A New Algorithm for Finding Initial Basic Feasible Solution of Spherical Fuzzy Transportation Problem with Applications
DOI:
https://doi.org/10.21123/bsj.2024.11263Keywords:
Initial basic feasible solution, MODI method, Spherical fuzzy sets, Spherical fuzzy transportation problem, Transportation problemAbstract
In operation research, a specific area being analyzed in great depth is the transportation problem (TP). The key objective of this problem is to find the lowest total transportation costs for commodities to meet consumer requirements at destinations incorporating resources acquired at their points of origin. In this work, the spherical fuzzy transportation problem (SFTP) determines the lowest cost of carrying items from origin to destination. Most of the time, accurate data has been used, but these variables are actually inaccurate and ambiguous. According to the literature, several generalizations and expansions of fuzzy sets have been proposed and investigated. One of the most recent innovations in fuzzy sets is the spherical fuzzy sets (SFSs), which characterize not only membership and non-membership degrees but also neutral degrees. In this study, a novel approach is developed to derive the initial basic feasible solution (IBFS) for each of all three forms of the SFTP, and then obtain an optimal answer by applying the modified distribution (MODI) technique. For such frameworks, the proposed approach is illustrated by numerical examples. The conclusion and future scope are given at the end.
Received 26/03/2024
Revised 21/06/2024
Accepted 23/06/2024
Published Online First 20/12/2024
References
Bera RK, Mondal SK. Analyzing a Two-Staged Multi-Objective Transportation Problem Under Quantity Dependent Credit Period Policy Using q-Fuzzy Number. Int J Appl Comput Math. 2020; 6: 1-33. https://doi.org/10.1007/s40819-020-00901-7.
Hemalatha K, Venkateswarlu B. Pythagorean Fuzzy Transportation Problem: New Way of Ranking for Pythagorean Fuzzy Sets and Mean Square Approach. Heliyon. 2023; 9(10): 1-11. https://doi.org/10.1016/j.heliyon.2023.e20775.
Zadeh LA. Fuzzy Sets. Inf control. 1965; 8(3): 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X. Atanassov KT. Intuitionistic Fuzzy Sets. Fuzzy Sets Syst. 1986; 20(1): 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3 .
Chanas S, Kołodziejczyk W, Machaj A. A Fuzzy Approach to the Transportation Problem. Fuzzy Sets Syst. 1984; 13(3): 211-221. https://doi.org/10.1016/0165-0114(84)90057-5 .
Das KN, Das R, Acharjya DP. Least-Looping Stepping-Stone-Based ASM Approach for Transportation and Triangular Intuitionistic Fuzzy Transportation Problems. Complex Intell Syst. 2021; 7: 2885-2894. https://doi.org/10.1007/s40747-021-00472-0.
El Sayed MA, Abo-Sinna MA. A Novel Approach for Fully Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem. Alex Eng J. 2021; 60(1): 1447-1463. https://doi.org/10.1016/j.aej.2020.10.063 .
Radhy ZH, Maghool FH, Kamal N. Fuzzy-Assignment Model by Using Linguistic Variables. Baghdad Sci J. 2021; 18(3): 539-542. http://dx.doi.org/10.21123/bsj.2021.18.3.0539.
Bagheri M, Ebrahimnejad A, Razavyan S, Lotfi FH, Malekmohammadi N. Fuzzy Arithmetic DEA Approach for Fuzzy Multi-Objective Transportation Problem. Oper Res Int J. 2022; 22: 1479-1509. https://doi.org/10.1007/s12351-020-00592-4.
Bharati SK, Singh SR. Transportation Problem Under Interval-Valued Intuitionistic Fuzzy Environment. Int J Fuzzy Syst. 2018; 20: 1511-1522. https://doi.org/10.1007/s40815-018-0470-y.
Anukokila P, Radhakrishnan B. Goal Programming Approach to Fully Fuzzy Fractional Transportation Problem. J Taibah Univ SCI. 2019; 13(1): 864-874. https://doi.org/10.1080/16583655.2019.1651520.
Gupta S, Ali I, Ahmed A. Efficient Fuzzy Goal Programming Model for Multi-Objective Production Distribution Problem. Int J Appl Comput Math. 2018; 4: 1-19. https://doi.org/10.1007/s40819-018-0511-0.
