Choquet Integral Under Pythagorean Fuzzy Environment and Their Application in Decision Making

Choquet integral is one of the aggregation operators that mainly used to aggregate interrelated information. This operator has been successfully embedded with intuitionistic fuzzy sets in solving various decision-making problems. However, the intuitionistic fuzzy sets have some limitations particularly on boundary of constraint where the sum of two memberships never exceeded one. Pythagorean fuzzy set (PFS) was coined to overcome this limitation where the square sum of two memberships could be less than or equal to one. In most cases, it is assumed that all elements of PFSs are independent. Nonetheless, in real life of multi-criteria decision-making problems, most of the criteria are interrelated. This paper aims to introduce Choquet integral operator based on PFSs of which interactions between elements of PFSs can be dealt with fuzzy measures. The proposed operators do not only consider the importance of elements or their ordered positions, but also consider the interaction among the criteria or ordered positions in criteria of decision-making process. The proposed aggregation operator is the combination of the PFSs and Choquet integral in which Choquet integral is used to handle interactions between criteria. A case of sustainable solid waste management problem of two major cities in Malaysia is presented to illustrate the application of the proposed aggregation operators. The proposed method successfully identified that Kuala Lumpur is the better city in managing solid waste based on the values of Pythagorean fuzzy Choquet integrals. Finally, this paper gives some suggestions for future research directions.