Some generalized Shapely interval-valued dual hesitant fuzzy uncertain linguistic Choquet geometric operators and their application to multiple attribute decision making

Abstract

To handle more complex multiple attribute decision making (MADM) problems, we define a novel type of fuzzy sets called interval-valued dual hesitant fuzzy uncertain linguistic (IVDHFUL) sets (IVDHFULSs) by combining interval-valued dual hesitant fuzzy sets with uncertain linguistic term sets. Then, the operations, the comparison method and the Hamming distance measure of IVDHFUL elements (IVDHFULEs) are defined. Besides, we propose the IVDHFUL Choquet geometric (IVDHFULCG) operator. This operator considers the interaction between adjacent coalitions of attributes. To overall capture the correlations among attributes, the Shapely IVDHFULCG (SIVDHFULCG) operator is proposed. In order to simplify the complexity of handling fuzzy measures, we further propose the 2-order additive SIVDHFULCG (2OA-SIVDHFULCG) operator. Moreover, when the weighting information is partly known, models for the optimal fuzzy measures are constructed. Finally, we propose two novel MADM methods and provide two cases to illustrate the specific application of the developed methods.