A Comparative Study of MCDM Approaches: Exploring the Influence of Additional Parameters in Mathematics

Authors

  • G Aruna * PG and Research Department of Mathematics, Auxilium College (Autonomous), Affiliated to Thiruvalluvar University, Gandhi Nagar, Vellore, 632006, Tamil Nadu, India.
  • J Jesintha Rosline PG and Research Department of Mathematics, Auxilium College (Autonomous), Affiliated to Thiruvalluvar University, Gandhi Nagar, Vellore, 632006, Tamil Nadu, India.

https://doi.org/10.22105/opt.v2i3.88

Abstract

This article introduces a Multi-Criteria decision-making approach that utilizes a scoring function within a bipolar fuzzy framework. TOPSIS is one of the most effective techniques for identifying the best solution. To achieve this, we examined the TOPSIS method along with bipolar fuzzy arithmetic and geometric weighted aggregators. Subsequently, we developed the new methodology by incorporating the bipolar score function. Also, we would like to compare the proposed method with the traditional TOPSIS approach. A comparative analysis was performed to illustrate the effectiveness and applicability of the suggested techniques. We also applied the new methodology to a Multi-Criteria Decision-Making problem. Moreover, we included the regression results using the bipolar scoring function to evaluate the influence of other parameters in mathematics.

Keywords:

