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Case-based reasoning in computers and human cognition: a mathematical framework

Authors: Michael Gr. Voskoglou;

Case-based reasoning in computers and human cognition: a mathematical framework

Abstract

Case-based reasoning (CBR) is a recent approach to problem solving and learning for computers and humans. In this paper, we introduce a finite Markov chain on the main steps of the CBR process. Using this approach we succeed in calculating the probabilities for the CBR process to be at a certain step in a certain phase of the solution of a real-world problem and we obtain a measure of the effectiveness of a CBR system in solving similar new problems. Next, the steps of the CBR process are represented as fuzzy subsets of a set of linguistic labels characterising the success of the CBR process in each of the above steps. Thus, we build a fuzzy model for the representation of a CBR system and we use the total possibilistic uncertainty as a measure of its effectiveness in solving new related problems. Examples are also given to illustrate our results.

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