Abstract
AbstractBased on the Choquet integral and the generalized Shapley function, two new induced Atanassov's interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal λ–fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under Atanassov...
Highlights
A wide range of aggregation operators are found in the literature
Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex
In order to globally reflect the interaction among elements and simplify the complexity of solving a fuzzy measure, we further introduce the induced generalized OShapley $WDQDVVRY¶V LQWHUYDO-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGOS-IVIFHCAA) operator and the induced generalized OShapley $WDQDVVRY¶V LQWHUYDO- valued intuitionistic fuzzy hybrid Choquet geometric mean (IGOS-IVIFHCGM) operator
Summary
A wide range of aggregation operators are found in the literature. One common aggregation method is the ordered weighted averaging (OWA) operator [1]. Based on the Choquet integral [41], many aggregation operators are proposed, such as the Choquet integral operator on fuzzy sets [30], the $WDQDVVRY¶V intuitionistic fuzzy correlated averaging (IFCA) operator [31, 32], the $WDQDVVRY¶V intuitionistic fuzzy correlated geometric (IFCG) operator [31], the $WDQDVVRY¶V LQWHUYDO-valued intuitionistic fuzzy correlated averaging (IVIFCA) operator [31, 33], the $WDQDVVRY¶V LQWHUYDO-valued intuitionistic fuzzy correlated geometric (IVIFCG) operator [31], the induced $WDQDVVRY¶V intuitionistic fuzzy Choquet ordered averaging (IIFCOA) operator [34], the combined continuous generalized Choquet integral aggregation (CC-GCIA) operator [35] and the induced generalized $WDQDVVRY¶V LQWHUYDO-valued intuitionistic fuzzy Choquet ordered averaging (I-GIVIFCOA) operator [36] These operators do consider the importance of elements or their ordered positions, and can reflect the correlations among them or their ordered positions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
