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Fuzzy multi-criteria decision making on combining fuzzy analytic hierarchy process with representative utility functions under fuzzy environment

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Abstract

In 1980, Saaty proposed the analytic hierarchy process (AHP) to evaluate alternatives with multi-criteria being multi-criteria decision making. Then, numerous approaches engaged on extension of AHP under fuzzy environment named fuzzy analytic hierarchy process (FAHP) for evaluation of multi-criteria alternatives under fuzzy environment being fuzzy multi-criteria decision making (FMCDM). In the current approaches, the extent analysis method proposed by Chang in 1996 was a famous FAHP method for FMCDM. However, computing priorities in matrix by Chang’s method is difficult for comparing pairwise fuzzy numbers, and calculating possibility degrees has drawback for some special fuzzy numbers. To resolve above ties, we combine FAHP with representative utility functions under fuzzy environment. Through combination of FAHP and representative utility functions to FMCDM, our method easily and quickly solves FMCDM problems.

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References

  • Bertolini M, Braglia M, Carmignani G (2006) Application of the AHP methodology in making a proposal for a public work contract. Int J Project Manag 24:422–430

    Article  Google Scholar 

  • Boender CGE, de Graan JG, Lootsma FA (1989) Multi-attribute decision analysis with fuzzy pairwise comparisons. Fuzzy Sets Syst 29:133–143

    Article  MATH  Google Scholar 

  • Celik M, Deha Er I, Ozok AF (2009) Application of fuzzy extended AHP methodology on shipping registry selection: the case of Turkish maritime industry. Expert Syst Appl 36:190–198

    Article  Google Scholar 

  • Chang CW, Wu CR, Chen HC (2008) Using expert technology to select unstable slicing machine to control wafer slicing quality via fuzzy AHP. Expert Syst Appl 34:2210–2220

    Article  Google Scholar 

  • Chang DY (1996) Applications of the extent analysis method on fuzzy AHP. Eur J Oper Res 95:649–655

    Article  MATH  Google Scholar 

  • Chen SH, Hsieh CH (1999) Graded mean integration representation of generalized fuzzy number. J Chin Fuzzy Syst Assoc 5:1–7

    Google Scholar 

  • Cheng CH (1997) Evaluating naval tactical missile systems by fuzzy AHP based on the grade value of membership function. Eur J Oper Res 96:343–350

    Article  MATH  Google Scholar 

  • Chou CC (2003) The canonical representation of multiplication operation on triangular fuzzy numbers. Comput Math Appl 45:1601–1610

    Article  MathSciNet  MATH  Google Scholar 

  • Dong Y, Xu Y, Li H, Dai M (2008) A comparative study of the numerical scales and the prioritization methods in AHP. Eur J Oper Res 186:229–242

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:183–224

    Article  MathSciNet  MATH  Google Scholar 

  • Fu HP, Chao P, Chang TH, Chang YS (2008) The impact of market freedom on the adoption of third-party electronic marketplaces: a fuzzy AHP analysis. Ind Mark Manag 37:698–712

    Article  Google Scholar 

  • Grabisch M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions, encyclopedia of mathematics and its applications, vol 127. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Hsu HM, Chen CT (1996) Aggregation of fuzzy opinions under group decision making. Fuzzy Sets Syst 79:279–285

    Article  MathSciNet  Google Scholar 

  • Hsu HM, Chen CT (1997) Fuzzy credibility relation method for multiple criteria decision-making problems. Inf Sci 96:79–91

    Article  MATH  Google Scholar 

  • Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and application. Springer, New York

    Book  MATH  Google Scholar 

  • Jain R (1978) A procedure for multi-aspect decision making using fuzzy sets. Int J Syst Sci 8:1–7

    Article  MATH  Google Scholar 

  • Kacprzyk J, Fedrizzi M, Nurmi H (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst 49:21–31

    Article  MathSciNet  MATH  Google Scholar 

  • Kahraman C, Cebeci U, Ruan D (2004) Multi-attribute comparison of catering service companies using fuzzy AHP: the case of Turkey. Int J Prod Econ 87:171–184

    Article  Google Scholar 

  • Keeney R, Raiffa H (1976) Decision with multiple objective: preference and value tradeoffs. Wiley, New Work

