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This paper describes a new fuzzy relational product that can be applied to two fuzzy relations to produce a new fuzzy relation, which contains the degrees of similarity between its elements. These degrees of similarity are determined according to relationships between the elements and their corresponding third-party elements that are defined in the two original fuzzy relations. This new fuzzy relational product has been developed as part of a research on social network analysis in an attempt to determine relationships among political figures based on their (current) opinions.