A note on “A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem”

Abstract

Moges et al. (Inf. Sci. 625 (2023) 457–475) proposed a method to find a Pareto-optimal solution (POS) of intuitionistic fuzzy multi-objective linear fractional optimization problem (MOLFOP). In this method, firstly, an intuitionistic fuzzy MOLFOP is transformed into a crisp MOLFOP with the help of a ranking function. Then, using the existing method (Fuzzy Sets Syst. 125 (2002) 335–342), the transformed crisp MOLFOP is transformed into a crisp multi-objective linear optimization problem (MOLOP). Finally, it is assumed that to find a POS of the considered intuitionistic fuzzy MOLFOP is equivalent to find a POS of the transformed crisp MOLOP. It is pertinent to mention that this assumption is valid only if the transformed crisp MOLFOP is equivalent to the considered intuitionistic fuzzy MOLFOP as well as the transformed crisp MOLOP is equivalent to the transformed crisp MOLFOP. In this note, a numerical example is considered to show that the transformed crisp MOLFOP is not equivalent to the considered intuitionistic fuzzy MOLFOP. Also, on the basis of the existing results (Fuzzy Sets Syst. 246 (2014) 156–159), it is pointed out that the transformed crisp MOLOP is not equivalent to the transformed crisp MOLFOP. Therefore, Moges et al.’s method is not valid and hence, the results of agricultural planning problem of Ethopia for cultivation of different crops, obtained by Moges et al. with their proposed method, are not correct.