Measuring the fuzziness of human thoughts: An application of fuzzy sets to sociological research

Conventionally, sociologists measure the membership of an individual to a group by a “0 or 1” characteristic function. But when the definition of that group is fuzzy and an individual is neither a full member nor a nonmember, this dichotomous characteristic function may distort the reality. Instead of the “0 or 1” characteristic function by classical set theory, fuzzy set theory introduces a membership function which is a gradation from 0 to 1 to measure the degree to which an object (an individual) belongs to a concept (a group). Based on the rationale of fuzzy set theory, we suggest some new methods of data collection and analysis. Among several noteworthy findings, two points are emphasized: 1) the fuzzy set is an appropriate way of measuring the fuzziness of human thought; and 2) it allows one to relax the conventional assumption that all individuals have identical distributions and deviations around their means.