Identifying Necessity and Sufficiency Relationships in Skeletal-Part Representation Using Fuzzy-Set Theory

Abstract

Traditional approaches to the analysis of skeletal representation in faunal assemblages that employ correlation analyses work well when there is a linear or curvilinear relationship or no relationship at all between the variables under investigation. However, in taphonomic applications in zooarchaeology, these approaches can mask meaningful variation in certain cases where the relationship between the causal variable and skeletal-part representation is one of limitation rather than absolute determination. Such relationships are typified by triangular distributions of points in scatter plots. Using fuzzy-set theory, these relationships can be interpreted more comprehensively by distinguishing necessity and sufficiency relationships between the causal variable and skeletal part representation. Graphs in which data points are distributed in a triangle in the lower-right part of the scatter plot are consistent with an interpretation of necessity, while graphs where data points are distributed in an upper-left triangle are consistent with an interpretation of sufficiency. Such interpretations parallel transport strategies inferred from graphs of utility and representation, and can be applied profitably to graphs of density and representation. In some cases, this leads not only to refinement of the interpretation of density effects, but also to retrieval of economic evidence that might otherwise be overlooked.