A distance measure, similarity measure and possibility degree for hesitant interval-valued fuzzy sets. (November 2019) - Hu, Mingming; Lan, Jibin; Wang, Zhongxing
Highlights: The existing distance measures for HIVFS ignore the triangle inequality property. Axiom definitions of the distance measure and possibility degree are defined separately. A series of distance, similarity and possibility degree models is generated. The distance, similarity and possibility degree models can be used to solve MADM or GDM. Abstract: A hesitant fuzzy set allows the membership degree to take a set of possible values. When experts cannot easily express their membership judgments with exact values, a hesitant fuzzy set can be extended to a hesitant interval-valued fuzzy set (HIVFS). This set bases the membership degree on a set of possible intervals. To improve the existing distance models that ignore the triangle inequality property and extend the possibility degree for interval numbers, axiom definitions of the distance measure and possibility degree of HIVFSs are proposed. Additionally, a series of distance measure models, similarity models and possibility degree models is generated. A comparative analysis shows that the new distance models satisfy the triangle inequality property but that the existing models cannot and that the possibility degree model can generate the priority degree for each pair of HIVFSs but the distance model cannot.