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

Published online by Cambridge University Press:  20 January 2017

Joseph E. Beaver
Joseph E. Beaver*
Affiliation:
Department of Anthropology, Emil W. Haury Building, University of Arizona, Tucson, AZ 85721
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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.

Resumen

Resumen

Técnicas analíticas que emplean análisis de correlación para la representación ósea de colecciones faunísticas, funcionan bien cuando hay una relación lineal o curvilínea entre las variables bajo investigación o cuando no hay relación entre ellas. Sin embargo, aplicaciones de técnicas tafonómicas para zooarqueología pueden esconder importantes variaciones en casos donde la relación entre la variable causal y las partes óseas representadas no está claramente determinada. En diagramas de dispersión este tipo de relaciones toman la forma de distribuciones triangulares. El uso de la teoría “fuzzy-set” puede resultar útil para mejorar la interpretación de relaciones de necesidady suficiencia entre las variables causales y la representación ósea. Cuando hay una relación de necesidad los datos se distribuyen en forma triangular en la esquina inferior derecha del diagrama de puntos y cuando hay una relación de capacidad estos se distribuyen en la esquina superior izquierda. Estas interpretaciones son análogas a las encontradas en diagramas de utilidady representación usadas para inferir estrategias de transportación y también pueden ser usadas en diagramas de densidad y representación. En algunos casos, estas no solamente conducen al mejoramiento de la interpretación de los efectos de densidad pero también a la recuperación de evidencia económica que de otra manera podría ser ignorada.

Type
Reports
Information
American Antiquity , Volume 69 , Issue 1 , January 2004 , pp. 131 - 140
Copyright
Copyright © The Society for American Archaeology 2004

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