Note on new solutions of LR fuzzy linear systems using ranking functions and ABS algorithms

Abstract

Recently, Ghanbari and Mahdavi-Amiri focused on solving LR fuzzy linear systems by use of ranking functions. They applied a ranking function introduced by Cheng, which is based on the centroid point, to illustrate their method. Also, they presented an important lemma using the centroid formulae provided by Cheng, to determine the centroid point for a class of fuzzy numbers. Unfortunately, they didn’t consider that the formulae are incorrect and have led to some misapplications as pointed out by Wang and his colleagues. Therefore, in this paper, we first show that Lemma 19 of Ghanbari and Mahdavi-Amiri’s paper is not true and then correct it using the centroid formulae suggested by Wang. Finally, we correct the results obtained in Ghanbari and Mahdavi-Amiri’s paper for a special example.