Methods to solve QPPs with fuzzy parameters and fuzzy variables

Article type: Research Article

Authors: Mahajan, Sumati^{; *} | Gupta, S.K.

Affiliations: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

Correspondence: [*] Corresponding author. Sumati Mahajan, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India. E-mail: sumatimahajan@pec.ac.in.

Abstract:  Quadratic programming is a special form of nonlinear programming and one of the most commonly used forms too. Linear programming is also none other than a particular case of quadratic programming. Ever-present impreciseness often makes way for natural inclination to fuzzy theory. In this paper, we intend to solve a quadratic programming problem (QPP) involving fuzzy parameters and fuzzy variables. We propose two approaches to solve such a QPP having not only fuzzy parameters in the objective function and constraints but fuzzy variables as well. This fully fuzzy QPP is eventually reduced to a crisp QPP and the solution is obtained in the form of fuzzy variables, first directly and later by applying Karush- Kuhn Tucker conditions. The proposed methods are also illustrated by some numerical examples.

Keywords: Quadratic programming, fuzzy parameters, fuzzy variables, KKT conditions, positive definite

DOI: 10.3233/JIFS-18692

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 2, pp. 2757-2767, 2019