Efficient Methods for Solving some Optimization Problems under Fuzzy Environment and Their Extensions

Abstract

After reviewing the literature, it may be concluded that (i) Only the existing methods [9, 10, 110] are proposed for solving FlFuLFtPs. (ii) There does not exist any method except Mahmoodirad et al. s method [117] for solving FuLFMiCfPs. (iii) Only the existing methods [102, 127, 163] are proposed for solving PyFuTpS (transportation problems in which the transportation cost for supplying one unit quantity of the product from a source to a destination is represented by a PyFuN. While, all other parameters are represented by a non-negative real number). (iv) There does not exist any method except Ebrahimnejad et al. s method [57] for solving IvTFuSpPs. (v) There does not exist any method except Enayattabar et al. s method [63] for solving IvPyFuSpPs. (vi) Only the existing methods [162, 175] are proposed for solving TsFuSpPs. (vii) Only the existing method [100] is proposed for solving SvNeLpPs by considering the attitude of the decision maker towards the risk. In this thesis, it is pointed out that (i) It is inappropriate to use the existing methods [9, 10, 110] for solving FlFuLFtPs. Also, an efficient method (named as Mehar method) is proposed for solving FlFuLFtPs. (ii) It is inappropriate to use the existing method [117] for solving FuLFMiCfPs. Also, an efficient method (named as Mehar method) is proposed for solving FuLFMiCfPs. (iii) It is inappropriate to use the existing methods [102, 127, 163] for solving PyFuTpS. Also, an efficient method (named as Mehar method) is proposed for solving PyFuTpS. (iv) Much computational efforts are required to apply Ebrahimnejad et al. s method [57] for solving IvTFuSpPs. Also, an efficient method (named as Mehar method) is proposed for solving IvTFuSpPs. (v) It is inappropriate to use Enayattabar et al. s method [63] for solving IvPyFuSpPs. Also, it is pointed out that the reasons for the inappropriateness in Enayattabar et al. s method [63] are the inappropriateness of existing expression [63] to evaluate sum of IvPyFuNs as well as the inappropriateness of existing method