The objective of this paper is to focus on multi-attribute decision-making for interval-valued intuitionistic fuzzy set environment based on set pair analysis (SPA). For it, the major component of the SPA known as connection number has been constructed based on the set pairs between two preference values consists of every attribute and ideal pairs of it. Based on these connection numbers, an extension of technique for order of preference by similarity to ideal solution method is developed by combining the proposed connection number for IVIFSs and hence finding the best alternative(s) using relative degree of closeness coefficient. An illustrative example has been given for demonstrating the approach and compares their performance with some existing measures.
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Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bai ZY (2013) An interval-valued intuitionistic fuzzy TOPSIS method based on an improved score function. Sci World J 2013:Article ID 879,089, 6
Chen C (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9
Fu S, Zhou H (2016) Triangular fuzzy number multi-attribute decision-making method based on set-pair analysis. J Softw Eng 1–7. doi:10.3923/jse.2016
Garg H (2016a) Generalized intuitionistic fuzzy interactive geometric interaction operators using einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69
Garg H (2016b) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999
Garg H (2016c) A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920
Garg H (2016d) A novel correlation coefficients between pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1253
Garg H (2016e) Some series of intuitionistic fuzzy interactive averaging aggregation operators. SpringerPlus 5(1):1–27
Hu J, Yang L (2011) Dynamic stochastic multi-criteria decision making method based on cumulative prospect theory and set pair analysis. Syst Eng Proc 1:432–439
Hwang CL, Yoon K (1981) Multiple attribute decision making. Methods and applications: a state-of-the-art survey. Lecture notes in economics and mathematical systems, vol 186. Springer, Heidelberg, p 269
Li D (2012) Linear programming method for madm with intervalvalued intuitionistic fuzzy sets. Expert Syst Appl 37:5939–5945
Li DF (2010) TOPSIS- based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18:299–311
Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 38(3):1464–1467
Park JH, Park IY, Kwun YC, Tan X (2011) Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy sets. Appl Math Model 35(5):2544–2556
Rui Y, Zhongbin W, Anhua P (2012) Multi-attribute group decision making based on set pair analysis. Int J Adv Comput Technol 4(10):205–213
Sivaraman G, Nayagam VLG, Ponalagusamy R (2013) Multi-criteria interval valued intuitionistic fuzzy decision making using a new score function. In: KIM 2013 knowledge and information management conference, pp 122–131
Tan C, Zhang Q (2006) Fuzzy multiple attribute decision making based on interval valued intuitionistic fuzzy sets. In: Proceedings of the 2006 IEEE international conference on system, man, and cybernetics, Taipei, Taiwan, Republic of China, vol 2, pp 1404–1407
Tsaur SH, Chang TY, Yen CH (2002) The evaluation of airline servcie quality by using mcdm. Tour Manag 23:107–115
Wang JQ, Gong L (2009) Interval probability stochastic multi-criteria decision-making approach based on set pair analysis. Control Decision 24:1877–1880
Wei GW, Wang HJ, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26(2):337–349
Wei X, Li J, Zhang C (2007) Application of the set pair analysis theory in multiple attribute decision-making. J Mech Strength 29:1009–1012
Xie Z, Zhang F, Cheng J, Li L (2013) Fuzzy multi-attribute decision making methods based on improved set pair analysis. Sixth Int Symp Comput Intell Des 2:386–389
Xu Z, Chen J (2007a) Approach to group decision making based on interval valued intuitionistic judgment matrices. Syst Eng Theory Pract 27(4):126–133
Xu Z, Chen J (2007b) On geometric aggregation over interval-valued intuitionistic fuzzy information. In: Fuzzy systems and knowledge discovery, 2007. FSKD 2007. Fourth international conference on, vol 2, pp 466–471. doi:10.1109/FSKD.2007.427
Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433
Yang J, Zhou J, Liu L, Li Y, Wu Z (2008) Similarity measures between connection numbers of set pair analysis. Springer, Berlin, pp 63–68. doi:10.1007/978-3-540-87732-5_8
Ye J (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval—valued intuitionistic fuzzy environment. Expert Syst Appl 36:6809–6902
Zhao K (1989) Set pair and set pair analysis-a new concept and systematic analysis method. In: Proceedings of the national conference on system theory and regional planning, pp 87–91
Communicated by Rosana Sueli da Motta Jafelice.
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Kumar, K., Garg, H. TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comp. Appl. Math. 37, 1319–1329 (2018). https://doi.org/10.1007/s40314-016-0402-0
- Set pair analysis
- Connection number
- Interval-valued intuitionistic fuzzy set
Mathematics Subject Classification