Abstract
The aim of this paper is to propose a new type of preference relation, the intuitionistic fuzzy linguistic preference relation (IFLPR). Taking as base the 2-tuple fuzzy linguistic representation model, we introduce the definition of the IFLPR, and its transitivity properties. We present an approach to group decision making based on IFLPRs and incomplete-IFLPRs, respectively. The score function and accuracy function are applied to the ranking and selection of alternatives. Finally, we give an example of IFLPRs in group decision making, and a comparative of the exploitation of the IFLPR with the exploitation of the traditional fuzzy linguistic preference relations.
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References
Alonso S, Chiclana F, Herrera F, Herrera-Viedma E (2004) A learning procedure to estimate missing values in fuzzy preference relations based on additive consistency. MDAI2004, LNAI, vol 3131, pp 227–238
Alonso S, Chiclana F, Herrera F, Herrera-Viedma E (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23:155–175
Alonso S, Cabrerizo FJ, Chiclana F, Herrera F, Herrera-Viedma E (2009) Group decision making with incomplete fuzzy linguistic preference relations. Int J Intell Syst 24(2):201–222
Atanssov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Bonissone PP, Decker KS (1986) Selecting uncertainty calculi and granularity: an experiment in trading-off precision and complexity. In: Kanal LH, Lemmer JF (eds) Uncertainty in artificial intelligence. North-Holland, Amsterdam, pp 217–247
Cabrerizo FJ, Heradio R, Perez IJ, Herrera-Viedma E (2010) A selection process based on additive consistency to deal with incomplete fuzzy linguistic information. J Univers Comput Sci 16(1):62–81
Carlsson C, Fuller R (2000) Benchmarking and linguistic importance weighted aggregations. Fuzzy Sets Syst 114:35–42
Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172
Chiclana F, Herrera-Viedma E, Alonso S (2009) A note on two methods for estimating missing pairwise preference values. IEEE Trans Syst Man Cybern B Cybern 39(6):1628–1633
Delgado M, Verdegay JL, Vila MA (1993) On aggregation operations of linguistic labels. Int J Intell Syst 8(3):351–370
Deschrijver G, Kerre EE (2003) On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst 136(3):333–361
Espinilla M, Liu J, Martínez L (2011) An extended hierarchical linguistic model for decision-making problems. Comput Intell 27:489–512
Fedrizzi M, Giove S (2007) Incomplete pairwise comparison and consistency optimization. Eur J Oper Res 183:303–313
Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115(1):67–82
Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
Herrera F, Martínez L (2001) The 2-tuple linguistic computational model. Advantages of its linguistic description, accuracy and consistency. Int J Uncertain Fuzziness Knowl Based Syst 9:33–48
Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inform Sci 85:223–239
Herrera F, Herrera-Viedma E, Verdegay JL (1996) Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst 79(2):175–190
Herrera F, Martínez L, Sanchez PJ (2005) Managing non-homogeneous information in group decision making. Eur J Oper Res 166:115–132
Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern B Cybern 37(1):176–189
Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114(1):103–113
Kim SH, Ahn BS (1997) Group decision making procedure considering preference strength under incomplete information. Comput Oper Res 24(12):1101–1112
Ngwenyama O, Bryson N (1999) Eliciting and mapping qualitative preferences to numeric rankings in group decision making. Eur J Oper Res 116(3):487–497
Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Szmidt E, Kacprzyk J (1998) Group decision making under intuitionistic fuzzy preference relations. In: Proceedings of 7th IPMU conference, Paris, pp 172–178
Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31(4):1037–1053
Wang JH, Hao J (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14(3):435–445
Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inform Sci 177:2363–2379
Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Making 8(2):123–139
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inform Sci 8(3):199–249
Zhang GQ, Dong YC, Xu YF (2012) Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations. Expert Syst Appl 39(3):2415–2420
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Zhang, Y., Ma, H., Liu, B. et al. Group decision making with 2-tuple intuitionistic fuzzy linguistic preference relations. Soft Comput 16, 1439–1446 (2012). https://doi.org/10.1007/s00500-012-0847-z
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DOI: https://doi.org/10.1007/s00500-012-0847-z