A measurement-theoretic analysis of the fuzzy logic model of perception
The fuzzy logic model of perception (FLMP) is analyzed from a measurement-theoretic perspective. FLMP has an impressive history of fitting factorial data, suggesting that its probabilistic form is valid. The authors raise questions about the underlying processing assumptions of FLMP. Although FLMP parameters are interpreted as fuzzy logic truth values, the authors demonstrate that for several factorial designs widely used in choice experiments, most desirable fuzzy truth value properties fail to hold under permissible rescalings, suggesting that the fuzzy logic interpretation may be unwarranted. The authors show that FLMP's choice rule is equivalent to a version of G. Rasch's (1960) item response theory model, and the nature of FLMP measurement scales is transparent when stated in this form. Statistical inference theory exists for the Rasch model and its equivalent forms. In fact, FLMP can be reparameterized as a simple 2-category logit model, thereby facilitating interpretation of its measurement scales and allowing access to commercially available software for performing statistical inference.
Crowther, C., Batchelder, W., & Hu, X. (1995). A measurement-theoretic analysis of the fuzzy logic model of perception. Psychological Review, 102 (2), 396-408. https://doi.org/10.1037/0033-295X.102.2.396