Algorithm to Solve Spherical Fuzzy Optimization Problems with Applications
DOI:
https://doi.org/10.24203/8me95f14Keywords:
TORA, SFAP, SFTPAbstract
In operation research, a specific area being analysed in great depth is the optimization problem. The primary objective of this issue is to determine the most economical costs for commodities in order to satisfy customer requirements at various destinations, while taking into account the resources available at their points of origin or deals with assigning tasks to locations. In this paper, the spherical fuzzy optimization problem (SFOP) determines the optimal cost of carrying items from origin to destination (or job to machine). While reliable data is frequently employed, these variables are actually ambiguous and inaccurate. Many generalizations and expansions of fuzzy sets have been proposed and investigated in the literature. The spherical fuzzy set (SFS) is one of the most recent developments in fuzzy sets. It is capable of identifying neutral degrees in addition to membership and non-membership degrees. In this study, a proposed approach is developed to find the solution for each of all three form of the SFOP. For a better understanding, the suggested article includes six solved situations together with screen grabs of the output summaries from the software used for the calculations. Additionally, the unique approach's advantages over the current work are mentioned. Finally, conclusion and future scope direction are also given.
References
[1] R.K. Bera, S.K. Mondal, “Analyzing a Two-Staged Multi Objective Transportation Problem Under Quantity Dependent Credit Period Policy Using q-Fuzzy Number,” Int. J. Appl. Comput. Math., vol. 6, pp. 1–33, 2020.
[2] K. Hemalatha, B. Venkateswarlu, “Pythagorean Fuzzy Transportation Problem: New Way of Ranking for Pythagorean Fuzzy Sets and Mean Square Approach,” Heliyon, vol. 9, no. 10, pp. 1–11, 2023.
[3] L.A. Zadeh, “Fuzzy Sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
[4] S. Chanas, W. Kołodziejczyk, A. Machaj, “A Fuzzy Approach to the Transportation Problem,” Fuzzy Sets Syst., vol. 13, no. 3, pp. 211–221, 1984.
[5] K.N. Das, R. Das, D.P. Acharjya, “Least-Looping Stepping-Stone-Based ASM Approach for Transportation and Triangular Intuitionistic Fuzzy Transportation Problems,” Complex Intell. Syst., vol. 7, pp. 2885–2894, 2021.
[6] Z.H. Radhy, F.H. Maghool, N. Kamal, “Fuzzy-Assignment Model by Using Linguistic Variables,” Baghdad Sci. J., vol. 18, no. 3, pp. 539–542, 2021.
[7] P. Anukokila, B. Radhakrishnan, “Goal Programming Approach to Fully Fuzzy Fractional Transportation Problem,” J. Taibah Univ. Sci., vol. 13, no. 1, pp. 864–874, 2019.
[8] M.A. Mehmood, S. Bashir, “Extended Transportation Models Based on Picture Fuzzy Sets,” Math. Probl. Eng., vol. 2022, no. 1, pp. 1–21, 2022.
[9] R.R. Yager, “Pythagorean Fuzzy Subsets,” in Proc. of IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, IEEE, pp. 57–61, 2013.
[10] M.A. Firozja, B. Agheli, E.B. Jamkhaneh, “A New Similarity Measure for Pythagorean Fuzzy Sets,” Complex Intell. Syst., vol. 6, no. 1, pp. 67–74, 2020.
[11] R. Kumar, S.A. Edalatpanah, S. Jha, R. Singh, “A Pythagorean Fuzzy Approach to the Transportation Problem,” Complex Intell. Syst., vol. 5, no. 2, pp. 255–263, 2019.
[12] B.C. Cuong, “Picture Fuzzy Sets,” J. Comput. Sci. Cybern., vol. 30, no. 4, pp. 409–420, Dec. 2014.
[13] S. Kumar, V. Arya, S. Kumar, A. Dahiya, “A New Picture Fuzzy Entropy and Its Application Based on Combined Picture Fuzzy Methodology with Partial Weight Information,” Int. J. Fuzzy Syst., vol. 24, no. 7, pp. 3208–3225, 2022.
[14] S. Ashraf, S. Abdullah, M. Aslam, M. Qiyas, M.A. Kutbi, “Spherical Fuzzy Sets and its Representation of Spherical Fuzzy t-Norms and t-Conorms,” J. Intell. Fuzzy Syst., vol. 36, no. 6, pp. 6089–6102, 2019.
[15] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, “Spherical Fuzzy Sets and Their Applications in Multi-Attribute Decision Making Problems,” J. Intell. Syst., vol. 36, no. 3, pp. 2829–2844, 2019.
[16] M. Akram, S. Alsulami, A. Khan, F. Karaaslan, “Multi Criteria Group Decision-Making Using Spherical Fuzzy Prioritized Weighted Aggregation Operators,” Int. J. Comput. Intell., vol. 13, no. 1, pp. 1429–1446, 2020.
[17] A. Sarucan, M.E. Baysal, O. Engin, “A Spherical Fuzzy TOPSIS Method for Solving the Physician Selection Problem,” J. Intell. Fuzzy Syst., vol. 42, no. 1, pp. 181–194, 2022.
[18] V. Kumar, A. Gupta, H.C. Taneja, “Solution of Transportation Problem Under Spherical Fuzzy Set,” in Proc. of IEEE 6th Int. Conf. on Computing, Communication and Automation (ICCCA), Arad, Romania, IEEE, pp. 444–448, 2021.
[19] Y.J. Shahzaib Ashraf, S. Abdullah, “Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems,” Int. J. Fuzzy Syst., vol. 21, no. 7, p. 628, 2019.
[20] N. Jam, J. Gwak, S. Hussain, A. Nasir, “Mathematical Investigation of Communication and Network Securities Under Interval-Valued Complex Spherical Fuzzy Information,” J. Intell. Fuzzy Syst., vol. 26, pp. 87–104, 2024.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Sudhir Kumar, Anita Kumari

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.