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Group Decisions with Intuitionistic Fuzzy Sets

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Handbook of Group Decision and Negotiation

Abstract

The intuitionistic fuzzy set has emerged as a powerful technique for presenting evaluations under uncertainty. It simultaneously describes an object from above and below, that is, by finding one description that includes the object and another that is included by it. Due to the increasing complexity of decision-making environments and the dynamic and uncertain characteristics of objects, the intuitionistic environment has proven valuable to support group decision-making over the past decades.

To help decision-makers interpret and apply intuitionistic fuzzy sets in group decision-making, this chapter provides an overview of intuitionistic fuzzy sets from the perspectives of information fusion, intuitionistic preference relations, and multi-attribute group decisions. Intuitionistic fuzzy information (1) supports information fusion, the fundamental technique for processing decision information and the basis for attaining reasonable decisions, (2) facilitates fuzzy preference relations, enabling decision-makers to express their evaluations and guaranteeing effective scientific decision-making, and (3) constitutes a significant tool for improving decision-making and a direct means for reaching final decision results. To illustrate these ideas, this chapter describes practical contributions of intuitionistic fuzzy sets in the fields of supply chain management, healthcare, and risk assessment in hydropower station assessments and elsewhere. In addition, the prospects and challenges for future research are briefly pointed out.

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References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  Google Scholar 

  • Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78(3):305–316

    Article  Google Scholar 

  • Chai J, Liu JNK, Xu ZS (2012) A new rule-based sir approach to supplier selection under intuitionistic fuzzy environments. Int J Uncertain Fuzz 20(3):451–471

    Google Scholar 

  • Gu J, Ren PJ, Xu ZS (2015) Study on the performance assessment method of venture capital guide fund under intuitionistic fuzzy information environment. Chin J Manag Sci 23:124–131

    Google Scholar 

  • Hao ZN, Xu ZS, Zhao H, Zhang R (2017) Novel intuitionistic fuzzy decision making models in the framework of decision field theory. Inf Fusion 33:57–70

    Article  Google Scholar 

  • Hwang CL, Yoon K (1981) Multiple attribute decision making methods and applications. Springer, Berlin

    Book  Google Scholar 

  • Liang DC, Xu ZS, Liu D (2017) Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators. Inf Sci 375:183–201

    Article  Google Scholar 

  • Liao HC, Xu ZS (2014a) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Trans Fuzzy Syst 22(6):1669–1681

    Article  Google Scholar 

  • Liao HC, Xu ZS (2014b) Multi-criteria decision making with intuitionistic fuzzy PROMETHEE. J Intell Fuzzy Syst 27:1703–1717

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Framework of group decision making with intuitionistic fuzzy preference information. IEEE Trans Fuzzy Syst 23(4):1211–1227

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Xu DL (2016) An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations. Inf Sci 329:274–286

    Article  Google Scholar 

  • Liao HC, Mi XM, Xu ZS, Xu JP, Herrera F (2018) Intuitionistic fuzzy analytic network process. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2788881

  • Mareschal B, Brans JP, Vincke P (1984) PROMETHEE: a new family of outranking methods in multicriteria analysis. ULB – Universite Libre de Bruxelles, Bruxelles

    Google Scholar 

  • Meng FY, Tang J, Xu ZS (2017) A 0–1 mixed programming model based method for group decision making with intuitionistic fuzzy preference relations. Comput Ind Eng 112:289–304

    Article  Google Scholar 

  • Opricovic S (1998) Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade 2(1):5–21

    Google Scholar 

  • PÈ©kala B, Szmidt E, Kacprzyk J (2018) Group decision support under intuitionistic fuzzy relations: the role of weak transitivity and consistency. Int J Intell Syst 33:2078–2095

    Article  Google Scholar 

  • Ren PJ, Xu ZS, Liao HC, Zeng XJ (2017) A thermodynamic method of intuitionistic fuzzy MCDM to assist the hierarchical medical system in China. Inf Sci 420:490–504

    Article  Google Scholar 

  • Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, Dordrecht

    Book  Google Scholar 

  • Shen F, Xu JP, Xu ZS (2016) An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets. Inf Sci 334–335:338–353

    Article  Google Scholar 

  • Shen F, Ma XS, Li ZY, Xu ZS, Cai DL (2018) An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Inform Sciences 428:105–119

    Google Scholar 

  • Simon HA (1947) Administrative behavior: a study of decision-making processes in administrative organization. Macmillan, New York

    Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2003a) An intuitionistic fuzzy set based approach to intelligent data analysis: an application to medical diagnosis. Recent advances in intelligent paradigms and applications. Physica-Verlag, GmbH, Heidelberg/New York

    Google Scholar 

  • Szmidt E, Kacprzyk J (2003b) A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst 18:837–852

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: International conference on artificial intelligence and soft computing, Zakopane, pp 388–393

    Google Scholar 

  • Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12(2):117–131

    Article  Google Scholar 

  • Tian XL, Xu ZS, Gu J, Herrera-Viedma E (2018) How to select a promising enterprise for venture capitalists with prospect theory under intuitionistic fuzzy circumstance? Appl Soft Comput 67:756–763

    Article  Google Scholar 

  • Wang ZJ (2013) Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations. Appl Math Model 37(9):6377–6388

    Article  Google Scholar 

  • Wang YY, Xu ZS (2018) Evaluation of the human settlement in Lhasa with intuitionistic fuzzy analytic hierarchy process. Int J Fuzzy Syst 20(1):29–44

    Article  Google Scholar 

  • Xia MM, Xu ZS (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19(4):430–452

    Google Scholar 

  • Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13:31–47

    Article  Google Scholar 

  • Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Article  Google Scholar 

  • Xu ZS (2007b) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Making 6:109–121

    Article  Google Scholar 

  • Xu ZS (2007c) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379

    Article  Google Scholar 

  • Xu ZS (2007d) Approaches to multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng Theory Pract 27(11):62–71

    Article  Google Scholar 

  • Xu ZS (2007e) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Making 6(3):221–236

    Article  Google Scholar 

  • Xu ZS (2009a) Intuitionistic fuzzy hierarchical clustering algorithms. J Syst Eng Electron 20(1):90–97

    Google Scholar 

  • Xu ZS (2009b) A method for estimating criteria weights from intuitionistic preference relations. Fuzzy Inf Eng 1(1):79–89

    Article  Google Scholar 

  • Xu ZS (2010a) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180(5):726–736

    Article  Google Scholar 

  • Xu ZS (2010b) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19(1):57–76

    Article  Google Scholar 

  • Xu ZS (2012) Intuitionistic fuzzy multiattribute decision making: an interactive method. IEEE Trans Fuzzy Syst 20(3):514–525

    Article  Google Scholar 

  • Xu ZS (2013) Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decis Negot 22(3):463–482

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzz 16(4):529–555

    Article  Google Scholar 

  • Xu ZS, Liao HC (2013) Intuitionistic fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst 22(4):749–761

    Article  Google Scholar 

  • Xu ZS, Liao HC (2015) A survey of approaches to decision making with intuitionistic fuzzy preference relations. Knowl-Based Syst 80:131–142

    Article  Google Scholar 

  • Xu ZS, Xia MM (2014) Iterative algorithms for improving consistency of intuitionistic preference relations. J Oper Res Soc 65(5):708–722

    Article  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433

    Article  Google Scholar 

  • Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48:246–262

    Article  Google Scholar 

  • Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern B 41(2):568–578

    Article  Google Scholar 

  • Xu ZS, Chen J, Wu JJ (2008) Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 178:3775–3790

    Article  Google Scholar 

  • Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int J Intell Syst 26:787–813

    Google Scholar 

  • Yu S, Xu ZS (2016) Definite integrals of multiplicative intuitionistic fuzzy information in decision making. Knowledge-Based Systems 100:59–73

    Google Scholar 

  • Zhang XM, Xu ZS (2012) A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optim Decis Making 11(2):135–146

    Article  Google Scholar 

  • Zhang XL, Xu ZS (2014) Deriving experts’ weights based on consistency maximization in intuitionistic fuzzy group decision making. J Intell Fuzzy Syst 27(1):221–233

    Article  Google Scholar 

  • Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30

    Article  Google Scholar 

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Correspondence to Zeshui Xu .

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Ren, P., Xu, Z., Kacprzyk, J. (2020). Group Decisions with Intuitionistic Fuzzy Sets. In: Kilgour, D., Eden, C. (eds) Handbook of Group Decision and Negotiation. Springer, Cham. https://doi.org/10.1007/978-3-030-12051-1_43-1

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  • DOI: https://doi.org/10.1007/978-3-030-12051-1_43-1

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  • Online ISBN: 978-3-030-12051-1

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