Trapezoidal Intuitionistic Fuzzy Aggregation Operator Based on Choquet Integral and Its Application to Multi-Criteria Decision-Making Problems

Abstract

The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.

Keywords

multi-criteria decision making / trapezoidal intuitionistic fuzzy numbers / Choquet integral / fuzzy measure / aggregation operator

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Nos. 71431006, 71401184), Key Project of Philosophy and Social Sciences Research, Ministry of Education, PRC (No. 13JZD0016), China Postdoctoral Science Foundation (No. 2014M552169) and Central South University Business Management Postdoctoral Research Station.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg