Real-Life Applications of New Type Spherical Fuzzy Sets and Its Extension Using Aggregation Operators

Main Article Content

M. Palanikumar, L. Mohan, M. S. Malchijah Raj, Aiyared Iampan

Abstract

The purpose of this article is to present a novel approach to the multiple attribute decision-making problem (MADM) based on (l1, l2) spherical fuzzy sets (SFS). This is an extension of the SFS. As a result of this article, we will discuss the concept of spherical fuzzy weighted averaging (SFWA), spherical fuzzy weighted geometric (SFWG), generalized spherical fuzzy weighted averaging (GSFWA) and generalized spherical fuzzy weighted geometric (GSFWG). Here is a flowchart that shows how these operators are used in the algorithm we discussed. With the help of a numerical example, we illustrate the extended Euclidean and Hamming distance measures. Additionally, the SFN approach is characterized by idempotency, boundedness, commutativity, and monotonicity. These tools help you find the best option faster, simpler, and more conveniently. The result is a more precise conclusion and a more intimate relationship between (l1, l2). We compare some of the current models with those that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study also revealed fascinating and intriguing findings.

Article Details

References

  1. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  3. R.R. Yager, Pythagorean Membership Grades in Multicriteria Decision Making, IEEE Trans. Fuzzy Syst. 22 (2014), 958–965. https://doi.org/10.1109/tfuzz.2013.2278989.
  4. S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multiattribute decision making problems, J. Intell. Fuzzy Syst. 36 (2019), 2829–2844. https://doi.org/10.3233/jifs-172009.
  5. B.C. Cuong, V. Kreinovich, Picture Fuzzy Sets - a New Concept for Computational Intelligence Problems, in: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, Hanoi, Vietnam, 2013: pp. 1–6. https://doi.org/10.1109/WICT.2013.7113099.
  6. P. Liu, G. Shahzadi, M. Akram, Specific Types of q-Rung Picture Fuzzy Yager Aggregation Operators for DecisionMaking, Int. J. Comput. Intell. Syst. 13 (2020), 1072–1091. https://doi.org/10.2991/ijcis.d.200717.001.
  7. W.F. Liu, J. Chang, X. He, Generalized Pythagorean Fuzzy Aggregation Operators and Applications in Decision Making, Control Decis. 31 (2016), 2280–2286.
  8. X. Peng, Y. Yang, Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators, Int. J. Intell. Syst. 31 (2015), 444–487. https://doi.org/10.1002/int.21790.
  9. F. Kutlu Gündo ˘gdu, C. Kahraman, Spherical Fuzzy Sets and Spherical Fuzzy TOPSIS Method, J. Intell. Fuzzy Syst. 36 (2019), 337–352. https://doi.org/10.3233/jifs-181401.
  10. X. Peng, J. Dai, Approaches to Single-Valued Neutrosophic MADM Based on MABAC, TOPSIS and New Similarity Measure With Score Function, Neural Comput. Appl. 29 (2016), 939–954. https://doi.org/10.1007/s00521-016-2607-y.
  11. X. Zhang, Z. Xu, Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets, Int. J. Intell. Syst. 29 (2014), 1061–1078. https://doi.org/10.1002/int.21676.
  12. C.L. Hwang, K. Yoon, Multiple Attribute Decision Making, Springer, Berlin, Heidelberg, 1981. https://doi.org/10.1007/978-3-642-48318-9.
  13. M. Riaz, M.R. Hashmi, Linear Diophantine Fuzzy Set and Its Applications Towards Multi-Attribute DecisionMaking Problems, J. Intell. Fuzzy Syst. 37 (2019), 5417–5439. https://doi.org/10.3233/jifs-190550.
  14. S.G. Quek, H. Garg, G. Selvachandran, M. Palanikumar, K. Arulmozhi, F. Smarandache, VIKOR and TOPSIS Framework With a Truthful-Distance Measure for the (t,s)-Regulated Interval-Valued Neutrosophic Soft Set, Soft Comput. (2023). https://doi.org/10.1007/s00500-023-08338-y.
  15. M. Palanikumar, K. Arulmozhi, A. Iampan, Multi Criteria Group Decision Making Based on VIKOR and TOPSIS Methods for Fermatean Fuzzy Soft with Aggregation Operators, ICIC Express Lett. 16 (2022), 1129–1138. https://doi.org/10.24507/icicel.16.10.1129.
