Approaches to Solve Some Mathematical Programming Problems Under Different Fuzzy Environments

Abstract

In this thesis, it is pointed out that (i) Moges et al. (2023)’s method for solving IFMOLFOPs is not valid. Therefore, it is mathematically incorrect to apply it for solving IFMOLFOPs. (ii) Bera and Mondal (2023)’s approach for solving IFMOTP can be used only under a specific condition. (iii) Rani and Manivannan (2024)’s approach for solving GTT2IFTPs is not valid in its present form. Also, a modified approach is proposed for solving GTT2IFTPs. (iv) Khalifa et al. (2021)’s approach for solving inverse NCTPs is not valid in its present form. Also, a modified approach is proposed to resolve the invalidity of Khalifa et al. (2021)’s approach. (v) The recently proposed ZN based approaches (Jiskani et al., 2022; Akram and Ullah, 2024) are not appropriate in their present form. Also, the required modifications are suggested to resolve the inappropriateness of these approaches. (vi) In the existing definition of PFS (Yager, 2013; Yager, 2014), the expression for evaluating the DOND of each element of the universal set is not correct. Also, the correct expression is proposed for the same. (vii) The existing graphical representation of IVIFS (Atanassov and Gargov, 1989) is not appropriate. Also, an appropriate graphical representation of IVIFS is proposed. (viii) The existing definition of IVIFS (Atanassov and Gargov, 1989) is not valid. Also, a valid definition of IVIFS is proposed