Group decision making with heterogeneous intuitionistic fuzzy preference relations

Abstract Intuitionistic fuzzy variables are powerful tools to denote positive and negative information simultaneously. Considering the situation where decision makers (DMs) may adopt different types of preference relations to express their judgements, this paper studies group decision making (GDM) with heterogeneous intuitionistic fuzzy preference relations (IFPRs), including intuitionistic fuzzy preference relations (IFPRs), multiplicative intuitionistic fuzzy preference relations (MIFPRs), additive linguistic intuitionistic fuzzy preference relations (ALIFPRs) and multiplicative linguistic intuitionistic fuzzy preference relations (MLIFPRs). We first study their consistency. Then, we discuss the transformation relationships among them. Using consistent MLIFPRs, we further offer a formula for ascertaining DMs’ weights and investigate the consensus. When the individual consensus level is lower than a predefined threshold, a model for increasing the consensus level is built that ensures the smallest total adjustment and allows the adjusted proportions of different judgements to be different. Moreover, we give a new GDM method with heterogeneous IFPRs. Finally, we use an example to illustrate the application of the proposed GDM method and make a comparison of different GDM methods with heterogeneous preference relations.

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