On solving fuzzy Linear programming problems: A revisit to zimmermann's approach

Article type: Research Article

Authors: Chandra, S. | Aggarwal, A.

Affiliations: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India | University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Delhi, India

Note: [] Corresponding author. S. Chandra, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. Tel.: +91 11 22796445; E-mails: [email protected]; [email protected] (A. aggarwal).

Abstract: The celebrated Zimmermann's approach for solving fuzzy linear programming problems is re-looked and apparently a new formulation leading to a new interpretation is presented. The basic feature of this formulation is that it attempts to trade-off between the twin objectives of ‘satisfaction of fuzzy constraints’ and ‘attainment of the aspiration level of the objective function’. For this a bi-objective optimization problem involving these twin objectives is constructed and its efficient solution is interpreted as a solution of the given fuzzy linear programming problem. As an outcome of this study a new two phase approach to solve fuzzy linear programming problems is obtained. This new two phase approach is different from those available in the literature and is in the true spirit of conventional two phase approach for solving crisp linear programming problems. Further, two additional models are also proposed on similar lines which also provide an efficient solution of the bi-objective optimization problem under consideration. Certain small numerical examples are included to illustrate the results.

Keywords: Fuzzy optimization, fuzzy goals, fuzzy decision

DOI: 10.3233/IFS-141233

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 5, pp. 2603-2610, 2014