TOPSIS method, Bipolar fuzzy set, Score function, Decision making

References

  1. [1] Mahmood, T., Abdullah, S., Bilal, M., Rashid, S., Multiple criteria decision making based on bipolar valued fuzzy set, Ann
  2. [2] Fuzzy Math Inf , 11(6), 1003–1009, 2016.
  3. [3] Zadeh, Lotfi A., Fuzzy sets, Information and control , 8(3), 338–353, 1965.
  4. [4] Pawlak, Zdzisław, Rough sets, International journal of computer & information sciences , 11, 341–356, 1982.
  5. [5] Molodtsov, Dmitriy, Soft set theory—first results, Computers & mathematics with applications , 37(4-5), 19–31, 1999.
  6. [6] Bellman, Richard E., Zadeh, Lotfi Asker, Decision-making in a fuzzy environment, Management science, 17(4), B–141, 1970. [6] Hwang, Ching-Lai, Multiple attributes decision making, Methods and Applications , 1981.
  7. [7] Triantaphyllou, Evangelos, Lin, Chi-Tun, Development and evaluation of five fuzzy multiattribute decision-making methods,
  8. [8] International Journal of Approximate reasoning , 14(4), 281–310, 1996.
  9. [9] Chen, Chen-Tung, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy sets and systems,
  10. [10] (1), 1–9, 2000.
  11. [11] Tsaur, Sheng-Hshiung, Chang, Te-Yi, Yen, Chang-Hua, The evaluation of airline service quality by fuzzy MCDM, Tourism
  12. [12] management, 23(2), 107–115, 2002.
  13. [13] Akram, Muhammad, Shumaiza, Arshad, Maham, Bipolar fuzzy TOPSIS and bipolar fuzzy ELECTRE-I methods to diagnosis,
  14. [14] Computational and Applied Mathematics , 39, 1–21, 2020.
  15. [15] Bai, Zhi-yong, An interval-valued intuitionistic fuzzy TOPSIS method based on an improved score function, The Scienti˝c
  16. [16] World Journal , 2013(1), 879089, 2013.
  17. [17] Jahanshahloo, Gholam Reza, Lotfi, F Hosseinzadeh, Izadikhah, Mohammad, Extension of the TOPSIS method for decision-
  18. [18] making problems with fuzzy data, Applied mathematics and computation , 181(2), 1544–1551, 2006.
  19. [19] Zhang, W-R, (Yin)(Yang) bipolar fuzzy sets, In 1998 IEEE international conference on fuzzy systems proceedings. IEEE world
  20. [20] congress on computational intelligence , 1, 835–840, 1998.
  21. [21] Deetae, Natthinee, Multiple criteria decision making based on bipolar fuzzy sets application to fuzzy TOPSIS, J. Math. Comput.
  22. [22] Sci., 12, Article-ID, 2021.
  23. [23] Alghamdi, MA, Alshehri, Noura Omair, Akram, Muhammad, Multi-criteria decision-making methods in bipolar fuzzy environ-
  24. [24] ment, International Journal of Fuzzy Systems , 20, 2057–2064, 2018.
  25. [25] Zhang, Wen-Ran, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision
  26. [26] analysis, In NAFIPS/IFIS/NASA'94 Proceedings of The First International Joint Conference of The North American Fuzzy
  27. [27] Information Processing Society , 305–309, 1994.
  28. [28] Wei, Guiwu, Alsaadi, Fuad E, Hayat, Tasawar, Alsaedi, Ahmed, Bipolar fuzzy Hamacher aggregation operators in multiple
  29. [29] attribute decision making, International Journal of Fuzzy Systems , 20, 1–12, 2018.
  30. [30] Ekel, P Ya, Fuzzy sets and models of decision making, Computers & Mathematics with Applications , 44(7), 863–875, 2002.
  31. [31] Ye, Jun, Improved method of multicriteria fuzzy decision-making based on vague sets, Computer-Aided Design , 39(2), 164–169,
  32. [32] Zhang, Wen-Ran, Zhang, Lulu, YinYang bipolar logic and bipolar fuzzy logic, Information Sciences , 165(3-4), 265–287, 2004.
  33. [33] Gul, Z, Some bipolar fuzzy aggregations operators and their applications in multicriteria group decision making (Doctoral
  34. [34] dissertation, M. Phil Thesis), Pakistan, 2015.
  35. [35] Jana, Chiranjibe, Pal, Madhumangal, Wang, Jian-qiang, Bipolar fuzzy Dombi aggregation operators and its application in
  36. [36] multiple-attribute decision-making process, Journal of Ambient Intelligence and Humanized Computing , 10, 3533–3549, 2019. [23] Wei, Guiwu, Alsaadi, Fuad E, Hayat, Tasawar, Alsaedi, Ahmed, Hesitant bipolar fuzzy aggregation operators in multiple
  37. [37] attribute decision making, Journal of Intelligent & Fuzzy Systems , 33(2), 1119–1128, 2017.
  38. [38] Jan, Naeem, Gwak, Jeonghwan, Pamucar, Dragan, A robust hybrid decision making model for human-computer interaction in
  39. [39] the environment of bipolar complex picture fuzzy soft sets, Information Sciences , 645, 119163, 2023.
  40. [40] Mani, Gunaseelan, Gnanaprakasam, Arul Joseph, Kausar, Nasreen, Munir, Muhammad, Khan, Salma, Ozbilge, Ebru, Solving an
  41. [41] integral equation via intuitionistic fuzzy bipolar metric spaces, Decision Making: Applications in Management and Engineering , 6(2), 536–556, 2023.
  42. [42] Alghazzawi, Dilshad, Abbas, Sajida, Alolaiyan, Hanan, Khalifa, Hamiden Abd El-Wahed, Alburaikan, Alhanouf, Xin, Qin,
  43. [43] Razaq, Abdul, Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration, AIMS Mathematics , 9(3), 5407–5430, 2024.
  44. [44] Deetae, Natthinee, Khamrot, Pannawit, Application of Fuzzy TOPSIS for Multiple criteria decision-making based on interval
  45. [45] bipolar fuzzy sets, Computer Science , 17(2), 569–582, 2022.
  46. [46] Kacprzyk, Janusz, Multistage fuzzy control: a prescriptive approach, John Wiley & Sons, Inc., 1997.
  47. [47] Zhang, Wen-Ran, Zhang, Lulu, YinYang bipolar logic and bipolar fuzzy logic, Information Sciences , 165(3-4), 265–287, 2004. [30] Wang, Yu Chung William, Ho, Shun Chuan, Information systems dispatching in the global environment, Acer, A case of
  48. [48] horizontal integration, Journal of Cases on Information Technology (JCIT) , 8(2), 45–61, 2006.
  49. [49] Riaz, Muhammad, Garg, Harish, Athar Farid, Hafiz Muhammad, Chinram, Ronnason, Multi-criteria decision making based on
  50. [50] bipolar picture fuzzy operators and new distance measures, Computer Modeling in Engineering & Sciences , 127(2), 771–800, 2021.
  51. [51] Lee, Keon Myung, Bipolar-valued fuzzy sets and their operations, In Proc. Int. Conf. on Intelligent Technologies, Bangkok,
  52. [52] Thailand , 307–312, 2000.
  53. [53] Sindhu, Muhammad Sarwar, Ahsan, Muhammad, Rafiq, Arif, Khan, IA, Multiple criteria decision making based on bipolar
  54. [54] picture fuzzy sets and extended TOPSIS, e Journal of Mathematics and Computer Science , 23(1), 49–57, 2021.
  55. [55] Akram, Muhammad, Arshad, Maham, A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making, Group
  56. [56] Decision and Negotiation , 28, 565–584, 2019.
  57. [57] Dincer, Hasan, Hacioglu, Umit, A comparative performance evaluation on bipolar risks in emerging capital markets using fuzzy
  58. [58] AHP-TOPSIS and VIKOR approaches, Engineering Economics , 26(2), 118–129, 2015.
  59. [59] Han, Ying, Lu, Zhenyu, Du, Zhenguang, Luo, Qi, Chen, Sheng, A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar
  60. [60] disorder diagnosis, Computer methods and programs in biomedicine , 158, 1–10, 2018.
  61. [61] Wei, Guiwu, Alsaadi, Fuad E, Hayat, Tasawar, Alsaedi, Ahmed, Bipolar fuzzy Hamacher aggregation operators in multiple
  62. [62] attribute decision making, International Journal of Fuzzy Systems , 20, 1–12, 2018.
  63. [63] Akram, Muhammad, Shumaiza, Smarandache, Florentin, Decision-making with bipolar neutrosophic TOPSIS and bipolar
  64. [64] neutrosophic ELECTRE-I, Axioms , 7(2), 33, 2018.
  65. [65] Neves, Rui Da Silva, Livet, Pierre, Bipolarity in human reasoning and affective decision making, International Journal of
  66. [66] Intelligent Systems , 23(8), 898–922, 2008.
  67. [67] Hung, Chia-Chang, Chen, Liang-Hsuan, A fuzzy TOPSIS decision making model with entropy weight under intuitionistic fuzzy
  68. [68] environment, In Proceedings of the International Multi Conference of Engineers and Computer Scientists (IMECS) , 1(1), 6–13, 2009.
  69. [69] Joshi, Deepa, Kumar, Sanjay, Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria
  70. [70] decision making, Egyptian informatics journal , 15(2), 97–104, 2014.
  71. [71] Li, Deng-Feng, Nan, Jiang-Xia, Extension of the TOPSIS for multi-attribute group decision making under Atanassov IFS
  72. [72] environments, International Journal of Fuzzy System Applications (IJFSA) , 1(4), 47–61, 2011.

Downloads

Published

2025-10-05

Issue

Vol. 2 No. 3 (2025): OPT

Section

Articles

How to Cite

Aruna, G., & Jesintha Rosline, J. (2025). A Comparative Study of MCDM Approaches: Exploring the Influence of Additional Parameters in Mathematics. Optimality, 2(3), 177-192. https://doi.org/10.22105/opt.v2i3.88

Similar Articles

1-10 of 29

You may also start an advanced similarity search for this article.