Hesitant fuzzy three-way concept lattice and its attribute reduction

Formal concept analysis is a widely studied mathematical tool for performing data analysis and processing. Three-way decision is a model of decision making based on human cognition, which decomposes the problem to be solved into three elements and then reprocesses them. Hesitant fuzzy sets use some possible values instead of one, which can reflect the hesitation and uncertainty of the decision makers. This paper combines the three elements together for the first time and proposes a hesitant fuzzy three-way concept lattice model, which not only extends the concept lattice model but also provides a new way to deal with imprecise data. Firstly, the hesitant fuzzy three-way concept lattice model is proposed and the related properties are investigated. Further, two methods of constructing the hesitant fuzzy three-way concept lattice are studied, and the related construction algorithms are given. Thirdly, the attribute reduction based on the hesitant fuzzy three-way concept lattice is proposed, and a heuristic reduction algorithm is given. Finally, the effectiveness of the proposed algorithms for constructing the hesitant fuzzy three-way concept lattice is verified through some experiments, and the efficiency of the algorithm is compared.