Using Fuzzy Set Theoretic Techniques to Identify Preference Rules from Interactions in the Linear Model: An Empirical Study

This paper seeks to establish a parametric linkage between fuzzy set theoretic techniques and commonly used preference formation rules in psychology and marketing. Such a linkage helps to benefit both fields. We accomplish this objective by using a linear model with interaction term which nests many common preference protocols; conjunction (fuzzy and), disjunction (fuzzy or), counterbalance (fuzzy xor) and linear compensatory. The resulting linear model with interactions can be employed when one has no a priori hypothesis about the individual's preference formation rule involved to determine the most likely preference rule or to test more formally the adequacy of a given rule. One illustrative application studies two-attribute decisions in six product categories and demonstrates differences in preference formation processes by product category. A second application demonstrates how fuzzy logical operators can be applied to situations involving more than two attributes.