Granular reduction in formal fuzzy contexts: graph representation, graph approach and its algorithm

Attribute reduction is one of the significant research issues in the formal fuzzy context (FFC). However, the extant method of computing the minimal granular reducts by Boolean reasoning is an NP problem. To this end, a graph-theoretic-based heuristic algorithm is proposed to compute the granular reducts in an FFC. We introduce the induced graph of the granular discernibility matrix and show that the minimal vertex cover of this induced graph is equivalent to the reduction of the FFC, thus transforming the problem of reduction the FFC into the problem of finding the minimal vertex cover of the graph. The manuscript also sets forth algorithms for finding minimal granular reducts based on graph theory. Further, data experiments are designed, and we formulate a transformation model from an information system with multi-valued attributes to an FFC, considering the characteristics of the continuous type of numerical attributes used in the experiments. Experimental results show that our proposed method performs well in terms of time complexity and running time.