A fuzzy set analysis of sociometric structure

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Abstract
A fuzzy set theoretical framework is proposed for the analysis of sociometric structure characterized by vagueness of liking between individuals and a person's relative degree of belonging to a social group. Max‐min transitivity of a fuzzy relation is employed as a basic concept to examine the degree of liking and clustering in group structures. A distance model based on min‐max transitivity is also formulated as a special case of transitivity analysis. Other notions of transitivity such as the max‐product and the max‐* are also discussed. An empirical analysis is performed to examine the applicability of the proposed transitivity concepts. It appears that the current methodological construct provides a more appropriate perspective in the analysis of the group structure properties.