Advertisement

Consistent fuzzy preference relation with geometric Bonferroni mean: a fused preference method for assessing the quality of life

  • Fatin Mimi Anira Alias
  • Lazim Abdullah
  • Xunjie Gou
  • Huchang LiaoEmail author
  • Enrique Herrera-Viedma
Article
  • 39 Downloads

Abstract

Fuzzy preference relation (FPR) is commonly used in solving multi-criteria decision making problems because of its efficiency in representing people’s perceptions. However, the FPR suffers from an intrinsic limitation of consistency in decision making. In this regard, many researchers proposed the consistent fuzzy preference relation (CFPR) as a decision-making approach. Nevertheless, most CFPR methods involve a traditional aggregation process which does not identify the interrelationship between the criteria of decision problems. In addition, the information provided by individual experts is indeed related to that provided by other experts. Therefore, the interrelationship of information on criteria should be dealt with. Based on this motivation, we propose a modified approach of CFPR with Geometric Bonferroni Mean (GBM) operator. The proposed method introduces the GBM as an operator to aggregate information. The proposed method is applied to a case study of assessing the quality of life among the population in Setiu Wetlands. It is shown that the best option derived by the proposed method is consistent with that obtained from the other methods, despite the difference in aggregation operators.

Keywords

Decision making Fuzzy preference relation Geometric Bonferroni mean Decision matrix Quality of life 

Notes

Acknowledgements

This study was supported by Niche Research Grant Scheme, Ministry of Higher Education, Malaysia and Universiti Malaysia Terengganu with vote no. NRGS 53131/7, the National Natural Science Foundation of China (Nos. 71501135 and 71771156), the 2019 Sichuan Planning Project of Social Science (No. SC18A007), the 2018 Key Project of the Key Research Institute of Humanities and Social Sciences in Sichuan Province (No. Xq18A01, No. LYC18-02), the Electronic Commerce and Modern Logistics Research Center Program, Key Research Base of Humanities and Social Science, Sichuan Provincial Education Department (No. DSWL18-2), the Spark Project of Innovation at Sichuan University (No. 2018hhs-43), and National Spanish project TIN2016-75850-R.

