Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making

  • Authors:

  • Weize Wang;Xinwang Liu

  • Affiliations:

  • School of Economics and Management, Southeast University, Nanjing, China;School of Economics and Management, Southeast University, Nanjing, China

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2013

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Abstract

The notion of interval-valued intuitionistic fuzzy set IVIFS is a generalization of that of Atanassov's intuitionistic fuzzy set AIFS. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. In this paper, we define some Einstein operations on IVIFS and develop three arithmetic averaging operators, such as the interval-valued intuitionistic fuzzy Einstein weighted averaging IVIFWAε operator, interval-valued intuitionistic fuzzy Einstein ordered weighted averaging IVIFOWAε operator, and interval-valued intuitionistic fuzzy Einstein hybrid weighted averaging IVIFHWAε operator, for aggregating interval-valued intuitionistic fuzzy information. The IVIFHWAε operator generalizes both the IVIFWAε and IVIFOWAε operators. Moreover, we establish various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. Finally, we apply the IVIFHWAε operator to multiple attribute decision making with interval-valued intuitionistic fuzzy information.