEZHAD N.A. | KHALILI F. | Issue Writer Certificate

Keywords

QUADRATIC PROGRAMMINGQ3

FUZZY NUMBERSQ3

FUZZY QUADRATIC PROGRAMMINGQ3

EXTENSION PRINCIPALQ3

MEMBERSHIP FUNCTIONQ3

α-CUTSQ3

Abstract

A QUADRATIC PROGRAMMING (QP) problem is a special class of nonlinear programming problems with the objective function of the quadratic form subject to linear constraint. The conventional QUADRATIC PROGRAMMING model requires the parameters to be known constants. However QP has been widely applied to solve real world problems. On the other hand, a wide variety of problems that we deal with in our real life, and we decide according to the solution of the mathematical models are inaccurate concepts or the sets with uncertain bounds. The parameter values used would be based on a prediction of future conditions which inevitably involves some degree of uncertainty. Consequently modeling these problems as QUADRATIC PROGRAMMING with fuzzy parameters is one of the interested fields in operations research. This paper presents a new approach to solve fuzzy QUADRATIC PROGRAMMING problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex FUZZY NUMBERS. This method reduces the fuzzy QUADRATIC PROGRAMMING problem to two classical QUADRATIC PROGRAMMING problems using fuzzy concepts. These conventional quadratic problems can be solved using the SQP algorithm, leading to the upper bound and the lower bound of the optimal value at specific a-level respectively. Moreover we extend this method for a more general QUADRATIC PROGRAMMING problem in which all parameters in the problem are all FUZZY NUMBERS. Finally an example is presented to describe and demonstrate the efficiency of the proposed method, of optimization problem.

Cites

OPTIMUM FUZZY NON-PARAMETRIC PREDICTIVE INFERENCE FOR SINGLE ACCEPTANCE SAMPLING

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APA: Copy

NASERI, S.H., TALESHIAN, F., TAGHINEZHAD, N.A., & KHALILI, F.. (2013). QUADRATIC PROGRAMMING WITH FUZZY PARAMETERS: AN EXTENSION PRINCIPLE APPROACH. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 9(4 (35)), 9-25. SID. https://sid.ir/paper/164723/en

Vancouver: Copy

NASERI S.H., TALESHIAN F., TAGHINEZHAD N.A., KHALILI F.. QUADRATIC PROGRAMMING WITH FUZZY PARAMETERS: AN EXTENSION PRINCIPLE APPROACH. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2013;9(4 (35)):9-25. Available from: https://sid.ir/paper/164723/en

IEEE: Copy

S.H. NASERI, F. TALESHIAN, N.A. TAGHINEZHAD, and F. KHALILI, “QUADRATIC PROGRAMMING WITH FUZZY PARAMETERS: AN EXTENSION PRINCIPLE APPROACH,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 9, no. 4 (35), pp. 9–25, 2013, [Online]. Available: https://sid.ir/paper/164723/en

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