Some Methods for Solving Multi-Attribute Decision Making Problems under Fuzzy Environment and Its Extensions

Abstract

Several methods have been proposed in the literature to solve IFMADMPrs having partially known attribute weights [50, 63, 81, 146, 222-225, 241], IVIFMADMPrs having partially known attribute weights [62, 108, 213, 258], IVPFMADMPrs having partially known attribute weights [84], IVIFMADMPrs having IVIF attribute weights [39-45, 47-49, 52, 55, 127-129, 132, 137, 209 211]. However, after a deep study, it is observed that all these existing methods are inappropriate. Also, it is observed that it is inappropriate to apply the existing method [98] for solving IVIFMAGDM problems having completely unknown attribute weights. Furthermore, it is observed that the existing definition of an IVIFS [9] and the existing definition of an IVPFS [164] are inappropriate. Keeping all above in mind, the aim of this thesis is (i) To point out the inappropriateness of the existing methods [50, 63, 81, 146, 222-225, 241] for solving IFMADMPrs having partially known attribute weights as well as to propose an appropriate method for solving IFMADMPrs having partially known attribute weights. (ii) To point out the inappropriateness of the existing methods [62, 108, 213, 258] for solving IVIFMADMPrs having partially known attribute weights as well as to propose an appropriate method for solving IVIFMADMPrs having partially known attribute weights. (iii) To point out the inappropriateness of the existing methods [84] for solving IVPFMADMPrs having partially known attribute weights as well as to propose an appropriate method for solving IVPFMADMPrs having partially known attribute weights. (iv) To point out the inappropriateness of the existing methods [39-45, 47-49, 52, 55, 127-129, 132, 137, 209- 211] for solving IVIFMADMPrs having IVIF weights as well as to propose an appropriate method for solving IVIFMADMPrs having IVIF weights.

(v) To point out the inappropriateness of the existing method [98] for solving IVIFMAGDM problems having completely unknown weights. Also, to make the researchers aware that it is inappropriate to propose a simplex method for solving an IVIF LPP without transforming it into a CLPP, inspired by Khan et al.’s simplex method [122], for resolving the inappropriateness of the existing method [98] due to the following facts: “Khan et al.’s claim [123] “No mathematical incorrect assumptions have been considered in the existing simplex method [122] for solving a fuzzy LPP without transforming it into a CLPP” against Bhardwaj and Kumar’s claim [16] is not valid. In fact, several mathematical incorrect assumptions, considered by Khan et al. [122], are not pointed out by Bhardwaj and Kumar [16] e.g., Bhardwaj and Kumar have not pointed out that some of the elements of the existing optimal simplex table [122] are not TFNs.” Furthermore, to make the researchers aware that it is not possible to resolve the inappropriateness of the existing methods [98].” (vi) To propose the appropriate definition of an IVIFS. (vii) To propose the appropriate definition of an IVPFS.