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International Journal of Neutrosophic Science
Volume 21 , Issue 4, PP: 94-105 , 2023 | Cite this article as | XML | Html |PDF

Title

A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments

  Shubham Kumar Tripathi 1 * ,   Ranjan Kumar 2

1  School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
    (shubhamt.vit22@gmail.com)

2  School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
    (ranjank.nit52@gmail.com)


Doi   :   https://doi.org/10.54216/IJNS.210410

Received: January 26, 2023 Revised: May 27, 2023 Accepted: July 18, 2023

Abstract :

This review article focuses on the integration of Neutrosophic Set Theory and Extended Fuzzy Set Theory in the context of Linear Programming (LP) problems. Neutrosophic set theory deals with uncertain, imprecise, and indeterminate information, while Extended Fuzzy Set Theory extends the classical fuzzy set theory to handle more complex and nuanced membership degrees. The combination of these two frameworks provides a powerful toolset for modeling and solving LP problems in environments where uncertainty and ambiguity are prevalent. This review aims to analyze and summarize the existing literature on Neutrosophic Linear Programming problems in extended fuzzy environments, exploring the theoretical foundations and practical applications. The review article seeks to contribute to the understanding of these integrated approaches and their potential for addressing decision-making problems under complex and uncertain conditions.

Keywords :

Operational research; Linear Programming problems; Uncertainty principle; fuzzy LP problems; Membership function; Extended fuzzy; NLPP.

References :

[1] Taha HA. Operations Research: An Introduction. Pearson Education India, 2013.

[2] VK Kapoor. Operations research techniques for management. Sultan Chand & Sons., New Delhi, 2003.

[3] Yaghini M; Momeni M; Sarmadi M. Solving train formation problem using simulated annealing algorithm in a simplex framework. Journal of Advanced Transportation, 48(5):402–416, 2014.

[4] Li Y; Tarlow D; Brockschmidt M; Zemel R. Gated graph sequence neural networks. 2015.

[5] Liu M; Wang S;Zheng F;Chu C. Algorithms for the joint multitasking scheduling and common due date assignment problem. International Journal of Production Research, 55(20):6052–6066, 2017.

[6] S; Oberoi T; Sharma T; Thakkar A Jhawar, S; Agarwaal. Application of game theory in water resource management. International Journal of Advance Research and Development, 3(10):63–8, 2018.

[7] N; SchmidtMBouman, P; Agatz. Dynamic programming approaches for the traveling salesman problem with drone. Networks, 72(4):528–542, 2018.

[8] Lotfi A Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.

[9] Nidhi Singh, Avishek Chakraborty, Soma Bose Biswas, and Malini Majumdar. Impact of social media in banking sector under triangular neutrosophic arena using mcgdm technique. Neutrosophic Sets And Systems, 35:153–176, 2020.

[10] RR Yager. A procedure for ordering fuzzy subsets of the unit interval. Information sciences, 24(2):143– 161, 1981.

[11] DJ Dubois. Fuzzy sets and systems: theory and applications, volume 144. Academic press, 1980.

[12] HJ Zimmermann. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1):45–55, 1978.

[13] FH;Kiani NA Sigarpich LA; Allahviranloo, T;Lotfi. Degeneracy in fuzzy linear programming and its application. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(06):999– 1012, 2011.

[14] Cagatay Iris and Emre Cevikcan. A fuzzy linear programming approach for aggregate production planning. Supply Chain Management Under Fuzziness: Recent Developments and Techniques, pages 355– 374, 2014.

[15] Shu-Ping Wan and Jiu-Ying Dong. Possibility method for triangular intuitionistic fuzzy multi-attribute group decision making with incomplete weight information. International Journal of Computational Intelligence Systems, 7(1):65–79, 2014.

[16] Xuelei Meng, Bingmou Cui, et al. Train repathing in emergencies based on fuzzy linear programming. The Scientific World Journal, 2014, 2014.

[17] JL Ebrahimnejad, A; Verdegay. A survey on models and methods for solving fuzzy linear programming problems. Fuzzy Logic in Its 50th Year New Developments, Directions and Challenges, pages 327–368, 2016.

[18] Krassimir T Atanassov and S Stoeva. Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1):87–96, 1986.

[19] N;Mishra Vishnu N Sharma, MK;Dhiman. Mediative fuzzy logic mathematical model: A contradictory management prediction in covid-19 pandemic. Applied Soft Computing, 105:107285, 2021.

[20] Florentin Smarandache. A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, 1999.

[21] M;Mohamed M;Smarandache F Abdel-Basset, M;Gunasekaran. A novel method for solving the fully neutrosophic linear programming problems. Neural Computing And Applications, 31:1595–1605, 2019.

[22] S Prabha, SK; Vimala. Neutrosophic assignment problem via bnb algorithm. In Advances in Algebra and Analysis: International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017-Volume I, pages 323–330. Springer, 2018.

[23] NK Bera T;Mahapatra. On solving linear programming problem by duality approach in neutrosophic environment. International Journal of Mathematics in Operational Research, 18(3):310–335, 2021.

[24] H Yao, Z; Ran. Operational efficiency evaluation of urban and rural residents’ basic pension insurance system based on the triangular fuzzy neutrosophic gra method. Journal of Intelligent and Fuzzy Systems, (Preprint):1–12, 2023.

[25] BC Pramanik S; banerjee D; giri. TOPSIS approach for multi attribute group decision making in refined neutrosophic environment. Infinite Study, 2016.

[26] Tuhin Bera and Nirmal Kumar Mahapatra. To solve assignment problem by centroid method in neutrosophic environment. TIF, page 84, 2020.

[27] Jun Ye. Neutrosophic number linear programming method and its application under neutrosophic number environments. Soft Computing, 22:4639–4646, 2018.

[28] SA Edalatpanah et al. A direct model for triangular neutrosophic linear programming. International Journal Of Neutrosophic Science, 1(1):19–28, 2020.

[29] Tuhin Bera and Nirmal Kumar Mahapatra. Neutrosophic linear programming problem and its application to real life. Afrika Matematika, 31(3-4):709–726, 2020.


Cite this Article as :
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MLA Shubham Kumar Tripathi, Ranjan Kumar. "A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments." International Journal of Neutrosophic Science, Vol. 21, No. 4, 2023 ,PP. 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)
APA Shubham Kumar Tripathi, Ranjan Kumar. (2023). A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)
Chicago Shubham Kumar Tripathi, Ranjan Kumar. "A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments." Journal of International Journal of Neutrosophic Science, 21 no. 4 (2023): 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)
Harvard Shubham Kumar Tripathi, Ranjan Kumar. (2023). A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)
Vancouver Shubham Kumar Tripathi, Ranjan Kumar. A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments. Journal of International Journal of Neutrosophic Science, (2023); 21 ( 4 ): 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)
IEEE Shubham Kumar Tripathi, Ranjan Kumar, A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments, Journal of International Journal of Neutrosophic Science, Vol. 21 , No. 4 , (2023) : 94-105 (Doi   :  https://doi.org/10.54216/IJNS.210410)