Kamini, Sharma MK. Zero-Point Maximum Allocation Method for Solving Intuitionistic Fuzzy Transportation Problem. Int J Appl Comput Math. 2020; 6: 1-11. https://doi.org/10.1007/s40819-020-00867-6
Maheswari PU, Ragavendirane MS, Ganesan K. A Max-Min Average Method for Solving Fuzzy Transportation Problems with Mixed Constraints Involving Generalized Trapezoidal Fuzzy Numbers. 2nd International Conference on Mathematical Techniques and Applications: ICMTA 2021, 24–26 March 2021, Kattankulathur, India. AIP Conf Proc. Nov 2022; 2516(1). https://doi.org/10.1063/5.0108900.
Dhanasekar S, Hariharan S, Gururaj DM. Fuzzy Zero Suffix Algorithm to Solve Fully Fuzzy Transportation Problems by Using Element-Wise Operations. Ital J Pure Appl Math. 2020; (43): 256-267.
Wang K, Wang Y, Yang Y, Goh M. A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion with Irregular Fuzzy Variables. IEEE Access. 2020; 8: 110306-110315. https://doi.org/10.1109/ACCESS.2020.3001589 .
Pratihar J, Kumar R, Edalatpanah SA, Dey A. Modified Vogel’s Approximation Method for Transportation Problem Under Uncertain Environment. Complex Intell Syst. 2021; 7(1): 29-40. https://doi.org/10.1007/s40747-020-00153-4.
Buvaneshwari TK, Anuradha D. Solving Stochastic Fuzzy Transportation Problem with Mixed Constraints Using the Weibull Distribution. J Math. 2022; 2022(1): 1-11. https://doi.org/10.1155/2022/6892342.
Juman ZAMS, Mostafa SA, Batuwita AP, AlArjani A, Sharif Uddin M, Jaber MM, et al. Close Interval Approximation Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems. Sustainability. 2022; 14(12): 7423. https://doi.org/10.3390/su14127423.
Bisht DCS, Srivastava PK. Trisectional Fuzzy Trapezoidal Approach to Optimize Interval Data Based Transportation Problem. J King Saud Univ Sci. 2020; 32(1): 195-199. https://doi.org/10.1016/j.jksus.2018.04.013 .
Chhibber D, Bisht DCS, Srivastava, PK. Pareto-Optimal Solution for Fixed-Charge Solid Transportation Problem under Intuitionistic Fuzzy Environment. Appl Soft Comput. 2021; 107: 107368. https://doi.org/10.1016/j.asoc.2021.107368 .
Aktar MS, De M, Maity S, Mazumder SK, Maiti M. Green 4D Transportation Problems with Breakable Incompatible Items under Type-2 Fuzzy-Random Environment. J Clean Prod. 2020; 275: 122376. https://doi.org/10.1016/j.jclepro.2020.122376.
Singh G, Singh A. Extension of Particle Swarm Optimization Algorithm for Solving Transportation Problem in Fuzzy Environment. Appl Soft Comput. 2021; 110: 107619. https://doi.org/10.1016/j.asoc.2021.107619 .
Kacher Y, Singh P. Fuzzy Harmonic Mean Technique for Solving Fully Fuzzy Multi-Objective Transportation Problem. J Comput Sci. 2022; 63: 101782. https://doi.org/10.1016/j.jocs.2022.101782 .
Mohammed RT, Yaakob R, Sharef NM, Abdullah R. Unifying The Evaluation Criteria Of Many Objectives Optimization Using Fuzzy Delphi Method. Baghdad Sci J. 2021; 18(4(Suppl.)): 1423-1430. https://dx.doi.org/10.21123/bsj.2021.18.4(Suppl.).1423.
Mehmood MA, Bashir S. Extended Transportation Models Based on Picture Fuzzy Sets. Math Probl Eng. 2022; 2022(1): 1-21. https://doi.org/10.1155/2022/6518976.
Yager RR. Pythagorean Fuzzy Subsets. IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 24-28 June, Edmonton, AB, Canada. IEEE. 2013; 57-61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375 .
