Abstract
This paper attempts to develop an interval-valued intuitionistic fuzzy preference ranking organization method for enrichment evaluations (IVIF-PROMETHEE) and attempts to apply it to multiple criteria decision analysis. The theory of interval-valued intuitionistic fuzzy sets is useful for modeling impressions and quantifying the ambiguous nature of subjective judgments in a convenient manner. PROMETHEE is a well-known and widely used outranking method, but it has not been investigated in depth within the interval-valued intuitionistic fuzzy environment. Based on the concepts of inclusion comparison possibilities, this paper proposes inclusion-based generalized criteria to determine preference functions and global preference indices for acquiring leaving flows, entering flows, and net flows of alternative actions. Using the score functions and accuracy functions of the flows, this paper develops IVIF-PROMETHEE I and IVIF-PROMETHEE II, which are methods for the partial ranking and complete ranking, respectively, of alternatives. The feasibility and applicability of the proposed methods are illustrated through a problem on the selection of bridge construction methods. Finally, a comparative discussion of other decision-making methods is conducted to demonstrate the advantages of the proposed IVIF-PROMETHEE methods.
Similar content being viewed by others
References
Atanassov, K. T. (1983). Intuitionistic fuzzy sets, Seventh Scientific Session of ITKR, Sofia, June (Dep. in CINTI, Nd 1697/84).
Atanassov, K. T., & Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349.
Behzadian, M., Kazemzadeh, R. B., Albadvi, A., & Aghdasi, M. (2010). PROMETHEE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research, 200(1), 198–215.
Boran, F. E., Genç, S., Kurt, M., & Akay, D. (2009). A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Systems with Applications, 36(8), 11363–11368.
Brans, J. P. (1982). L’ingenierie de la decision; Elaboration d’instruments d’aide a la decision. La methode PROMETHEE. In R. Nadeau & M. Landry (Eds.), L’aide a la decision: nature. instruments et perspectives d’avenir (pp. 183–213). Quebec: Presses de l’Universite Laval.
Brans, J. P., & Mareschal, B. (2005). PROMETHEE methods. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 163–195). Boston: Springer.
Brans, J. P., Vincke, P. H., & Mareschal, B. (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research, 24(2), 228–238.
Chai, J., Liu, J. N. K. (2010). A novel multicriteria group decision making approach with intuitionistic fuzzy sir method. 2010 World Automation Congress, WAC 2010, Kobe, 19 September 2010 through 23 September, Article number 5665589.
Chai, J., Liu, J. N. K., & Xu, Z. (2012). A new rule-based sir approach to supplier selection under intuitionistic fuzzy environments. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 20(3), 451–471.
Chen, T. Y. (2012). Nonlinear assignment-based methods for interval-valued intuitionistic fuzzy multi-criteria decision analysis with incomplete preference information. International Journal of Information Technology and Decision Making, 11(4), 821–855.
Chen, T. Y. (2014). Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Information Sciences, 261, 149–169.
Dias, L. C., Costa, J. P., & Climaco, J. N. (1998). A parallel implementation of the PROMETHEE method. European Journal of Operational Research, 104(3), 521–531.
Grzegorzewski, P. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 148(2), 319–328.
Hu, Y. C., & Chen, C. J. (2011). A PROMETHEE-based classification method using concordance and discordance relations and its application to bankruptcy prediction. Information Sciences, 181(22), 4959–4968.
Hsu, T.-H., & Lin, L.-Z. (2014). Using fuzzy preference method for group package tour based on the risk perception. Group Decision and Negotiation, 23(2), 299–323.
Park, J. H., Cho, H. J., & Kwun, Y. C. (2011). Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optimization and Decision Making, 10(3), 233–253.
Parvathi, R., Malathi, C., Akram, M., & Atanassov, K. T. (2013). Intuitionistic fuzzy linear regression analysis. Fuzzy Optimization and Decision Making, 12(2), 215–229.
Vahdani, B., Mousavi, S. M., Tavakkoli-Moghaddam, R., & Hashemi, H. (2013). A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment. Applied Mathematical Modelling, 37(4), 1781–1799.
Xu, Z. S. (2007). Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision, 22(2), 215–219.
Xu, Z. S. (2008). An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, 16(4), 529–555.
Xu, Z., & Cai, X. (2010). Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optimization and Decision Making, 9(4), 359–381.
Xu, Z. S., & Chen, J. (2007). Approach to group decision making based on interval-valued intuitionistic judgment matrices. Systems Engineering-Theory & Practice, 27(4), 126–133.
Xu, Z. S., & Da, Q. L. (2002). The uncertain OWA operator. International Journal of Intelligent Systems, 17(6), 569–575.
Xu, Z. S., & Yager, R. R. (2008). Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning, 48(1), 246–262.
Zhang, X., & Xu, Z. (2012). A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making, 11(2), 135–146.
Acknowledgments
The author is very grateful to the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The study was supported by the Taiwan Ministry of Science and Technology, Grant No. MOST 102-2410-H-182-013-MY3.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, TY. IVIF-PROMETHEE outranking methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Fuzzy Optim Decis Making 14, 173–198 (2015). https://doi.org/10.1007/s10700-014-9195-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-014-9195-z