Abstract
In this paper, we propose some new aggregation operators which are based on the Choquet integral and Einstein operations. The operators not only consider the importance of the elements or their ordered positions, but also consider the interactions phenomena among the decision making criteria or their ordered positions. It is shown that the proposed operators generalize several intuitionistic fuzzy Einstein aggregation operators. Moreover, some of their properties are investigated. We also study the relationship between the proposed operators and the existing intuitionistic fuzzy Choquet aggregation operators. Furthermore, an approach based on intuitionistic fuzzy Einstein Choquet integral operators is presented for multiple attribute decision-making problem. Finally, a practical decision making problem involving the water resource management is given to illustrate the multiple attribute decision making process.
Highlights
The concept of intuitionistic fuzzy set (IFS) was introduced by Atanassov (1986, 1999) to generalize the concept of Zadeh’s fuzzy set (Zadeh 1965)
We introduce the Einstein operations and extend them to Technological and Economic Development of Economy, 2014, 20(2): 227–253 the intuitionistic fuzzy operations. Based on these intuitionistic fuzzy Einstein operations and fuzzy measure, we develop some new aggregation operators, such as intuitionistic fuzzy Einstein Choquet averaging (IFCAε ) operator, intuitionistic fuzzy Einstein Choquet geometric (IFCGε ) operator, and study various special cases of the operators, and investigate some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc
Based on the Einstein operational laws of intuitionistic fuzzy values and Choquet integral, in what follows we develop some new operators for aggregating IFVs with correlative weights: Definition 7
Summary
The concept of intuitionistic fuzzy set (IFS) was introduced by Atanassov (1986, 1999) to generalize the concept of Zadeh’s fuzzy set (Zadeh 1965). Based on these intuitionistic fuzzy Einstein operations and fuzzy measure, we develop some new aggregation operators, such as intuitionistic fuzzy Einstein Choquet averaging (IFCAε ) operator, intuitionistic fuzzy Einstein Choquet geometric (IFCGε ) operator, and study various special cases of the operators, and investigate some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc. We compare these operators with the existing intuitionistic fuzzy averaging operators. The final section ends this paper with some concluding remarks
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