Abstract
This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.
Highlights
The modeling of a real life optimization problem in general needs to address several objective functions and become a multiobjective programming problem in a natural way
The goal programming developed by Charnes and Cooper [1] emerged a powerful tool to solve such multiobjective programming problems
It undoubtedly established that goal programming has been one of the major breakthroughs in dealing with multi objective linear programming problems but still it fails to deal with situa
Summary
In view of resolving this difficulty of setting appropriate priority and aspiration levels to various objective functions, Mohanty and Vijayraghavan [10] gave a fuzzy approach to multiobjective linear programming problem to get an equivalent goal programming problem by developing a method to compute appropriate priority levels. The subject has been vastly envisaged by several workers and various approaches have been developed to solve fractional programming problems by fuzzy goal programming method given by Mehrjerdi [31], Singh and Kumar [32], Biswas and Dewan [33] and Ohta and Yamaguchi [34]. Motivated with above studies, we have extended the work of Ohta and Yamaguchi [34] to solve the fractional goal programming problem with imprecise parameters by computing the appropriate priority and weight to each goals to find optimal solution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
