Abstract
The intuitionistic fuzzy set (IFS), a popular tool to present decision makers’ cognitive information, has received considerable attention from researchers. To extend the interaction operational laws in the computation of cognitive information, this paper focuses on investigating extensions of geometric interaction aggregation operators by means of the t-norm and the corresponding t-conorm under an intuitionistic fuzzy environment. We develop the extending intuitionistic fuzzy-weighted geometric interaction averaging (EIFWGIA) operator, the extending intuitionistic fuzzy-ordered weighted geometric interaction averaging (EIFOWGIA) operator, the intuitionistic fuzzy weighted geometric interaction quasi-arithmetic mean (IFWGIQAM), and the intuitionistic fuzzy-ordered weighted geometric interaction quasi-arithmetic mean (IFOWGIQAM). We investigate the properties of the proposed extensions and apply the extensions to the cognitive microcredit origination problem. For different generator functions h and ϕ, the proposed IFWGIQAM and IFOWGIQAM degenerate into existing intuitionistic fuzzy aggregation operators or extensions, some of which consider situations that in which no interactions exist between membership and non-membership functions, which can be used in more decision situations. The methods developed in this paper can be used to account for several decision situations. The numerical example demonstrates the validity of the proposed approaches by means of comparisons.
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