A Novel Approach for Solving the Triangular Fuzzy Neutrosophic Assignment Problem
DOI:
https://doi.org/10.2298/YJOR240316025SKeywords:
Neutrosophic number, triangular fuzzy neutrosophic number, triangular fuzzy Neutrosophic Assignment problem, score function, range, optimal solutionAbstract
The assignment problem (AP) is a fundamental challenge in linear programming and operations research focused on optimizing assignments to minimize costs or maximize profits. This study extends the traditional AP to address uncertainties and ambiguities through the neutrosophic assignment problem (NAP). Further advancing this concept, the triangular fuzzy neutrosophic assignment problem (TFNAP) is introduced, utilizing triangular fuzzy neutrosophic numbers (TFNNs) to represent fuzziness and neutrosophy, thus offering a more comprehensive depiction of uncertainty and indeterminacy. The primary aim of this research is to identify the optimal assignment that either minimizes cost or maximizes profit within the TFNAP framework, a task known for its computational complexity. The TFNAP is represented through a triangular fuzzy neutrosophic assignment matrix (TFNAM), which employs TFNNs as its core elements. This study develops and refines algorithms tailored to address these complexities, ensuring originality through a stepwise procedure that simplifies computations in a neutrosophic manner. The methodology includes resolving the problem using a neutrosophic approach and incorporating a score function to convert triangular fuzzy neutrosophic values to their equivalent crisp numbers for comparative purposes. The proposed method’s effectiveness is validated through its application to real-world problems, with the results compared against previously established solutions. The findings demonstrate that the TFNAP framework provides more accurate and insightful outcomes in dealing with uncertainties compared to traditional methods. This study introduces significant innovations in handling ambiguity and indeterminacy in assignment problems, offering a robust tool for optimization in complex, uncertain environments. Conclusively, the developed approach not only enhances the understanding of neutrosophic assignments but also presents a practical solution for real-world applications.References
L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338-353, 1965.
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
F. Smarandache, “Neutrosophic set-a generalization of the intuitionistic fuzzy set,” in 2006 IEEE international conference on granular computing. IEEE, 2006, pp. 38-42.
S. K. De and S. Nandi, “The exact defuzzification method under polynomial approximation of various fuzzy sets,” Yugoslav Journal of Operations Research, vol. 34, no. 1, pp. 51-72, 2023.
M. Kamran, S. Ashraf, and M. Naeem, “A promising approach for decision modeling with single-valued neutrosophic probabilistic hesitant fuzzy dombi operators,” Yugoslav Journal of Operations Research, vol. 33, no. 4, pp. 549-575, 2023.
P. Biswas, S. Pramanik, and B. C. Giri, “Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making,” Neutrosophic sets and systems, vol. 12, pp. 20-40, 2016.
I. Irvanizam, N. N. Zi, R. Zuhra, A. Amrusi, and H. Sofyan, “An extended mabac method based on triangular fuzzy neutrosophic numbers for multiple-criteria group decision making problems,” Axioms, vol. 9, no. 3, p. 104, 2020.
S. K. Das, S. Edalatpanah et al., “A new ranking function of triangular neutrosophic number and its application in integer programming,” International Journal of Neutrosophic Science, vol. 4, no. 2, pp. 82-92, 2020.
S. Geetha and S. Narayanamoorthy, “Superiority and inferiority ranking method with hesitant pythagorean fuzzy set for solving mcdm problems,” Malaya J. Mat, vol. 1, pp. 11-15, 2020.
S. Geetha, S. Narayanamoorthy, D. Kang, and D. Baleanu, “An adoptive renewable energy resource selection using hesitant pythagorean fuzzy dematel and vikor methods,” Journal of Intelligent & Fuzzy Systems, vol. 43, no. 4, pp. 4285-4302, 2022.
A. Chakraborty, S. P. Mondal, A. Ahmadian, N. Senu, S. Alam, and S. Salahshour, “Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications,” Symmetry, vol. 10, no. 8, p. 327, 2018.
S. Dhouib, “Solving the trapezoidal fuzzy transportation problems via new heuristic: the dhouib-matrix-tp1,” International Journal of Operations Research and Information Systems (IJORIS), vol. 12, no. 4, pp. 1-16, 2021.
K. P. Sikkannan and V. Shanmugavel, “Sorting out fuzzy transportation problems via ecct and standard deviation,” International Journal of Operations Research and Information Systems (IJORIS), vol. 12, no. 2, pp. 1-14, 2021.
