Optimal Scale Combinations Selection for Incomplete Generalized Multi-scale Decision Systems

In the real world, objects are usually measured at different scales and information is often incomplete. The main objective of this study is how to quickly obtain the optimal scale combinations of incomplete generalized multi-scale decision systems (IGMDSs). First, the concept of IGMDSs is introduced, and the sequential three-way decision model of scale space is developed. Second, a stepwise optimal scale selection algorithm is proposed to obtain an optimal scale combination of IGMDS quickly. Finally, to describe the relationships among the scale combinations, the adjacency matrix of the Hasse diagram and updating method for the adjacency matrix are proposed. Accordingly, an efficient optimal scale combinations selection algorithm based on sequential three-way decision is proposed to obtain all optimal scale combinations of IGMDS. Experimental results demonstrate that the proposed algorithms can significantly reduce computational time.