Algorithm for constructing three-way concepts

The theory of three-way concept analysis is newly developed, but so far there is no concrete algorithm for constructing three-way concepts. In order to solve this problem, a three-way concept construction algorithm named CbO3C is firstly proposed in this paper. The CbO3C adopts the idea of the construction algorithm CbO of formal concepts in formal concept analysis. At the same time, in order to improve the efficiency and lower the memory overhead, the CbO3C employs the partial closure canonicity test and inherited failure test to reduce the repeated computations of three-way concepts, applies the reduction condition to filter the non-core three-way concepts, and implements set operations on the basis of bits. The experiments with UCI and random data sets show that the CbO3C can correctly and efficiently calculate all core three-way concepts of a formal context.