A novel method for solving the fully neutrosophic linear programming problems: Suggested modifications

Article type: Research Article

Authors: Singh, Akanksha^a | Kumar, Amit^a | Appadoo, S.S.^{b; *}

Affiliations: [a] School of Mathematics, Thapar Institute of Engineering and Technology (Deemed to be University), Patiala, Punjab, India | [b] Department of Supply Chain Management, University of Manitoba, Winnipeg, Manitoba, Canada

Correspondence: [*] Corresponding author. S.S. Appadoo, Department of Supply Chain Management, University of Manitoba, 630 Drake Centre – 181 Freedman Crescent, Winnipeg, Manitoba, Canada R3T 5V4. Tel.: +204 474 6870; Fax: +204 474 7545. E-mail: [email protected].

Abstract: Abdel-Basset et al. (Neural Computing and Applications, 2018, https://doi.org/10.1007/s00521-018-3404-6) proposed methods for solving different types of neutrosophic linear programming problems (NLPPs) (NLPPs in which some/all the parameters are represented as trapezoidal neutrosophic numbers (TrNNs)). Abdel-Basset et al. also pointed out that as a trapezoidal fuzzy number is a special case of trapezoidal neutrosophic number. Therefore, the fuzzy linear programming problems which can be solved by the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33) can also be solved by thier proposed method. In addition to that, to show the advantages of their proposed method over the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33), Abdel-Basset et al. solved the same fuzzy linear programming problems by their proposed method as well as the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33) and shown that the results, obtained on applying by their proposed method are better than the results, obtained on applying the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33). After a deep study of Abdel-Basset et al. ’s method, it is observed that Abdel-Basset et al. have considered several mathematical incorrect assumptions in their proposed method and hence, it is scientifically incorrect to use Abdel-Basset et al. ’s method in its present form. The aim of this paper is to make the researchers aware about the mathematical incorrect assumptions, considered by Abdel-Basset et al. in their proposed method, as well as to suggest the required modifications in Abdel-Basset et al. ’s method.

Keywords: Trapezoidal neutrosophic number (TrNNs), linear programming, neutrosophic set, ranking function

DOI: 10.3233/JIFS-181541

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 885-895, 2019