Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment

Document Type : Article


School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India.


The objective of this work is to present a novel multi-criteria group decision making (MCGDM) method under cubic intuitionistic fuzzy (CIF) environment by integrating extended TOPSIS method. In the existing studies, the uncertainties which are present in the data are handled either an interval-valued intuitionistic fuzzy sets (IVIFS) or an intuitionistic fuzzy set (IFS) information, which may lose some useful information of alternatives. On the other hand, CIF set (CIFS) handles the uncertainties by considering both the IVIFS and IFS instantaneously. Thus, motivated by this, in the present work, we presented some series of distance measures between the pairs of CIFSs and investigated their various relationship. Further, under this environment, a group decision-making method based on the proposed measure is presented by taking the different priority pairs of the decision makers. A practical example is provided to verify the developed approach and to demonstrate its practicality and feasibility, we compared their results with the several existing approaches results.


Main Subjects

1. Garg, H. and Arora, R. \Dual hesitant fuzzy soft  aggregation operators and their application in decision  making", Cognitive Computation, 10(5), pp. 769{789  (2018).  2. Garg, H. \Some arithmetic operations on the generalized  sigmoidal fuzzy numbers and its application",  Granular Computing, 3(1), pp. 9{25 (2018).  3. Zadeh, L.A. \Fuzzy sets", Information and Control, 8,  pp. 338{353 (1965).  4. Atanassov, K.T. \Intuitionistic fuzzy sets", Fuzzy Sets  and Systems, 20, pp. 87{96 (1986).  5. Atanassov, K. and Gargov, G. \Interval-valued intuitionistic  fuzzy sets", Fuzzy Sets and Systems, 31, pp.  343{349 (1989).  6. Arora, R. and Garg, H. \Robust aggregation operators  for multi-criteria decision making with intuitionistic  fuzzy soft set environment", Scientia Iranica, E, 25(2),  pp. 931{942 (2018).  7. Bagheri, M., Shojaei, P., and Khorami, M. \A comparative  survey of the condition of tourism infrastructure  in Iranian provinces using VIKOR and TOPSIS",  Decision Science Letters, 7(1), pp. 87{102 (2018).  8. Garg, H. and Ansha, \Arithmetic operations on generalized  parabolic fuzzy numbers and its application",  Proceedings of the National Academy of Sciences, India  Section A: Physical Sciences, 88(1), pp. 15{26 (2018).  9. Wang, X. and Triantaphyllou, E. \Ranking irregularities  when evaluating alternatives by using some  ELECTRE methods", Omega - International Journal  of Management Science, 36, pp. 45{63 (2008).  10. Peng, X.D. and Garg, H. \Algorithms for intervalvalued  fuzzy soft sets in emergency decision making  based on WDBA and CODAS with new information  measure", Computers & Industrial Engineering, 119,  pp. 439{452 (2018).  11. Xu, Z.S. and Yager, R.R. \Some geometric aggregation  operators based on intuitionistic fuzzy sets", International  Journal of General Systems, 35, pp. 417{433  (2006).  12. Peng, X.D. and Selvachandran, G. \Pythagorean fuzzy  set: state of the art and future directions", Arti_cial  Intelligence Review, 52, pp. 1873{1927 (2019).  13. Arora, R. and Garg, H. \Prioritized averaging/  geometric aggregation operators under the intuitionistic  fuzzy soft set environment", Scientia Iranica,  E, 25(1), pp. 466{482 (2018).  14. Peng, X.D. \New operations for interval-valued  Pythagorean fuzzy set", Scientia Iranica, E, 26(2), pp.  1049{1076 (2019).  H. Garg and G. Kaur/Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 396{410 409  15. Garg, H. and Kumar, K. \Some aggregation operators  for linguistic intuitionistic fuzzy set and its application  to group decision-making process using the set pair  analysis", Arabian Journal for Science and Engineering,  43(6), pp. 3213{3227 (2018).  16. Garg, H. \Linguistic Pythagorean fuzzy sets and its applications  in multiattribute decision-making process",  International Journal of Intelligent Systems, 33(6),  pp. 1234{1263 (2018).  17. Hwang, C.L. and Yoon, K., Multiple Attribute Decision  Making Methods and Applications A State-of-the-Art  Survey, Springer-Verlag Berlin Heidelberg (1981).  18. Szmidt, E. and Kacprzyk, J. \Distances between  intuitionistic fuzzy sets", Fuzzy Sets and Systems, 114,  pp. 505{518 (2000).  19. Hung, W.L. and Yang, M.S. \Similarity measures of  intuitionistic fuzzy sets based on hausdor_ distance",  Pattern Recognition Letters, 25, pp. 1603{1611 (2004).  20. Boran, F.E., Gen_c S., and Akay, D. \Personnel selection  based on intuitionistic fuzzy sets", Human  Factors and Ergonomics in Manufacturing & Service  Industries, 21(5), pp. 493{503 (2011).  21. Dugenci, M. \A new distance measure for interval  valued intuitionistic fuzzy sets and its application  to group decision making problems within complete  weights information", Applied Soft Computing, 41, pp.  120{134 (2016).  