Two Integral Models and Applications of Hesitant Fuzzy Information Fusion

The existing fuzzy multiattribute decision making methods rely too much on discrete information fusion operators. In the context of big data, it cannot meet the needs of rapid fusion of massive data, nor can it reflect the continuous change of decision-makers thinking over time. In this article, we study how to integrate large-scare continuous hesitant fuzzy information more efficiently. We define the concepts of continuous hesitant fuzzy sets and continuous hesitant fuzzy functions. Based on these, we further explore definite line integrals of continuous hesitant fuzzy functions and their related properties. Two continuous hesitant fuzzy information integration models based on the hesitant fuzzy calculus are proposed. We also commit to revealing the internal connections between the first line integral model, the second line integral model, and the hesitant fuzzy weighted operator. We state why it is necessary to introduce novel aggregation models based on definite line integrals, and then provide applications of the proposed models to prove their validity and rationality. Finally, we compare the proposed models with other aggregation operators to further demonstrate their effectiveness and rationality.