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

Authors: Michael Gr. Voskoglou

Addresses: School of Technological Applications, Graduate Technological Educational Institute (T.E.I.), 263 34 Patras, Greece

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.

Keywords: finite Markov chains; case-based reasoning; CBR; human cognition; fuzzy sets; uncertainty; machine intelligence; fuzzy modelling.

DOI: 10.1504/IJMISSP.2013.052868

International Journal of Machine Intelligence and Sensory Signal Processing, 2013 Vol.1 No.1, pp.3 - 22

Received: 25 Feb 2012
Accepted: 23 Mar 2012
Published online: 19 Jul 2014 *