A note on Taylor series approach to fuzzy multiple objective linear fractional programming
Toksari, in his paper Taylor series approach to fuzzy multiobjective linear fractional programming, published in Information Sciences 178 (2008), proposed a new method to solve multiple objective linear fractional programming problems and declared that it is more effective when compare to previous methods. He constructed fuzzy goals and then used first order Taylor-polynomials to approximate the corresponding linear fractional membership functions by linear functions. Aggregating the linear functions Toksari obtained a crisp linear programming problem and claimed that it is equal to the fuzzy fractional one. In this paper, we indicate the fallacy that arises by using Taylor approximation and propose an improved method that guarantees the efficiency of the solution it provides. Both practical applications from Toksaris paper are recalled to show that the improvements we suggest are effective.
linear fractional programming fuzzy mathematical programming multi-objective optimization