S. Narayanamoorthy and S. Kalyani, “Finding the initial basic feasible solution of a fuzzy transportation problem by a new method,” International Journal of Pure and Applied Mathematics, vol. 101, no. 5, pp. 687-692, 2015.
J. Pratihar, R. Kumar, A. Dey, and S. Broumi, “Transportation problem in neutrosophic environment,” in Neutrosophic graph theory and algorithms. IGI Global, 2020, pp. 180-212.
S. Subasri and K. Selvakumari, Solving neutrosophic travelling salesaman problem in triangular fuzzy number using ones assignment method. Infinite Study, 2018.
S. Dhouib, “Optimization of travelling salesman problem on single valued triangular neutrosophic number using dhouib-matrix-tsp1 heuristic,” International Journal of Engineering, vol. 34, no. 12, pp. 2642-2647, 2021.
S. Subasri and K. Selvakumari, “Neutrosophic travelling salesman problem in trapezoidal fuzzy number using branch and bound technique,” in Journal of Physics: Conference Series, vol. 1362, no. 1. IOP Publishing, 2019, p. 012098.
S. Dhouib, “Neutrosophic triangular fuzzy travelling salesman problem based on dhouibmatrix- tsp1 heuristic,” International Journal of Computer and Information Technology (2279- 0764), vol. 10, no. 5, 2021.
D. H. D. Afroz and M. A. Hossen, “Divide column and subtract one assignment method for solving assignment problem,” American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), vol. 32, no. 1, pp. 289-297, 2017.
T. Esakkiammal et al., “Mass-a new ones assignment method for finding optimal solution of assignment problems,” Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 12, no. 10, pp. 2737-2744, 2021.
R. Kar and A. K. Shaw, “A new approach to find optimal solution of assignment problem using hungarian method by triangular fuzzy data.” Mathematics in Engineering, Science & Aerospace (MESA), vol. 11, no. 4, 2020.
S. Muruganandam and K. Hema, “Solving fully fuzzy assignment problem using branch and bound technique,” Global Journal of Pure and Applied Mathematics, vol. 13, no. 9, pp. 4515- 4522, 2017.
S. Dhouib, “Unravelling the assignment problem under intuitionistic triangular fuzzy environment by the novel heuristic dhouib-matrix-ap1,” Yugoslav Journal of Operations Research, vol. 33, no. 3, pp. 467-480, 2023.
M. Lone, S. Mir, Y. Ismail, and R. Majid, “Intustinistic fuzy assignment problem, an application in agriculture,” Asian Journal of Agricultural Extension, Economics and Socialogy, vol. 15, no. 4, pp. 1-6, 2017.
B. Srinivas and G. Ganesan, “A method for solving intuitionistic fuzzy assignment problem using branch and bound method,” International Journal of Engineering Technology Management and Applied Sciences, vol. 3, no. 2, 2015.
T. Bera and N. K. Mahapatra, “Assignment problem with neutrosophic costs and its solution methodology,” Asia Mathematika, vol. 3, no. 1, pp. 21-32, 2019.
S. K. Prabha and S. 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. Springer, 2018, pp. 323-330.
R. Mallick, S. Pramanik, and B. C. Giri, “Neutrosophic magdm based on critic-edas strategy using geometric aggregation operator,” Yugoslav journal of operations research, vol. 33, no. 4, pp. 683-698, 2023.
M. Abdel-Basset, M. Mohamed, A.-N. Hussien, and A. K. Sangaiah, “A novel group decisionmaking model based on triangular neutrosophic numbers,” Soft Computing, vol. 22, pp. 6629- 6643, 2018.
W. Yang, L. Cai, S. A. Edalatpanah, and F. Smarandache, “Triangular single valued neutrosophic data envelopment analysis: application to hospital performance measurement,” Symmetry, vol. 12, no. 4, p. 588, 2020.
A. Hamza, M. N. Jafar, A. Habib, S. Farooq, E. T¨urkarslan et al., “Cryptography in terms of triangular neutrosophic numbers with real life applications,” Int. J. Neutrosophic Sci, vol. 11, pp. 39-52, 2021.
B. Xie, “Modified gra methodology for madm under triangular fuzzy neutrosophic sets and applications to blended teaching effect evaluation of college english courses,” Soft Computing, pp. 1-12, 2023.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