  16. M. Palanikumar, K. Arulmozhi, MCGDM Based on TOPSIS and VIKOR Using Pythagorean Neutrosophic Soft With Aggregation Operators, Neutrosophic Sets Syst. 51 (2022), 538–555.
  17. M. Palanikumar, S. Broumi, Square Root Diophantine Neutrosophic Normal Interval-Valued Sets and Their Aggregated Operators in Application to Multiple Attribute Decision Making, Int. J. Neutrosophic Sci. 19 (2022), 63–84. https://doi.org/10.54216/ijns.190307.
  18. M. Palanikumar, K. Arulmozhi, Novel Possibility Pythagorean Interval Valued Fuzzy Soft Set Method for a Decision Making, TWMS J. Appl. Eng. Math. 13 (2023), 327–340.
  19. M. Palanikumar, N. Kausar, H. Garg, A. Iampan, S. Kadry, M. Sharaf, Medical Robotic Engineering Selection Based on Square Root Neutrosophic Normal Interval-Valued Sets and Their Aggregated Operators, AIMS Math. 8 (2023), 17402–17432. https://doi.org/10.3934/math.2023889.
  20. A. Al-Quran, A.G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, Int. J. Neutrosophic Sci. 20 (2023), 08–19. https://doi.org/10.54216/ijns.200201.
  21. F. Al-Sharqi, M.U. Romdhini, A. Al-Quran, Group Decision-Making Based on Aggregation Operator and Score Function of Q-Neutrosophic Soft Matrix, J. Intell. Fuzzy Syst. 45 (2023), 305–321. https://doi.org/10.3233/jifs-224552.
  22. F. Al-Sharqi, Y. Al-Qudah, N. Alotaibi, Decision-Making Techniques Based on Similarity Measures of Possibility Neutrosophic Soft Expert Sets, Neutrosophic Sets Syst. 55 (2023), 358–382.
  23. F. Al-Sharqi, A. G. Ahmad and A. Al-Quran, Mapping on interval complex neutrosophic soft sets, Int. J. Neutrosophic Sci., 19(4), (2022), 77-85.
  24. F.A. Al-Sharqi, A.G. Ahmad, A.A. Al-Quran, Mapping on Interval Complex Neutrosophic Soft Sets, Int. J. Neutrosophic Sci. 19 (2022), 77–85. https://doi.org/10.54216/ijns.190406.
  25. S. Ashraf, S. Abdullah, T. Mahmood, Spherical Fuzzy Dombi Aggregation Operators and Their Application in Group Decision Making Problems, J. Ambient. Intell. Human Comput. 11 (2019), 2731–2749. https://doi.org/10.1007/s12652-019-01333-y.
  26. D.F. Li, Multiattribute Decision Making Method Based on Generalized Owa Operators With Intuitionistic Fuzzy Sets, Expert Syst. Appl. 37 (2010), 8673–8678. https://doi.org/10.1016/j.eswa.2010.06.062.
  27. M. Palanikumar, K. Arulmozhi, C. Jana, Multiple Attribute Decision-Making Approach for Pythagorean Neutrosophic Normal Interval-Valued Fuzzy Aggregation Operators, Comput. Appl. Math. 41 (2022), 90. https://doi.org/10.1007/s40314-022-01791-9.
  28. X. Peng, H. Yuan, Fundamental Properties of Pythagorean Fuzzy Aggregation Operators, Fundam. Inform. 147 (2016), 415–446. https://doi.org/10.3233/fi-2016-1415.
  29. T. Temel, S.B. Aydemir, Y. Ho¸scan, Power Muirhead Mean in Spherical Normal Fuzzy Environment and Its Applications to Multi-Attribute Decision-Making, Complex Intell. Syst. 8 (2022), 3523–3541. https://doi.org/10.1007/s40747-022-00688-8.
  30. K. Ullah, H. Garg, T. Mahmood, N. Jan, Z. Ali, Correlation Coefficients for T-Spherical Fuzzy Sets and Their Applications in Clustering and Multi-Attribute Decision Making, Soft Comput. 24 (2019), 1647–1659. https://doi.org/10.1007/s00500-019-03993-6.
  31. K. Ullah, T. Mahmood, H. Garg, Evaluation of the Performance of Search and Rescue Robots Using Tspherical Fuzzy Hamacher Aggregation Operators, Int. J. Fuzzy Syst. 22 (2020), 570–582. https://doi.org/10.1007/s40815-020-00803-2.
  32. R. N. Xu and C. L. Li, Regression prediction for fuzzy time series, Appl. Math. J. Chinese Univ. 16 (2001), 451–461.
  33. Z. Xu, R.R. Yager, Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets, Int. J. Gen. Syst. 35 (2006), 417–433. https://doi.org/10.1080/03081070600574353.
  34. S. Zeng, W. Su, Intuitionistic Fuzzy Ordered Weighted Distance Operator, Knowl.-Based Syst. 24 (2011), 1224–1232. https://doi.org/10.1016/j.knosys.2011.05.013.