A novel approach to concepts via knowledge graph theory and AFS theory

In this paper we combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic fuzzy set theory (AFS). In both theories concepts are studied and concepts can be set in correspondence. This enables to use algebraic results in the context of knowledge graph theory. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. We apply AFS theory to calculate fuzzy decision trees for the knowledge graph of the concepts “democracy”. Then the fuzzy rules derived from the obtained fuzzy decision tree were used to determine the most relevant elements of the concept. The results demonstrate that the proposed method can provide effective and human understandable fuzzy rules for the recognition of the important elements of the word graph of a concept.