Firozja MA, Agheli B, Jamkhaneh EB. A New Similarity Measure for Pythagorean Fuzzy Sets. Complex Intell. Syst. 2020; 6(1): 67-74. https://doi.org/10.1007/s40747-019-0114-3.
Kumar R, Edalatpanah SA, Jha S, Singh R. A Pythagorean Fuzzy Approach to the Transportation Problem. Complex Intell Syst. 2019; 5(2): 255-263. https://doi.org/10.1007/s40747-019-0108-1.
Cuong BC. Picture Fuzzy Sets. J Comput Sci Cybern. 2014 Dec; 30(4): 409-420. https://doi.org/10.15625/1813-9663/30/4/5032 .
Kumar S, Arya V, Kumar S, Dahiya A. A New Picture Fuzzy Entropy and Its Application Based on Combined Picture Fuzzy Methodology with Partial Weight Information. Int J Fuzzy Syst. 2022; 24(7): 3208-3225. https://doi.org/10.1007/s40815-022-01332-w.
Ashraf S, Abdullah S, Aslam M, Qiyas M, Kutbi MA. Spherical Fuzzy Sets and its Representation of Spherical Fuzzy t-Norms and t-Conorms. J Intell Fuzzy Syst. 2019; 36(6): 6089-6102. https://doi.org/10.3233/JIFS-181941 .
Ashraf S, Abdullah S, Mahmood T, Ghani F, Mahmood T. Spherical Fuzzy Sets and Their Applications in Multi-Attribut Decision Making Problems. J ntell Fuzzy Syst. 2019; 36(3): 2829-2844. https://doi.org/10.3233/JIFS-172009 .
Akram M, Alsulami S, Khan A, Karaaslan F. Multi-Criteria Group Decision-Making Using Spherical Fuzzy Prioritized Weighted Aggregation Operators. Int J Comput Intell. 2020; 13(1): 1429-1446. https://doi.org/10.2991/ijcis.d.200908.001.
Garg H, Sharaf IM. A New Spherical Aggregation Function with the Concept of Spherical Fuzzy Difference for Spherical Fuzzy EDAS and its Application to Industrial Robot Selection. Comput Appl Math. 2022; 41(5): 1-26. https://doi.org/10.1007/s40314-022-01903-5 .
Akram M, Zahid K, Kahraman C. Integrated Outranking Techniques Based on Spherical Fuzzy Information for the Digitalization of Transportation System. Appl Soft Comput. 2023; 134: 109992. https://doi.org/10.1016/j.asoc.2023.109992.
Mathew M, Chakrabortty RK, Ryan MJ. A Novel Approach Integrating AHP and TOPSIS under Spherical Fuzzy Sets for Advanced Manufacturing System Selection. Eng Appl Artif Intell. 2020; 96: 103988. https://doi.org/10.1016/j.engappai.2020.103988 .
Donyatalab Y, Seyfi-Shishavan SA, Farrokhizadeh E, Kutlu Gündoğdu F, Kahraman C. Spherical Fuzzy Linear Assignment Method for Multiple Criteria Group Decision-Making Problems. Informatica. 2020; 31(4): 707-722. https://doi.org/10.15388/20-INFOR433 .
Sarucan A, Baysal ME, Engin O. A Spherical Fuzzy TOPSIS Method for Solving the Physician Selection Problem. J Intell Fuzzy Syst. 2022; 42(1): 181-194. https://doi.org/10.3233/JIFS-219185.
Ajay D, Selvachandran G, Aldring J, Thong PH, Son LH, Cuong BC. Einstein Exponential Operation Laws of Spherical Fuzzy Sets and Aggregation Operators in Decision Making. Multimed Tools Appl. 2023; 82: 41767–41790. https://doi.org/10.1007/s11042-023-14532-9.
Wei G, Wang J, Lu M, Wu J, Wei C. Similarity Measures of Spherical Fuzzy Sets Based on Cosine Function and Their Applications. IEEE Access. 2019; 7: 159069-159080. https://doi.org/10.1109/ACCESS.2019.2949296 .
Kumar V, Gupta A, Taneja HC. Solution of Transportation Problem Under Spherical Fuzzy Set. In 2021 IEEE 6th International Conference on Computing, Communication and Automation (ICCCA), 17-19 December 2021, Arad, Romania. IEEE. 2021; 444-448.
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