    MATH  Google Scholar 

  • Kuo RJ, Chi SC, Kao SS (1999) A decision support system for locating convenience store through fuzzy AHP. Comput Ind Eng 37:323–326

    Article  Google Scholar 

  • Lee HS (2005) A fuzzy multi-criteria decision making model for the selection of the distribution center. Lect Notes Artif Intell 3612:1290–1299

    Google Scholar 

  • Lee HS (2005) On fuzzy preference relation in group decision making. Int J Comput Math 82:133–140

    Article  MathSciNet  MATH  Google Scholar 

  • Leung LC, Cao D (2000) On consistency and ranking of alternatives in fuzzy AHP. Eur J Oper Res 124:102–113

    Article  MATH  Google Scholar 

  • Liang GS (1999) Fuzzy MCDM based on ideal and anti-ideal concepts. Eur J Oper Res 112:682–691

    Article  MATH  Google Scholar 

  • Lin MC, Wang CC, Chen MS, Chang CA (2008) Using AHP and TOPSIS approaches in customer-driven product design process. Comput Ind 59:17–31

    Article  Google Scholar 

  • Nakamura K (1986) Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst 20:147–162

    Article  MathSciNet  MATH  Google Scholar 

  • Nurmi H (1981) Approaches to collect decision making with fuzzy preference relations. Fuzzy Sets Syst 6:249–259

    Article  MathSciNet  MATH  Google Scholar 

  • Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    MATH  Google Scholar 

  • Saaty TL, Vargas LG (1982) Assessing attribute weights by ratios. Omega 11:9–13

    Google Scholar 

  • Tsaur SH, Chang TY, Yen CH (2002) The evaluation of airline service quality by fuzzy MCDM. Tour Manag 23:107–115

    Article  Google Scholar 

  • van Laarhoven PJM, Predrycs W (1983) A fuzzy extension of Saaty’s priority theory. Fuzzy Sets Syst 11:229–241

    Article  MathSciNet  MATH  Google Scholar 

  • Wang TC, Chen YH (2008) Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Inf Sci 178:3755–3765

    Article  MathSciNet  MATH  Google Scholar 

  • Wang YJ (2008) Applying FMCDM to evaluate financial performance of domestic airlines in Taiwan. Expert Syst Appl 34:1837–1845

    Article  Google Scholar 

  • Wang YJ, Fang CL, Han TC, Chou MT (2015) Applying utility representative function for fuzzy analytic hierarchy process. In: The 11th international conference on fuzzy systems and knowledge discovery (FSKD’15), Zhangjiajie, China, pp 496–500

  • Wang YM, Luo Y, Hua Z (2008) On the extent analysis method for fuzzy AHP and its applications. Eur J Oper Res 186:735–747

    Article  MATH  Google Scholar 

  • Weck M, Klocke F, Schell H, Ruenauver E (1997) Evaluating alternative production cycles using the extended fuzzy AHP method. Eur J Oper Res 100:351–366

    Article  MATH  Google Scholar 

  • Yufei Y (1991) Criteria for evaluating fuzzy ranking methods. Fuzzy Sets Syst 44:139–157

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhu KJ, Jing Y, Chang DY (1999) A discussion on extent analysis method and applications of fuzzy AHP. Eur J Oper Res 116:450–456

    Article  MATH  Google Scholar 

  • Zimmermann HJ (1987) Fuzzy set, decision making and expert system. Kluwer, Boston

    Book  Google Scholar 

  • Zimmermann HJ (1991) Fuzzy set theory—and its application, 2nd edn. Kluwer, Boston

    Book  MATH  Google Scholar 

Download references

Acknowledgments

This research work was partially supported by the National Science Council of the Republic of China under Grant No. NSC 101-2410-H-346-001-.

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Authors and Affiliations

  1. Department of Shipping and Transportation Management, National Penghu University of Science and Technology, Penghu, 880, Taiwan, ROC

    Yu-Jie Wang

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  1. Yu-Jie Wang
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Correspondence to Yu-Jie Wang.

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Communicated by V. Loia.

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Wang, YJ. Fuzzy multi-criteria decision making on combining fuzzy analytic hierarchy process with representative utility functions under fuzzy environment. Soft Comput 22, 1641–1650 (2018). https://doi.org/10.1007/s00500-016-2428-z

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