An approach to intuitionistic fuzzy multi-attribute group decision making based on hybrid Einstein aggregation operators

With respect to intuitionistic fuzzy information, this paper presents the induced intuitionistic fuzzy hybrid weighted Einstein aggregation (I-IFHWEA) operator and the induced intuitionistic fuzzy hybrid geometric Einstein aggregation (I-IFHGEA) operator, which overcome the drawback in the existing reference. To deal with the situations where elements in a set are correlative, the induced intuitionistic fuzzy hybrid Shapley weighted Einstein aggregation (I-IFHSWEA) operator and the induced intuitionistic fuzzy hybrid Shapley geometric Einstein aggregation (I-IFHSGEA) operator are defined, which can be seen as an extension of some intuitionistic fuzzy operators based on additive measures. When the information about the weight vector is partly known, models based on the relative projection are established, by which the optimal fuzzy measure can be obtained. After that, an approach to multi-attribute group decision making under intuitionistic fuzzy environment is developed, and an illustrative example is provided to demonstrate its practicality and feasibility. © 2016 Inderscience Enterprises Ltd.