FUZZY APPROACHES TO THE MULTI OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM INCLUDING INTERVAL COEFFICIENTS

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Published: 2015-05-19

Page: 83-94


MOJTABA BORZA *

School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia.

AZMIN SHAM RAMBELY

School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia.

MANSOUR SARAJ

Department of Mathematics, Faculty of Mathematical Sciences & Computer, Shahid Chamran University, Ahvaz, Iran.

*Author to whom correspondence should be addressed.


Abstract

In this paper, weighted sum and goal programming approach are considered to address multi-objective linear fractional programming problems including interval coefficients in the objective functions. The membership functions are defined after identifying fuzzy goals of the objective functions. Using first-order Taylor series transforms the fractional membership functions into linear functions for the weighted sum approach. Maximizing the sum of the linearzed functions yields the results of the solution. The membership functions are transformed by the use of suitable variable transformations in the goal programming approach. The sum of the deviational variables of the membership functions to their aspiration levels is minimized to achieve the solution. Numerical examples demonstrate the feasibility and effectiveness of the methods.

Keywords: Membership function, fuzzy goal, pareto optimal solution, Taylor series, interval operations


How to Cite

BORZA, M., RAMBELY, A. S., & SARAJ, M. (2015). FUZZY APPROACHES TO THE MULTI OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM INCLUDING INTERVAL COEFFICIENTS. Asian Journal of Mathematics and Computer Research, 4(2), 83–94. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/76

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