22. Garg, H. \A new generalized improved score function  of interval-valued intuitionistic fuzzy sets and applications  in expert systems", Applied Soft Computing, 38,  pp. 988{999 (2016).  23. Mohammadi, A., Shojaei, P., Kaydan, B., and Akbari,  Z. \Prioritizing the performance of civil development  projects in governmental administration agencies, using  gray relational analysis (GRA) and TOPSIS approach",  Decision Science Letters, 5(4), pp. 487{498  (2016).  24. Garg, H., Agarwal, N., and Tripathi, A. \Generalized  intuitionistic fuzzy entropy measure of order _ and  degree _ and its applications to multi-criteria decision  making problem", International Journal of Fuzzy System  Applications, 6(1), pp. 86{107 (2017).  25. Biswas, A. and Kumar, S. \An integrated TOPSIS  approach to MADM with interval-valued intuitionistic  fuzzy settings", in: Advanced Computational  and Communication Paradigms, Springer, pp. 533{543  (2018).  26. Vommi, V. \TOPSIS with statistical distances: A new  approach to MADM", Decision Science Letters, 6(1),  pp. 49{66 (2017).  27. Singh, S. and Garg, H. \Distance measures between  type-2 intuitionistic fuzzy sets and their application to  multicriteria decision-making process", Applied Intelligence,  46(4), pp. 788{799 (2017).  28. Li, D.F. \TOPSIS- based nonlinear-programming  methodology for multiattribute decision making with  interval-valued intuitionistic fuzzy sets", IEEE Transactions  on Fuzzy Systems, 18, pp. 299{311 (2010).  29. Garg, H. and Arora, R. \A nonlinear-programming  methodology for multi-attribute decision-making problem  with interval-valued intuitionistic fuzzy soft sets  information", Applied Intelligence, 48(8), pp. 2031{  2046 (2018).  30. Lu, Z. and Ye, J. \Logarithmic similarity measure  between interval-valued fuzzy sets and its fault diagnosis  method", Information, 9(2), p. 36 (2018). DOI:  10.3390/info9020036  31. Garg, H. and Kumar, K. \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 Computing, 22(15), pp. 4959{  4970 (2018).  32. Askarifar, K., Mota_ef, Z., and Aazaami, S. \An  investment development framework in Iran's seashores  using TOPSIS and best-worst multi-criteria decision  making methods", Decision Science Letters, 7(1), pp.  55{64 (2018).  33. Wang, C.Y. and Chen, S.-M. \A new multiple attribute  decision making method based on intervalvalued  intuitionistic fuzzy sets, linear programming  methodology, and the TOPSIS method", in: Advanced  Computational Intelligence (ICACI), 2017  Ninth International Conference on, IEEE, pp. 260{263  (2017).  34. Gupta, P., Mehlawat, M.K., Grover, N., and Pedrycz,  W. \Multi-attribute group decision making based on  extended TOPSIS method under interval-valued intuitionistic  fuzzy environment", Applied Soft Computing,  69, pp. 554{567 (2018).  35. Kumar, K. and Garg, H. \TOPSIS method based  on the connection number of set pair analysis under  interval-valued intuitionistic fuzzy set environment",  Computational and Applied Mathematics, 37(2), pp.  1319{1329 (2018).  36. Kumar, K. and Garg, H. \Connection number of set  pair analysis based TOPSIS method on intuitionistic  fuzzy sets and their application to decision making",  Applied Intelligence, 48(8), pp. 2112{2119 (2018).  37. Jun, Y.B., Kim, C.S., and Yang, K.O. \Cubic sets",  Annals of Fuzzy Mathematics and Informatics, 4(1),  pp. 83{98 (2012).  38. Khan, M., Abdullah, S., Zeb, A., and Majid, A.  \Cubic aggregation operators", International Journal  of Computer Science and Information Security, 14(8),  pp. 670{682 (2016).  39. Mahmood, T., Mehmood, F., and Khan, Q. \Some  generalized aggregation operators for cubic hesitant  fuzzy sets and their applications to multi criteria  decision making", Journal of Mathematics, 49(1), pp.  31{49 (2017).  40. Fahmi, A., Abdullah, S., Amin, F., and Ali, A.  \Precursor selection for sol{gel synthesis of titanium  carbide nanopowders by a new cubic fuzzy multiattribute  group decision-making model", Journal of  Intelligent Systems, 28(5), pp. 699{720 (2019).  410 H. Garg and G. Kaur/Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 396{410  41. Kaur, G. and Garg, H. \Multi-attribute decisionmaking  based on bonferroni mean operators under  cubic intuitionistic fuzzy set environment", Entropy,  20(1), p. 65 (2018). DOI: 10.3390/e20010065  42. Kaur, G. and Garg, H. \Cubic intuitionistic fuzzy  aggregation operators", International Journal for Uncertainty  Quanti_cation, 8(5), pp. 405{428 (2018).  43. Garg, H. \New exponential operational laws and their  aggregation operators for interval-valued pythagorean  fuzzy multicriteria decision-making", International  Journal of Intelligent Systems, 33(3), pp. 653{683  (2018).  44. Garg, H. \Hesitant Pythagorean fuzzy sets and their  aggregation operators in multiple attribute decision  making", International Journal for Uncertainty Quanti  _cation, 8(3), pp. 267{289 (2018).  45. Garg, H. and Rani, D. \Some generalized complex  intuitionistic fuzzy aggregation operators and their  application to multicriteria decision-making process",  Arabian Journal for Science and Engineering, 44(3),  pp. 2679{2698 (2019).