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Three-way decisions provide a trisecting-and-acting framework for complex problem solving. For a cost-sensitive decision-making problem under multiple levels of granularity, sequential three-way decisions have come into being. Within this framework, how to act upon the three pair-wise disjoint regions is the most important issue. To this end, we propose a generalized model of sequential three-way decisions via multi-granularity in this paper. Subsequently, we adopt the typical aggregation strategies to implement the following five kinds of multigranulation sequential three-way decisions—the weighted arithmetic mean multigranulation sequential three-way decisions, the optimistic multigranulation sequential three-way decisions, the pessimistic multigranulation sequential three-way decisions, the pessimistic-optimistic multigranulation sequential three-way decisions and the optimistic-pessimistic multigranulation sequential three-way decisions. Furthermore, we discuss the rightness and rationality of the five kinds of multigranulation sequential three-way decisions and also analyze the relationships and differences between them. Finally, the experimental results demonstrate that the first four different multigranulation sequential three-way decisions are effective. These models will accelerate and enrich the development of multigranulation three-way decisions. [ABSTRACT FROM AUTHOR]

• We generalize the concepts of the conditional and decision attributes through concept hierarchy tree, and define a generalized hierarchical decision table. • We decompose and aggregate condition and decision attribute granules under different levels of granularity. • We propose the optimistic and pessimistic generalized multigranulation three-way decision models for hierarchical classification. • We compare the advantages under different sequential three-way decision models experimentally. Hierarchical classification is an important research hotspot in machine learning due to the widespread existence of data with hierarchical class structures. The existing sequential three-way decision models mainly constructed the hierarchical condition information granules via concept hierarchy tree to discuss the three probabilistic regions for flat classification. However, in real-world applications, one may face not only the tree-structured data with hierarchical condition attributes but also more often the multi-level data with hierarchical decision attribute (hierarchical class labels). How to obtain acceptable decisions under different levels of granularity is the most important issue within the multi-level and multi-view data. To this end, we construct a generalized hierarchical decision table and propose a generalized hierarchical multigranulation sequential three-way decision model by combining multi-granularity and sequential three-way decisions. Specifically, we first design a generalized hierarchical decision table using concept hierarchy trees of all conditional attributes and decision attribute, and explore some basic properties. Then we decompose and aggregate condition and decision granules under different levels of granularity, propose the optimistic and pessimistic generalized hierarchical multigranulation three-way decision models to update the three probabilistic regions for flat and hierarchical classification, and discuss the relationships between these two models. Finally, the experimental results demonstrate that the proposed models are more suitable for different applications. These models will provide a novel insight and enrich the development of multigranulation three-way decisions from the perspective of multi-level and multi-view. [ABSTRACT FROM AUTHOR]