Advertisement

Soft Computing

, Volume 22, Issue 22, pp 7423–7433 | Cite as

Fuzzy multiple criteria decision-making via an inverse function-based total utility approach

  • Ta-Chung Chu
  • Wei-Chang Yeh
Focus

Abstract

This work presents ranking alternatives under fuzzy multiple criteria decision making (MCDM) via an inverse function-based total utility approach, where ratings of alternatives versus qualitative criteria as well as importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. Membership functions of the final fuzzy values of alternatives can be developed; some of their properties are investigated and proved. The right utility is obtained from the inverse function of right membership function of the final fuzzy value and the inverse function of maximizing set, while the left utility is obtained from the inverse function of left membership function of the final fuzzy value and the inverse function of minimizing set. Total utility is the sum of the right and left utilities. A larger total utility indicates that the corresponding alternative is more favorable. The ranking of fuzzy numbers can be clearly formulated to increase the applicability of the suggested fuzzy MCDM model. A numerical example demonstrates the feasibility of the proposed method, and some comparisons are provided to reveal robustness and advantages of the proposed method.

Keywords

Ranking Fuzzy number Fuzzy MCDM Inverse function Total utility 

Notes

Acknowledgements

The authors would like to thank the two anonymous referees, Prof. Genovese and Prof. Bruno for providing very helpful comments and suggestions. Their insights and comments led to a better presentation of the ideas expressed in this paper. This work was supported in part by Ministry of Science and Technology of the Republic of China, Taiwan, under Grant MOST 105-2410-H-218-002.

Funding

This study was funded in part by Ministry of Science and Technology of the Republic of China, Taiwan, under Grant MOST 105-2410-H-218-002.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

Ethical approval

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

References

  1. Akdag H, Kalayc T, Karagöz S, Zülfikar H, Giz D (2014) The evaluation of hospital service quality by fuzzy MCDM. Appl Soft Comput 23:239–248CrossRefGoogle Scholar
  2. Chen SH (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 17(2):113–129MathSciNetCrossRefGoogle Scholar
  3. Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making. Springer, BerlinCrossRefGoogle Scholar
  4. Chu TC, Charnsethikul P (2013) Ordering alternatives under fuzzy multiple criteria decision making via a fuzzy number dominance based ranking approach. Int J Fuzzy Syst 15(3):263–273MathSciNetGoogle Scholar
  5. Çifçi G, Büyüközkan G (2011) A fuzzy MCDM approach to evaluate green suppliers. Int J Comput Intell Syst 4(5):894–909CrossRefGoogle Scholar
  6. Das S, Guha D (2016) A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problem. Fuzzy Inf Eng 8(1):41–74MathSciNetCrossRefGoogle Scholar
  7. Destercke S, Couso I (2015) Ranking of fuzzy intervals seen through the imprecise probabilistic lens. Fuzzy Sets Syst 278:20–39MathSciNetCrossRefGoogle Scholar
  8. Dinagar DS, Kamalanathan S (2015) A method for ranking of fuzzy numbers using new area method. Int J Fuzzy Math Arch 9(1):61–71Google Scholar
  9. Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9(6):613–626MathSciNetCrossRefGoogle Scholar
  10. Duzce SA (2015) A new ranking method for trapezial fuzzy numbers and its application to fuzzy risk analysis. J Intell Fuzzy Syst 28(3):1411–1419MathSciNetGoogle Scholar
  11. Gu Q, Xuan Z (2017) A new approach for ranking fuzzy numbers based on possibility theory. J Comput Appl Math 309:674–682MathSciNetCrossRefGoogle Scholar
  12. Hari Ganesh A, Jayakumar S (2014) Ranking of fuzzy numbers using radius of gyration of centroids. Int J Basic Appl Sci 3(1):17–22Google Scholar
  13. Kahraman C (2008) Fuzzy multi-criteria decision making: theory and applications with recent developments. Springer, BerlinCrossRefGoogle Scholar
  14. Kaufmann A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and application. Van Nostrand Reinhold, New YorkzbMATHGoogle Scholar
  15. Liou TS, Wang MJJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50(3):247–255MathSciNetCrossRefGoogle Scholar
  16. Moghimi R, Anvari A (2014) An integrated fuzzy MCDM approach and analysis to evaluate the financial performance of iranian cement companies. Int J Adv Manuf Technol 71(1–4):685–698CrossRefGoogle Scholar
  17. Pedrycz W, Ekel P, Parreiras R (2010) Fuzzy multicriteria decision-making: theory, methods and applications. Wiley, LondonCrossRefGoogle Scholar
  18. Ribeiro RA (1996) Fuzzy multiple attribute decision making: a review and new preference elicitation techniques. Fuzzy Sets Syst 78(2):155–181MathSciNetCrossRefGoogle Scholar
  19. Salehi K (2015) A hybrid fuzzy MCDM approach for project selection problem. Decis Sci Lett 4(1):109–116CrossRefGoogle Scholar
  20. Shen KY, Hu SK, Tzeng GH (2017) Financial modeling and improvement planning for the life insurance industry by a rough knowledge based hybrid MCDM model. Inf Sci 375:296–313CrossRefGoogle Scholar
  21. Torfi F, Farahani RZ, Mahdavi I (2016) Fuzzy MCDM for weight of object’s phrase in location routing problem. Appl Math Model 40(1):526–541MathSciNetCrossRefGoogle Scholar
  22. Ülker B (2015) A fuzzy MCDM algorithm and practical decision aid tool to determine the best ROV design alternative. Kybernetes 44(4):623–645CrossRefGoogle Scholar
  23. Wang X, Kerre EE (2001a) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst 118(3):375–385MathSciNetCrossRefGoogle Scholar
  24. Wang X, Kerre EE (2001b) Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets Syst 118(3):387–405MathSciNetCrossRefGoogle Scholar
  25. Wang Z, Zhang-Westmant L (2014) New ranking method for fuzzy numbers by their expansion center. J Artif Intell Soft Comput Res 4(3):181–187CrossRefGoogle Scholar
  26. Wu Z, Ahmad J, Xu J (2016) A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information. Appl Soft Comput 42:314–324CrossRefGoogle Scholar
  27. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
  28. Zadeh LA (1975a) The concept of a linguistic variable and its application to approximate reasoning, part 1. Inf Sci 8(3):199–249CrossRefGoogle Scholar
  29. Zadeh LA (1975b) The concept of a linguistic variable and its application to approximate reasoning, part 2. Inf Sci 8(4):301–357CrossRefGoogle Scholar
  30. Zadeh LA (1975c) The concept of a linguistic variable and its application to approximate reasoning, part 3. Inf Sci 9(1):43–80CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial Management and InformationSouthern Taiwan University of Science and TechnologyTainan CityTaiwan
  2. 2.Department of Industrial Engineering and Engineering ManagementNational Tsing Hua UniversityHsinchuTaiwan

Personalised recommendations