Abstract
Group decision making with intuitionistic fuzzy preference information contains two key issues: acceptability measurement and priority weight determination. In this paper, we investigate the above two issues with respect to multiplicative interval-valued intuitionistic fuzzy preference relation (IVIFPR). Firstly, a consistency index is defined to measure the multiplicative consistency degree of IVIFPR and an optimization model is established to improve the consistency degree of IVIFPR to an acceptable one. Next, in terms of priority weight determination, an error-analysis-based extension method is proposed to obtain priority weight vector from the acceptable IVIFPR. For GDM problems, decision makers’ weights are derived by the proposed multiplicative consistency index. Subsequently, the collective IVIFPR is obtained by using an interval-valued intuitionistic fuzzy (IVIF) weighted averaging operator. Finally, a step-by step algorithm for GDM with IVIFPRs is given, and an example of enterprise innovation partner selection is analyzed, and comparative analyses with existing approaches are performed to demonstrate that the proposed algorithm is both effective and practical in dealing with GDM problems.
Highlights
In Group decision making (GDM), various decision makers (DMs or experts) would be employed to express their preferences via pairwise comparison over decision alternatives
To measure the consistency degree of an interval-valued intuitionistic fuzzy preference relation (IVIFPR), according to the multiplicative consistency definition in Reference [18], this paper proposes a new concept of multiplicative consistency index of an IVIFPR
Following the work of Method [18], based on two principles of decision making, this paper proposes a new definition of consistency index of an IVIFPR, which can measure the multiplicative consistency degree of an IVIFPR
Summary
In Group decision making (GDM), various decision makers (DMs or experts) would be employed to express their preferences via pairwise comparison over decision alternatives. As for the determination of priority weights of alternatives for IVIFPRs, the existing studies [15,22,24] have directly adopted the formulas to rank the alternatives Such formulas are only applicable to consistent IVIFPRs and would be ineffective for inconsistent. To fill the literature review gap, this paper concentrates on developing a novel algorithm for IVIFPRs in GDM problems based on acceptability measurement and priority weight determination. To measure the consistency degree of an IVIFPR, according to the multiplicative consistency definition in Reference [18], this paper proposes a new concept of multiplicative consistency index of an IVIFPR by considering various decision-making principles (i.e., the majority and minority principles).
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