A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

• Published in: Asia-Pacific Journal of Operational Research (APJOR) Vol. 24; no. 4; pp. 557 - 573
• Main Authors: ZANGIABADI, M., MALEKI, H. R.
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Co. & Operational Research Society of Singapore 01.08.2007; World Scientific Publishing Co. Pte. Ltd; World Scientific Publishing Co. Pte., Ltd
• Series: Asia-Pacific Journal of Operational Research (APJOR)
• Subjects: fuzzy number; Fuzzy sets; Linear optimization; Linear programming; multiobjective linear programming; Operations research; Optimization; ranking function; Simplex method; Studies; Theorems; ranking function; multiobjective linear programming; Linear optimization; fuzzy number
• ISSN: 0217-5959; 1793-7019; 1793-7019; 0217-5959
• DOI: 10.1142/S0217595907001395

In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.