Prediction and Fuzzy Logic

Abstract

While fuzzy logic has enjoyed considerable development and some popularity in applications to expert systems and artificial intelligence problems, it has been little used in the human sciences. Yet there is a set of recurring problems in behavioral and social scientific research for which fuzzy logic is well suited. These problems may be referred to as logical or causal entailment. Statements of entailment involve linguistic equivalent of logical predicates (e.g., “if X is high then Y will be high”), but these are seldom explicitly operationalized in conventional techniques for data analysis. Instead, they implicitly reside in the techniques themselves. Simple correlation and regression, for instance, assume not only a linear model but also a one-to-one entailment between the dependent and independent variables. A test of correlation is equivalent to testing a linear version of the statement “Y is high iff X is high”. Only in the bivariate analysis of categorical variables are one-to-many entailments recognized, and even then only for certain measures of association (cf. Reynolds 1977 for a popular review of this concept). There are no conventional statistical techniques for testing one-to-many entailments for numerical variables.