This paper presents a new mathematical approach, fuzzy mathematics, for defining, classifying, and analyzing concepts within communications. Fuzzy mathematics is based on the premise that real world phenomena contain characteristics that overlap any artifically created category system or classification rules. Therefore, set membership is characterized by values of a function ranging between zero and one; each value indicates the degree of an element's membership in a given set. Applications of fuzzy mathematics are described for taxonomies in communication, consensus measurement, interaction analysis, and influence hierarchies. (Author/AA)