Fuzzy models in analogy and case-based reasoning

Analogy is a natural means of drawing a conclusion on the basis of past experience. Several of its forms have been identified in psychology and some of them have given rise to developments in artificial intelligence. The capability of fuzzy logic to model human reasoning and to cope with the imprecision common in human judgements provides interesting solutions for knowledge representation and approximate reasoning. We start from the two basic components of analogy, namely a link between two universes on the one hand, for instance a universe of cases and a universe of decisions, and a relation defined on each of the universes on the other hand, for instance a similarity relation. We study these elements in a fuzzy setting and we present fuzzy models of decision-making based on analogy. We introduce a particular analogical scheme based on measures of similitude, assuming that gradual knowledge is involved in the analogy. We insist on the expressiveness of the obtained decision, proposing to use linguistic modifiers for this purpose, appropriately chosen according to the context and the selected measure of similitude. We focus on two paradigms taking advantage of an analogical approach. The first paradigm is case-based reasoning, and methods are proposed for the adaptation of solutions to already solved cases in order to determine a solution to a new case, taking into account similarities, and having in mind the necessity to obtain linguistic descriptions of results. We point out several methods enabling the user to perform the transformational adaptation of the solution to a similar problem, based on the utilization of specific linguistic modifiers associated with measures of similitude. Their interest is to ensure a gradual passage between cases and the global utilization of the set of already solved problems. The second paradigm is related to interpolative reasoning in a fuzzy environment, with the purpose of using sparse rules or incomplete knowledge in decision-making. It is also presented as a method available for the above-mentioned transformational adaptation of solutions in case-based reasoning.