AIMS Mathematics, 2020, 5(4): 2944-2966. doi: 10.3934/math.2020190.

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information

School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University Patiala, Punjab, India

The theory of intuitionistic fuzzy soft set (IFSS) is an extension of the soft set theory which is utilized to precise the deficiency, indeterminacy, and uncertainty of the evaluation while making decisions. The conspicuous characteristic of this mathematical concept is that it considers two distinctive sorts of information, namely the membership and non-membership degrees. The present paper partitioned into two folds: (i) to define the correlation measures for IFSSs; (ii) to introduce the Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS) for IFSS information. Further, few properties identified with these measures are examined thoroughly. In view of these techniques, an approach is presented to solve decision-making problems by utilizing the proposed TOPSIS method based on correlation measures. At last, an illustrative example is enlightened to demonstrate the appropriateness of the proposed approach. Also, its suitability and attainability are checked by contrasting its outcomes and the prevailing methodologies results.
  Figure/Table
  Supplementary
  Article Metrics

Keywords intuitionistic fuzzy soft sets; correlation coefficient; TOPSIS method; decision-making

Citation: Harish Garg, Rishu Arora. TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information. AIMS Mathematics, 2020, 5(4): 2944-2966. doi: 10.3934/math.2020190

References

  • 1. L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.    
  • 2. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87-96.    
  • 3. H. Garg, G. Kaur, Cubic intuitionistic fuzzy sets and its fundamental properties, J. Mult-valued Log. S., 33 (2019), 507-537.
  • 4. K. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst., 31 (1989), 343-349.    
  • 5. H. Garg, K. Kumar, Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems, IEEE T. Fuzzy Syst., 27 (2019), 2302-2311.    
  • 6. J. Zhan, X. Zhang, Y. Yao, Covering based multigranulation fuzzy rough sets and corresponding applications, Artificial Intelligence Review, 53 (2020), 1093-1126.    
  • 7. M. I. Ali, F. Feng, T. Mahmood, et al. A graphical method for ranking Atanassov's intuitionistic fuzzy values using the uncertainty index and entropy, Int. J. Intell. Syst., 34 (2019), 2692-2712.    
  • 8. F. Feng, M. Liang, H. Fujita, et al. Lexicographic orders of intuitionistic fuzzy values and their relationships, Mathematics, 7 (2019), 166.
  • 9. H. Garg, Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application, Engineering Applications of Artificial Intelligence, 60 (2017), 164-174.    
  • 10. H. Garg, Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making, Comput. Ind. Eng., 101 (2016), 53-69.    
  • 11. X. Liu, H. S. Kim, F. Feng, et al. Centroid transformations of intuitionistic fuzzy values based on aggregation operators, Mathematics, 6 (2018), 215.
  • 12. Z. S. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35 (2006), 417-433.    
  • 13. H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Comput., 22 (2018), 4959-4970.    
  • 14. W. L. Hung, J. W. Wu, A note on the correlation of fuzzy numbers by expected interval, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9 (2001), 517-523.    
  • 15. T. Gerstenkorn, J. Manko, Correlation of intuitionistic fuzzy sets, Fuzzy Set. Syst., 44 (1991), 39-43.    
  • 16. E. Szmidt, J. Kacprzyk, Correlation of intuitionistic fuzzy sets, Lecture Notes in Computer Science, 6178 (2010), 169-177.    
  • 17. H. Bustince, P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst., 74 (1995), 237-244.    
  • 18. H. Garg, A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes, International Journal of Intelligent Systems, 31 (2016), 1234-1252.    
  • 19. H. Garg, Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision - making process, Journal of Industrial and Management Optimization, 14 (2018), 1501-1519.    
  • 20. H. Garg, K. Kumar, A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application, Scientia Iranica E, 25 (2018), 2373-2388.
  • 21. C. L. Hwang, K. Yoon, Multiple Attribute Decision Making Methods and Applications A State-ofthe-Art Survey, Springer-Verlag, Berlin Heidelberg, 1981.
  • 22. E. Szmidt, J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Set. Syst., 114 (2000), 505-518.    
  • 23. W. L. Hung, M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on hausdorff distance, Pattern Recogn. Let., 25 (2004), 1603-1611.    
  • 24. M. Düğenci, A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information, Appl. Soft Comput., 41 (2016), 120-134.    
  • 25. H. Garg, A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems, Applied Soft Comput., 38 (2016), 988-999.    
  • 26. A. Mohammadi, P. Shojaei, B. Kaydan, Z. Akbari, Prioritizing the performance of civil development projects in governmental administration agencies, using gray relational analysis (GRA) and TOPSIS approach, Decision Science Letters, 5 (2016), 487-498.
  • 27. H. Garg, N. Agarwal, A. Tripathi, Generalized intuitionistic fuzzy entropy measure of order α and degree β and its applications to multi-criteria decision making problem, International Journal of Fuzzy System Applications, 6 (2017), 86-107.    
