Response to a Note on "A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment"

The research article of Nishad and Abhishekh (Journal of Control, Automation and Electrical Systems 31: 900-911, 2020) proposed a method to solve fully intuitionistic fuzzy transportation problems via new ranking method for intuitionistic fuzzy number (IFN). Nishad and Abhishekh claimed that their proposed ranking method is superior than ranking of different existing researchers such as Nehi (International Journal of Fuzzy Systems 12: 80-86, 2010), Li (Computer and Mathematics with Applications 60: 1557-1570, 2010), Kumar and Kaur (Journal of Applied Research and Technology 11: 381-396, 2013), Wan and Dong (Applied Soft Computing 29: 153-168, 2015), and Prakash et al. (Mathematical Sciences 10: 177-184, 2016). Also, some of ranking method of these existing researchers are incorrect and also not satisfy the general ranking axioms of Wang and Kerre (Fuzzy Sets and Systems 118: 375-385, 2001) method. Comparison Table 1 for IFN have given by Nishad and Abhishekh's (2020) method is incorrect and some IFN are missing by which we cannot properly compare between two IFN. So in this note, a proper comparison ranking Table is given in place of Table 1 of Nishad and Abhishekh's (2020) with comparison along these existing researchers and shows the superiority of the proposed ranking method. Furthermore, Bhatia et al. (Journal of Control, Automation and Electrical Systems. iittps://doi.org/10.1007/s40313-022-00964-5) submitted a note on Nishad and Abhishekh's (2020) publication in the Journal of Control, Automation and Electrical Systems and they claimed that Nishad and Abhishekh's (2020) method is not appropriate to solve fully fuzzy transportation problems in intuitionistic fuzzy environment (FFTPIFL), the claim of the authors are totally based on hypothetical and based on wrong perception about the Nishad and Abhishekh's article. These are the wrong claims of Bhatia et al. (2022) and their consequences are as follows: (i) In line numbers 21 and 27 Bhatia et al. written wrong formula of ranking function defined by Nishad and Abhishekh. (ii) In section 2, line number 9 authors claim that Nishad and Abhishekh take dual problem of fully intuitionistic fuzzy linear programming problem (FIFLPP) by using ranking function defined by Nishad and Abhishekh but in the original paper there is no such transformation of any FIFLPP to its dual problem. (iii) In line 17, Step 1 authors claimed that Nishad and Abhishekh convert the Fl-LPP into crisp linear programming problem by using ranking function defined by them, to solve the problem which is totally wrong claimed about the paper. Nishad and Abhishekh in their paper never convert FIFLPP into crisp linear programming problem. So that claims of the author Bhatia et al. cannot be consider about the validation of Nishad and Abhishekh's Method.