Conditional subjective probability and fuzzy theory

Abstract

Our aim is to propose an interpretation of fuzzy set theory in terms of conditional events and coherent conditional probabilities. During the past few years, a large number of papers have been devoted to support either the thesis that probability theory is all that is required for reasoning about uncertainty, or the negative view maintaining that probability is inadequate to capture what is usually treated by fuzzy theory. In this paper (containing only some preliminaries results: our research is still in progress) we emphasize the role of conditioning (in a proper framework, i.e. de Finetti's approach to subjective probability through coherence) to get rid of many controversial aspects.