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Soft Computing

, Volume 23, Issue 23, pp 12221–12231 | Cite as

Triangular cubic linguistic uncertain fuzzy topsis method and application to group decision making

  • Aliya FahmiEmail author
  • Fazli Amin
Foundations
  • 66 Downloads

Abstract

In this paper, we define the idea of cubic linguistic uncertain fuzzy numbers. We define the idea of triangular cubic linguistic uncertain fuzzy number. We discuss some basic operational laws of triangular cubic linguistic uncertain fuzzy number and hamming distance of TCLUFNs. We introduce the new concept of triangular cubic linguistic uncertain fuzzy TOPSIS method. Furthermore, we extend the classical triangular cubic linguistic uncertain fuzzy TOPSIS method to solve the MCDM method based on triangular cubic linguistic uncertain fuzzy TOPSIS method. The new ranking method for TCLUFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method.

Keywords

Cubic linguistic fuzzy sets Triangular cubic linguistic uncertain fuzzy number MCDM Triangular cubic linguistic uncertain fuzzy TOPSIS method Numerical application 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Ethical approval

This study is not supported by any source or any organizations.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Alam MG, Baulkani S (2019) Geometric structure information based multi-objective function to increase fuzzy clustering performance with artificial and real-life data. Soft Comput 4(23):1079–1098Google Scholar
  2. Amin F, Fahmi A, Abdullah S, Ali A, Ahmad R, Ghanu F (2018) Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Int Fuzzy Syst 34(1):1–15Google Scholar
  3. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96zbMATHGoogle Scholar
  4. Büyüközkan G, Çifçi G (2012) A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers. Expert Syst Appl 39(3):3000–3011Google Scholar
  5. Chan FTS, Kumar N (2007) Global supplier development considering risk factors using fuzzy extended AHP-based approach. Omega 35:417–431Google Scholar
  6. Chen ZC, Liu PH (2015) An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int J Comput Intell Syst 8(4):747–760Google Scholar
  7. El-Sappagh S, Elmogy M, Ali F, Kwak KS (2019) A case-base fuzzification process: diabetes diagnosis case study. Soft Comput 23(14):5815–5834Google Scholar
  8. Fahmi A, Abdullah S, Amin F, Siddiqui N, Ali A (2017a) Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. J Intell Fuzzy Syst 33(6):3323–3337Google Scholar
  9. Fahmi A, Abdullah S, Amin F, Ali A (2017b) Precursor selection for sol-gel synthesis of titanium carbide nanopowders by a new cubic fuzzy multi-attribute group decision-making model. J Intell Syst.  https://doi.org/10.1515/jisys-2017-0083 Google Scholar
  10. Fahmi A, Abdullah S, Amin F (2017c) Trapezoidal linguistic cubic hesitant fuzzy topsis method and application to group decision making program. J New Theory 19:27–47 zbMATHGoogle Scholar
  11. Fahmi A, Abdullah S, Amin F, Ali A (2018a) Weighted average rating (War) method for solving group decision making problem using triangular cubic fuzzy hybrid aggregation (Tcfha). Punjab Univ J Math 50(1):23–34MathSciNetGoogle Scholar
  12. Fahmi A, Amin F, Abdullah S, Ali A (2018b) Cubic fuzzy Einstein aggregation operators and its application to decision-making. Int J Syst Sci 49(1):1–13.  https://doi.org/10.1080/00207721.2018.1503356 MathSciNetGoogle Scholar
  13. Gabus A, Fontela E (1972)World problems, an invitation to further thought within the framework of DEMATEL. Battelle Geneva Research Centre, Switzerland, GenevaGoogle Scholar
  14. He S, Chaudhry SS, Lei Z, Baohua W (2009) Stochastic vendor selection problem: chance-constrained model and genetic algorithms. Ann Oper Res 168, 169–179MathSciNetzbMATHGoogle Scholar
  15. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and application. Springer, New YorkzbMATHGoogle Scholar
  16. Jun YB, Kim CS, Yang KO (2011) Cubic sets. Ann Fuzzy Math Inform 4(1):83–98MathSciNetzbMATHGoogle Scholar
  17. Lee AHI, Kang Y, Hsu HC-F, Hung H-C (2009) A green supplier selection model for high-tech industry. Expert Syst Appl 36:7917–7927Google Scholar
  18. Kumar M, Vrat P, Shankar R (2006) A fuzzy goal programming approach for vendor selection problem in a supply chain. Int J Prod Econ 101:273–285Google Scholar
