Abstract
Combining the concepts of fuzzy set theory, entropy, ideal, and grey relation analysis, a fuzzy grey relation method for multiple criteria decision-making problems is proposed. First, triangular fuzzy numbers and linguistic values characterized by triangular fuzzy numbers are used to evaluate the importance weights of all criteria and the superiority of all alternatives versus various criteria above the alternative level. Then, the concept of entropy is utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Furthermore, using the concepts of ideal, the grey ration grades of various alternatives versus ideal solution are ranked to determine the best alternative. Finally, a numerical example of selecting most appropriate company to build a new highway is used to demonstrate the applicability of proposed method. The study results show that this method is an effective means for tackling MCDM problems in fuzzy and grey environments.
Similar content being viewed by others
References
Chen S.H., Hsieh C.H.: Representation, ranking, distance, and similarity of L-R type fuzzy number and application. Aust. J. Intell. Process. Syst. 6(4), 217–229 (2000)
Chou T.Y., Liang G.S., Han T.C.: Application of fuzzy regression on air cargo volume forecast. Qual. Quant. 45, 1539–1550 (2011)
Deng J.L.: The control problems of grey systems. Syst. Control Lett. 5, 288–294 (1982)
Deng J.L.: Introduction to grey systems. J. Grey Syst. 1, 1–24 (1989)
Ding J.F., Liang G.S.: Using fuzzy MCDM to select partners of strategic alliances for liner shipping. Inf. Sci. 173, 197–225 (2005)
Dubois D., Prade H.: Operation on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (1978)
Feng C.M., Chen C.F.: The determination of criteria weights-compromised weighting method. Traffic Transp. 14, 51–67 (1992)
Feng C.M., Wang R.T.: Performance evaluation for airlines including the consideration of financial ratios. J. Air Transp. Manag. 6, 133–142 (2000)
Gao X.W., Ma H.X.: International petroleum price risk early-warning based on grey theory. J. Grey Syst. 14(1), 9–19 (2011)
Hsu Y.L., Li W.C., Chen K.W.: Structuring critical success factors of airline safety management system using a hybrid model. Transp. Res. E 46, 222–235 (2010)
Lee K.L., Huang W.C., Teng J.Y.: Locating the competitive relation of global logistics hub using quantitative SWOT analytical method. Qual. Quant. 43, 87–107 (2009)
Liang G.S.: Fuzzy MCDM based on ideal and anti-ideal concepts. Eur. J. Oper. Res. 112, 682–691 (1999)
Liang G.S., Chou T.Y., Hang T.C.: Cluster analysis based on fuzzy equivalence relation. Eur J. Oper. Res. 166, 160–170 (2005)
Liu S., Guo B., Dang Y.: Grey System Theory and Applications. Scientific Press, Beijing (1999)
Liu C.P., Liang G.S., Su Y.L., Chu C.W.: Navigation safety analysis in Taiwanese ports. J. Navig. 59, 201–211 (2006)
Min C.H., Tang H.W., Yin H.S.: The application of grey relational analysis (GRA) to prioritizing the emotional intelligence (EI) training needs. J. Grey Syst. 12(4), 191–200 (2009)
Saaty T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Tsai H.Y., Chang C.W., Lin H.L.: Fuzzy hierarchy sensitive with Delphi method to evaluate hospital organization performance. Exp. Syst. Appl. 37(8), 5533–5541 (2010)
Wang R.T., Ho C.T., Feng C.M., Yang Y.K.: A comparative analysis of the operational performance of Taiwan’s major airports. J. Air Transp. Manag. 10, 353–360 (2004)
Wen K.L., Wu J.H.: On distinguishing coefficient & relational grade. J. Grey Syst. 8, 11–18 (1996)
Wong C.C., Lai H.R.: A new grey relational measurement. J. Grey Syst. 12, 341–346 (2000)
Wu H.H., Liao A.Y.H., Wang P.C.: Using grey theory in quality function deployment to analyse dynamic customer requirements. Int. J. Adv. Manuf. Technol. 25, 1241–1247 (2005)
Zadeh L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Zadeh L.A.: The concept of a linguistic variable and its application to approximate reasoning, part 1. Inf. Sci. 8, 199–249 (1975a)
Zadeh L.A.: The concept of a linguistic variable and its application to approximate reasoning, part 2. Inf. Sci. 8, 301–357 (1975b)
Zadeh L.A.: The concept of a linguistic variable and its application to approximate reasoning, part 3. Inf. Sci. 9, 43–58 (1976)
Zeleny M.: Multiple Criteria Decision Making. McGraw-Hill Book Company, Singapore (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liao, MS., Liang, GS. & Chen, CY. Fuzzy grey relation method for multiple criteria decision-making problems. Qual Quant 47, 3065–3077 (2013). https://doi.org/10.1007/s11135-012-9704-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-012-9704-5