Using fuzzy set theory to investigate polyadic grooming relationships among captive chimpanzees

A novel methodology is proposed for the analysis of primate social groups. Fuzzy set theory can provide quantitative information about the social dependence of one individual on another, in relation to the entire group. Instead of mapping one-to-one relationships, this procedure maps one-to-many relations. Whereas classical set theory is limited to crisp set membership (membership of x in set A = 0 or 1), fuzzy set theory allows degrees of membership (membership of x in set A = range 0–1). The latter is more suitable for analysing primate social interactions because primate social relationships (measured as number of interactions) typically follow a pattern whereupon relationships can be classified within a range of 0–1 (depending on number of interactions). Here, fuzzy set theory methods are demonstrated on a large dataset of social grooming interactions amongst captive chimpanzee group at Chester Zoo, UK. Consider the relationship between chimpanzees A and B, in relation to all others in the group (C, D, E, etc.). Sets A and B include those who groom chimpanzee A and B, respectively. Degrees of membership in these sets are assigned according to number of interactions. Several analyses are possible, the most pertinent being that of ‘fuzzy inclusion’. Here, an ‘inclusion co-efficient’ is presented as a very useful method for measuring the extent (as a continuous variable) that one set can be included within another – applicable to situations for measuring general social dependence of one chimpanzee within the social context of another individual (or clusters of individuals).