Fuzzy concepts vary their boundaries in different contexts and conditions. This interesting paper looks at less-explored aspects of fuzzy concepts in continuums. This notion of continuous propositions, such as “to-be-an-adult,” is what distinguishes this paper’s work from traditional work on fuzzy sets, and what links this work to type-II fuzzy logic. There are, however, few explicit links to type-II fuzzy logic, and very few references to fuzzy logic at all. The reason may be that the paper focuses on conceptualization and categorization, and is motivated by type theory.

Beyond the short introduction, which attempts to justify the reported work, the paper is a mathematical description of how different concepts can be defined using the continuum representation. The author defines sharp concepts, which almost takes us back to basic set theory, and vague concepts, which are almost continuous fuzzy sets. Freund also introduces compound concepts, providing a synthetic operator to concatenate concepts together, leading to linguistic representation.

The paper fails to live up to its title: the concept I, which often leads to a discussion of self referencing, is not discussed explicitly. The use of type theory provides some justification; nonetheless, a cognitive scientist will be disappointed. Also, the paper fails to provide clear links to existing work in the area, and fails to explain how the method described compares to and contrasts with existing techniques. The short list of references is another minor weakness.