Sugeno Integral of Set-Valued Functions with Respect to Multi-submeasures and Its Application in MADM

Based on theoretical analysis of fuzzy integrals, this paper firstly defines the Sugeno integral of set-valued mappings with respect to multi-submeasures, which is an extension of Sugeno integrals of single-valued mappings and Sugeno integrals of set-valued mappings with respect to fuzzy measures. Some desirable properties and the computing rule of it are also discussed and proved in this paper. Then, a novel multi-attribute decision-making (MADM) method is established based on the computing rule of the Sugeno integral defined in this paper under an interval-valued hesitant fuzzy environment, in which all values assigned to alternatives, experts and attributes are all expressed by interval-values. Finally, a numerical MADM example is established to verify the practicality and effectiveness of the proposed definition, during the decision process, the positive interaction, negative interaction or non-interaction among attributes can be fully considered.