Much of our cognitive activity depends on our ability to reason analogically. When we encounter a new problem we are often reminded of similar problems solved in past and may use the solution procedure of an old problem to solve the new one (analogical problem solving). In this paper we develop two mathematical models for the description of the process of analogical problem solving. The first one is a stochastic model constructed by introducing a finite, ergodic Markov chain on the steps of the analogical reasoning process. Through this we obtain a measure of the solvers’ difficulties during the process. The second is a fuzzy model constructed by representing the main steps of the process as fuzzy subsets of a set of linguistic labels characterizing the individuals’ performance in each of these steps. In this case we introduce the Shannon’s entropy (total probabilistic uncertainty) - properly modified for use in a fuzzy environment - as a measure of the solvers’ performance. The two models are compared to each other by listing their advantages and disadvantages. Classroom experiments are also performed to illustrate their use in practice.
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