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 [63] for comparing two IvPyFuNs. Then, an appropriate expression to evaluate sum of IvPyFuNs is proposed. Thereafter, the existing method [78] for comparing two interval-valued intuitionistic fuzzy numbers is extended for comparing two IvPyFuNs. Finally, using the proposed expression as well as the extended method for comparing IvPyFuNs, an efficient method (named as Mehar method) is proposed for solving IvPyFuSpPs. (vi) It is inappropriate to use the existing methods [162, 175] for solving TsFuSpPs. Also, it is pointed out that the reasons for the inappropriateness in the existing methods [162, 175] are the inappropriateness of existing expression [162, 175] to evaluate sum of TsFuNs as well as the inappropriateness of existing methods [162, 175] for comparing two TsFuNs. Then, an appropriate expression to evaluate sum of TsFuNs is proposed. Thereafter, by aggregating the existing methods [5, 115] for comparing two TsFuNs, a new method is proposed for comparing two TsFuNs. Finally, using the proposed expression as well as the proposed method for comparing TsFuNs, an efficient method (named as Mehar method) is proposed for solving TsFuSpPs. (vii) It is inappropriate to use the existing method [100] for solving SvNeLpPs. Also, an efficient method (named as Mehar method) is proposed for solving SvNeLpPs.