Fuzzy Models for Analogical Reasoning

In this paper we present two fuzzy models for the description of the process of AR by representing its main steps as fuzzy subsets of a set of linguistic labels characterizing the individuals’ performance in each step. In the first model we used the ShannonWiener diversity index as a measure of the individuals’ abilities in analogical problem solving, while in the second one we measure the individuals’ performance in AR by graphically representing the information as a two dimensional figure and work with coordinates of the center of mass of this figure. Our first model gives to the researcher the opportunity to study the combined results of the behaviour of two or more groups during the AR process or alternatively to study the combined results of the behaviour of the same group during different analogical problem solving processes. Depending on evaluation criteria, the approach developed in our second model could be used for comparing the groups’ performance or just for individual independent assessment. Our fuzzy models are compared with a stochastic model presented in earlier papers by introducing a Voskoglou & Subbotin 20 finite Markov chain on the steps of the process of Analogical Reasoning. A classroom experiment is also presented illustrating the use of our results in practice.