  • 28. A. Biswas, S. Kumar, An integrated TOPSIS approach to MADM with interval-valued intuitionistic fuzzy settings, Advanced Computational and Communication Paradigms, Springer, 2018.
  • 29. D. F. Li, TOPSIS- based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets, IEEE T. Fuzzy Syst., 18 (2010), 299-311.
  • 30. H. Garg, R. Arora, A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information, Appl. Intell., 48 (2018), 2031-2046.    
  • 31. C. Y. Wang, S. M. Chen, A new multiple attribute decision making method based on interval-valued intuitionistic fuzzy sets, linear programming methodology, and the TOPSIS method, in: Advanced Computational Intelligence (ICACI), 2017 Ninth International Conference on, IEEE, 2017.
  • 32. P. Gupta, M. K. Mehlawat, N. Grover, et al. Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment, Appl. Soft Comput., 69 (2018), 554-567.    
  • 33. K. Kumar, H. Garg, Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making, Appl. Intell., 48 (2018), 2112-2119.    
  • 34. K. Kumar, H. Garg, TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment, Comput. Appl. Math., 37 (2018), 1319-1329.    
  • 35. L. Zhang, J. Zhan, Y. Yao, Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems, Information Sciences, 517 (2020), 315-339.    
  • 36. D. Molodtsov, Soft set theory-first results, Computer and Mathematics with Applications, 27 (1999), 19-31.
  • 37. P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 589-602.
  • 38. P. K. Maji, R. Biswas, A. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 677-692.
  • 39. M. Bora, T. J. Neog, D. K. Sut, Some new operations of intuitionistic fuzzy soft sets, Inter. J. Soft Comput. Eng., 2 (2012), 2231-2307.
  • 40. Y. Jiang, Y. Tang, H. Liu, et al Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets, Information Sciences, 240 (2013), 95-114.    
  • 41. T. M. Athira, S. J. John, H. Garg, A novel entropy measure of Pythagorean fuzzy soft sets, AIMS Mathematics, 5 (2020), 1050-1061.    
  • 42. P. Rajarajeswari, P. Dhanalakshmi, Similarity measures of intuitionistic fuzzy soft sets and its application in medical diagnosis, International Journal of Mathematical Archive, 5 (2014), 143-149.
  • 43. A. Khalid, M. Abbas, Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory, Inter. J. Fuzzy Syst., 17 (2015), 490-497.    
  • 44. R. Arora, H. Garg, Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment, Scientia Iranica E, 25 (2018), 931-942.
  • 45. R. Arora, H. Garg, Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment, Scientia Iranica, 25 (2018), 466-482.
  • 46. H. Garg, R. Arora, Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making, Appl. Intell., 48 (2018), 343-356.    
  • 47. F. Feng, H. Fujita, M. I. Ali, et al. Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods, IEEE T. Fuzzy Syst., 27 (2019), 474-488.    
  • 48. R. Arora, H. Garg, A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making, Engineering Applications of Artificial Intelligence, 72 (2018), 80-92.    
  • 49. H. Garg, R. Arora, Generalized intuitionistic fuzzy soft power aggregation operator based on tnorm and their application in multi criteria decision-making, Inter. J. Intell. Syst., 34 (2019), 215-246.    
  • 50. N. Sarala, B. Suganya, An application of similarity measure of intuitionistic fuzzy soft set based on distance in medical diagnosis, International Journal of Science and Research, 4 (2016), 2298-2303.
  • 51. P. Muthukumar, G. S. S. Krishnan, A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis, Appl. Soft Comput., 41 (2016), 148-156.    
  • 52. S. Petchimuthu, H. Garg, H. Kamacı, et al. The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM, Comput. Appl. Math., 39 (2020), 1-32.    
  • 53. J. Zhan, Q. Liu, T. Herawan, A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making, Appl. Soft Comput., 54 (2017), 393-402.    
  • 54. H. Garg, R. Arora, Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making, Journal of the Operational Research Society, 69 (2018), 1711-1724.    
  • 55. J. Zhan, M. I. Ali, N. Mehmood, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Appl. Soft Comput., 56 (2017), 446-457.    
  • 56. H. Garg, R. Arora, Distance and similarity measures for dual hesistant fuzzy soft sets and their applications in multi criteria decision-making problem, Int. J. Uncertain. Quan., 7 (2017), 229-248.    
  • 57. J. Hu, L. Pan, Y. Yang, et al. A group medical diagnosis model based on intuitionistic fuzzy soft sets, Appl. Soft Comput., 77 (2019), 453-466.    
  • 58. H. Garg, G. Kaur, Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information, Comput. Ind. Eng., 140 (2020), 106211.
  • 59. P. F. A. Perveen, J. J. Sunil, K. Babitha, et al. Spherical fuzzy soft sets and its applications in decision-making problems, J. Intell. Fuzzy Sys., 37 (2019), 8237-8250.    
  • 60. T. M. Athira, S. J. John, H. Garg, Entropy and distance measures of pythagorean fuzzy soft sets and their applications, J. Intell. Fuzzy Syst., 37 (2019), 4071-4084.    

 

This article has been cited by

  • 1. Xian-Wei Xin, Ji-Hua Song, Zhan-Ao Xue, Wei-Ming Peng, Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degree, Journal of Intelligent & Fuzzy Systems, 2020, 1, 10.3233/JIFS-200002

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved