| In many real management decision making problems, such as the assessment of venture capital projects, the selection of suppliers, the evaluation of virtual enterprise parters and contingency management, due to limitations of experts' work experience and knowledge level and the fuzziness of human thinking, some hesitancy degrees or uncertain degrees often exist while experts are handling decision making problems. An interval-valued intuitionistic fuzzy set employs interval numbers to express the membership, non-membership and hesitancy degrees of one element belonging to a given set. Therefore, the interval-valued intuitionistic fuzzy set can simultaneously describe hesitancy degrees and uncertainty degrees which appear in the process of decision making, and neatly express decision making information supplied by experts.Hence, the interval-valued intuitionistic fuzzy set is more and more popular in the decision making field. On the other hand, group decision making can overcome imperfection of single experts' knowledge and experiences, and derive a more reasonable decision making result. Meanwhile, group decision making can reflect the democracy of modern decision making. Thereby, group decision making has become a hot topic in current complex decision making scenario. Thus, research on the group decision making under interval-valued intuitionistic fuzzy environment has some theoretical significances and higher practical values. Based on existing research, this paper addresses some key topics of group decision making under interval-valued intuitionistic fuzzy environment, including the determination of experts' weights and attributes' weights and decision making methods. Some interesting results are derived and outlined as follows:(1) By using mathematical analysis tools, the asymptotic property of an interval-valued intuitionistic fuzzy matrix is investigated. An important conclusion is given. Namely, it is not appropriate to weight an interval-valued intuitionistic fuzzy matrix many times. Otherwise, all elements in this weighted interval-valued intuitionistic fuzzy matrix will approach to the same interval-valued intuitionistic fuzzy value regardless of initial values of elements.(2) Interval-valued intuitionistic fuzzy multiple attribute group decision making problems are intensively studied. Based on knowledge of interval fuzzy program, a group decision making method is presented. First, by considering the similarity degree and proximity degree simultaneously, an improved TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) approach is proposed to determine experts'weights. A desirable characteristic of the proposed approach is that the determined weights of each expert are different with respect to different attributes. Subsequently,to avoid weighting individual interval-valued intuitionistic fuzzy decision making matrices too many times, the collective matrix, which is generated by weighting individual interval-valued intuitionistic fuzzy decision making matrices with experts'weights, is transformed into an interval matrix using a risk coefficient of experts.Comprehensive values of alternatives are expressed employing attributes' weights which are unknown in advance. Maximizing comprehensive values of alternatives, an interval fuzzy programming model is constructed to determine attributes' weights. The determined attributes' weights are in the form of intervals. At length, a Shapely ranking approach is put forward to rank obtained comprehensive values. Thus, alternatives are sorted and the best alternative is selected. Thereby, a new group decision making method is formed under interval-valued intuitionistic fuzzy environment. A case of a venture capital project selection and comparison analysis illustrate the application of the proposed method in management decision making.(3) This paper addresses interval-valued intuitionistic fuzzy multiple attribute group decision making problems where some attributes interact with each other.Considering interactions among attributes, an intuitionistic fuzzy analytic network process (IF-ANP) approach is presented to determine attributes' weights objectively.Then, improving the classical ELECTRE ? (Elimination and Choice Translating Reality ?) and extending the improved ELECTRE ? into the interval-valued intuitionistic fuzzy environment, an interval-valued intuitionistic fuzzy ELECTRE ?(IVIF-ELECTRE ?) is proposed to rank alternatives. Fusing the proposed IF-ANP and IVIF-ELECTRE ?, a new hybrid group decision making method is formed. Employing this hybrid method, a real case of the supplier selection of Yutong bus limited company is solved. This case implies that the presented method can effectively solve related problems in the supply chain.(4) For solving the group decision making problems with additive consistent interval-valued intuitionistic fuzzy preference relations, an intuitionistic fuzzy program method is proposed considering decision makers' risk attitudes. First, the method analyzes the additive consistency of interval-valued intuitionistic fuzzy preference relations, including defining a new additive consistency, proposing a new index for checking the additive consistency and a new approach to improving the additive consistency of interval-valued intuitionistic fuzzy preference relations. Subsequently,to derive priority weights of alternatives, an intuitionistic fuzzy programming model is established and solved by three approaches considering experts' different risk preferences. Thus, a method is put forward for group decision making with additive consistent interval-valued intuitionistic fuzzy preference relations. Finally, the proposed method is applied into a case of a nuclear accident contingency management,and availably solves the selection of contingency plans.(5) The group decision making problems with multiplicative consistent interval-valued intuitionistic fuzzy preference relations are studied, including the multiplicative consistency of interval-valued intuitionistic fuzzy preference relations,the determination of experts' weights and the priority weights of alternatives. By defining left and right matrices of an interval-valued intuitionistic fuzzy preference relation and employing the multiplicative consistency of intuitionistic fuzzy preference relations, a new multiplicative consistency of interval-valued intuitionistic fuzzy preference relations is defined. Meanwhile, a new indicator for examining the multiplicative consistency of interval-valued intuitionistic fuzzy preference relations is presented and two approaches are presented to modify the multiplicative consistency.Then, based on different group integrating criteria, a generalized objective program model is built to determine experts' weights. Finally, by analyzing relations between priority weights of an interval-valued intuitionistic fuzzy preference relation and those of corresponding intuitionistic fuzzy preference relations, a linear programming model is constructed to derive alternatives' priority weights which are in the form of interval-valued intuitionistic fuzzy values. To rank these priority weights, a TOPSIS ranking approach is presented. A case of a virtual enterprise parter selection illustrates applications of the proposed method in management decision making. |
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