Choquet integrals of weighted generalized and group generalized intuitionistic fuzzy soft sets

Abstract

For many real multi-criteria decision-making (MCDM) problems under intuitionistic fuzzy environment, most criteria have interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. To approximate the human subjective decision-making process, this paper puts forward the new aggregation operators of generalized intuitionistic fuzzy soft set (GIFSS) and group generalized intuitionistic fuzzy soft sets (G-GIFSS) through the Chqouet integral. These new operators not only demonstrate the interaction phenomena among elements, experts (or moderators) or the ordered positions of them, but also consider their importance or the order positions of them. Furthermore, the new operators are not necessary to assume additivity and independence among decision-making criteria. It should be noted that the existing aggregation operators of GIFSS and G-GIFSS are special cases of the new Choquet integral operators. Two Choquet integral operator-based approaches are developed to solve the MCDM under the intuitionistic fuzzy soft set environment. Finally, a practical example of MCDM is given to validate the effectiveness of the proposal.