  19. Li ZF, Liu PD, Qin XY (2017) An extended VIKOR method for decision making problem with linguistic intuitionistic fuzzy numbers based on some new operational laws and entropy. J Intell Fuzzy Syst 33(2017):1919–1931zbMATHGoogle Scholar
  20. Liu KFR, Lai J-H (2009) Decision-support for environmental impact assessment: a hybrid approach using fuzzy logic and fuzzy analytic network process. Expert Syst Appl 36:5119–5136Google Scholar
  21. Liu PD, Liu X (2017) Multiple attribute group decision making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators. Complexity 1–15. Article ID 3571459Google Scholar
  22. Liu PD, Qin XY (2017a) Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making. J Intell Fuzzy Syst 32(1):1029–1043MathSciNetzbMATHGoogle Scholar
  23. Liu PD, Qin XY (2017b) Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and application to multiple-attribute decision making. J Exp Theor Artif Intell 29(6):1173–1202MathSciNetGoogle Scholar
  24. Liu PD, Wang P (2017) Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Inf Technol Decis Mak 16(3):817–850Google Scholar
  25. Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl Based Syst 76:127–138Google Scholar
  26. Nemati Y, Alavidoost MH (2019) A fuzzy bi-objective MILP approach to integrate sales, production, distribution and procurement planning in a FMCG supply chain. Soft Comput 23(13):4871–4890Google Scholar
  27. Qu J, Meng X, Yu H, You H (2016) A triangular fuzzy TOPSIS-based approach for the application of water technologies in different emergency water supply scenarios. Environ Sci Pollut Res 23(17):17277–17286Google Scholar
  28. Rajab S, Sharma V (2019) An interpretable neuro-fuzzy approach to stock price forecasting. Soft Comput 23(3):921–936Google Scholar
  29. Rao P, Holt D (2005) Do green supply chains lead to competitiveness and economic performance? Int J Oper Prod Manage 25(9):898–916Google Scholar
  30. Ren A, Wang Y (2019) An approach based on reliability-based possibility degree of interval for solving general interval bilevel linear programming problem. Soft Comput 23(3):997–1006zbMATHGoogle Scholar
  31. Rodriguez RM, Martinez L, Herrera F (2011) Hesitant fuzzy linguistic term sets. Found Intell Syst 122:287–295Google Scholar
  32. Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119Google Scholar
  33. Saaty TL (1996)The analytic network process. RWS Publications, PittsburghGoogle Scholar
  34. Sen S, Basligil H, Sen CG, Baraçli H (2007) A framework for defining both qualitative and quantitative supplier selection criteria considering the buyer supplier integration strategies. Int J Prod Res 46(7):1825–1845zbMATHGoogle Scholar
  35. Sevkli M, Koh SCL, Zaim S, Demirbag M, Tatoglu E (2007) An application of data envelopment analytic hierarchy process for supplier selection: a case study of BEKO in Turkey. Int J Prod Res 45:1973–2003zbMATHGoogle Scholar
  36. Tsai W-H, Hung S-J (2009) A fuzzy goal programming approach for green supply chain optimization under activity-based costing and performance evaluation with a value-chain structure. Int J Prod Res 47(18):4991–5017zbMATHGoogle Scholar
  37. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539zbMATHGoogle Scholar
  38. Tuzkaya UR, Önüt S (2008) A fuzzy analytic network process based approach to transportation-mode selection between Turkey and Germany: A case study. Inf Sci 78:3133–3146Google Scholar
  39. Wang JQ, Wang J, Chen Q, Zhang H, Chen X (2014) An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf Sci 280:338–351MathSciNetzbMATHGoogle Scholar
  40. Wu D (2009) Supplier selection: a hybrid model using DEA, decision tree and neural network. Expert Syst Appl 36:9105–9112Google Scholar
  41. Yang T, Chou P (2005) Solving a multi-response simulation-optimization problem with discrete variables using a multipleattribute decision making method. Math Comput Simulat 68:9–21zbMATHGoogle Scholar
  42. Yang T, Hung C (2005) Multiple-attribute decision making methods for plant layout design problem. Robot Comput Integr Manuf 23:126–137Google Scholar
  43. Yoon K (1987) A reconciliation among discrete compromise situations. J Oper Res Soc 38(3):277–286Google Scholar
  44. Yoon K, Hwang C (1995) Multiple attribute decision making. Sage Publication, Thousand OaksGoogle Scholar
  45. Zadeh LA (1965) Fuzzy sets. Inf Control 18:338–353zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHazara University MansehraMansehraPakistan

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