References

  1. 1.
    Saaty TL (2013) Analytic Hierarchy Process. In: Gass SI, Fu MC (eds) Encyclopedia Oper Res Manage Sci. Springer, Boston, p 2–64Google Scholar
  2. 2.
    Xu ZS, Liao HC (2014) Intuitionistic fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst 22(4):749–761CrossRefGoogle Scholar
  3. 3.
    Liao HC, Mi XM, Xu ZS, Xu JP, Herrera F (2018) Intuitionistic fuzzy analytic network process. IEEE Trans Fuzzy Syst 26(5):2578–2590CrossRefGoogle Scholar
  4. 4.
    Figueira J, Mousseau V, Roy B (2016) ELECTRE methods. In: International Series in Operations Research & Management Science, p 155-185Google Scholar
  5. 5.
    Liao HC, Yang LY, Xu ZS (2018) Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets. Appl Soft Comput 63:223–234CrossRefGoogle Scholar
  6. 6.
    Brans J, Vincke P (1985) A preference ranking organization method: the PROMETHEE method for MCDM. Manag Sci 31(6):647–656CrossRefzbMATHGoogle Scholar
  7. 7.
    Liao HC, Wu D, Huang YL, Ren PJ, Xu ZS, Verma M (2018) Green logistic provider selection with a hesitant fuzzy linguistic thermodynamic method integrating prospect theory and PROMETHEE. Sustainability 10(4):1291CrossRefGoogle Scholar
  8. 8.
    Zavadskas EK, Turskis Z, Antucheviciene J, Zakarevicius A (2012) Optimization of weighted aggregated sum product assessment. Elektrotechnika 122:3–6Google Scholar
  9. 9.
    Dahooie JH, Zavdskas EK, Abolhasani M, Vanaki A, Turskis Z (2018) A novel approach for evaluation of projects using an interval–valued fuzzy additive ratio assessment (ARAS) method: a case study of oil and gas well drilling projects. Symmetry 10(45):1–32Google Scholar
  10. 10.
    Maghsoodi AI, Abouhamzeh G, Khalilzadeh M, Zavdskas EK (2018) Ranking and selecting the best performance appraisal method using the MULTIMOORA approach integrated Shannon’s entropy. Front Bus Res China 12(2):1–21Google Scholar
  11. 11.
    Liao HC, Qin R, Gao CY, Wu XL, Hafezalkotob A, Herrera F (2019) Score-HeDLiSF: a score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: an application to unbalanced hesitant fuzzy linguistic MULTIMOORA. Inform Fusion 48:39–54CrossRefGoogle Scholar
  12. 12.
    Orlovsky SA (1978) Decision making with a fuzzy preference relation. Fuzzy Sets Syst 1:155–167MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Urena R, Chiclana F, Morento-Molinera JA, Herrera-Viedma E (2015) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14–32MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Cabrerizo FJ, Herrera-Viedma E, Pedrycz W (2013) A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur J Oper Res 230(3):624–633MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Cabrerizo FJ, Al-Hmouz R, Morfeq A, Balamash AS, Martínez MA, Herrera-Viedma E (2017) Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Comput 21(11):3037–3050CrossRefzbMATHGoogle Scholar
  16. 16.
    Xu ZS, Liao HC (2015) A survey of approaches to decision making with intuitionistic fuzzy preference relations. Knowl-Based Syst 80:131–142CrossRefGoogle Scholar
  17. 17.
    Liao HC, Xu ZS, Xia MM (2014) Multiplicative consistency of interval-valued intuitionistic fuzzy preference relation. J Intell Fuzzy Syst 27:2969–2985MathSciNetzbMATHGoogle Scholar
  18. 18.
    Liao HC, Xu ZS, Xia MM (2014) Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int J Inf Technol Decis Mak 13(1):47–76CrossRefGoogle Scholar
  19. 19.
    Wang TC, Lin LY (2009) Applying the consistent fuzzy preference relations to select merger strategy for commercial banks in new financial environments. Expert Syst Appl 36:7019–7026MathSciNetCrossRefGoogle Scholar
  20. 20.
    Chen YH, Chao RJ (2012) Supplier selection using consistency fuzzy preference relations. Expert Syst Appl 39:3233–3240CrossRefGoogle Scholar
  21. 21.
    Chao RJ, Chen YH (2009) Evaluation of the criteria and effectiveness of distance e-learning with consistent fuzzy preference relations. Expert Syst Appl 36:10657–10662CrossRefGoogle Scholar
  22. 22.
    Chiclana F, Herrera F, Herrera-Viedma E (2002) A note on the internal consistency of various preference representations. Fuzzy Sets Syst 131:75–78MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Xu ZS, Da QL (2003) An approach to improving consistency of fuzzy preference matrices. Fuzzy Optim Decis Making 2:3–12MathSciNetCrossRefGoogle Scholar
  24. 24.
    Ma J, Fan PZ, Jiang PY, Mao YJ, Ma L (2006) A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets Syst 157:20–33MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Herrera-Viedma E, Herrera F, Chiclana F, Luque M (2004) Some issues on consistency of fuzzy preference relation. Eur J Oper Res 1:98–109MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Alonso S, Chiclana F, Herrera F, Herrera-Viedma E, Alcalá-Fdez J, Porcel C (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23(2):155–175CrossRefzbMATHGoogle Scholar
  27. 27.
    Xia MM, Xu ZS, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl-Based Syst 40:88–100CrossRefGoogle Scholar
  28. 28.
    Bonferroni C (1950) Sulle medie multiple di potenzo. Bolletino dell Unione Matematica Italiana 5:267–270MathSciNetzbMATHGoogle Scholar
  29. 29.
    Saaty TL (1980) The analytic hierarchy process: planning, priority setting & resource allocation. McGraw Hill, New YorkzbMATHGoogle Scholar
  30. 30.
    Economic Planning Unit (2012) Kualiti Hidup Malaysia (2011). Prime Minister Department, MalaysiaGoogle Scholar
  31. 31.
    Alireza SA, Sadjadi SJ, Molana SMH, Soheil SN (2018) A new MCDM-based approach using BWM and SAW for optimal search model. Decis Sci Letters 7:395–404Google Scholar
  32. 32.
    Abdullah L, See XQ (2016) A fuzzy decision making model for assessing quality of life: a case of a coastal wetland community. J Eng Appl Sci 11:1628–1632Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Fatin Mimi Anira Alias
    • 1
  • Lazim Abdullah
    • 1
    • 2
  • Xunjie Gou
    • 2
    • 3
  • Huchang Liao
    • 2
    • 4
    Email author
  • Enrique Herrera-Viedma
    • 3
    • 4
    • 5
  1. 1.School of Informatics and Applied MathematicsUniversity Malaysia TerengganuKuala TerengganuMalaysia
  2. 2.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Business SchoolSichuan UniversityChengduChina
  4. 4.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  5. 5.Faculty of Computing and Information TechnologyKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations