A Novel Approach to Group Decision-Making with Interval- Valued Intuitionistic Fuzzy Preference Relations via Shapley Value Han Zhou 1 • Xiyuan Ma 2 • Ligang Zhou 1,3 • Huayou Chen 1 • Weiran Ding 1 Received: 8 April 2017 / Revised: 25 September 2017 / Accepted: 26 October 2017 Ó Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017 Abstract This paper proposes a novel weighting approach to group decision-making (GDM) with interval-valued intuitionistic fuzzy preference relations (IVIFPRs) based on a fuzzy cooperative game method and the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (CIVIFOWA) operator. First of all, a continuous IVIFPR (CIVIFPR) is defined based on the CIVIFOWA operator, and then considering the contribution of each decision-maker (DM), an iterative algorithm is designed to redistribute weights of DMs by using cooperative method. Moreover, a logarithm least optimal model is developed to deriving interval priority weights of IFPR and a two-stage resolution process is proposed for the GDM with IVIFPRs. Finally, a practical example with cooperation and compe- tition is provided to verify the feasibility and efficiency of the proposed method. The characteristics of the proposed method are as follows: (1) the iterative algorithm is devoted to deriving DMs’ weights in GDM by using fuzzy cooperative game based on the CIVIFOWA operator in which the contribution of each DM’s opinion to the group indicates the rationality and importance in GDM of their opinions; (2) the weighting algorithm can be adjusted by modifying the attitude parameter based on the CIVIFOWA operator, which makes the proposed method more flexible. Keywords Group decision-making  Interval-valued intuitionistic fuzzy preference relations  Shapley value  CIVIFOWA operator 1 Introduction Group decision-making (GDM) with preference relations gained extensive attentions in recent researches. Problems of GDM with preference relations can be solved by using the general GDM with suitable aggregation techniques. In the previous literature, GDM problems with multiplicative preference relations [1], fuzzy preference relations [2], linguistic preference relations [3, 4], and intuitionistic preference relations [5, 6] are finely discussed and demonstrated. Nevertheless, constrained by the high com- plexity of socioeconomic environments and the insufficient level of knowledge in real-life decision-making problems, it is reasonable for DMs utilizing interval variables [7], interval linguistic variables [8], or interval-valued intu- itionistic fuzzy variables [9] to express their preferences over alternatives. Thus, preference relations are extended to fuzzy environment, such as the uncertain preference relations [7, 10–14], the uncertain linguistic preference relations [8, 15], and the interval-valued intuitionistic fuzzy preference relations [16, 17]. In GDM problems with preference relations, the absence of consistency or consensus may lead to misleading con- clusions, therefore fruitful results are investigated to mea- sure the consistency and consensus of preference relations. Saaty and Vargas [18] proposed a consistency degree by measuring the divergence between any two multiplicative preference relations. To estimate the consistency of lin- guistic preference relations, Dong and Herrera-Viedma [19] converted linguistic preference relations into interval & Ligang Zhou shuiqiaozlg@126.com 1 School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China 2 School of Mathematics, The University of Edinburg, JCMB, King’s Buildings, Edinburg EH9 3JZ, UK 3 China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing 210044, China 123 Int. J. Fuzzy Syst. DOI 10.1007/s40815-017-0412-0