Abstract

The author reports on a literature search on fuzzy sets. Fuzzy sets differ from classical sets in the following sense: elements can partly belong to fuzzy sets, whereas elements do or don't belong to classical sets. Fuzzy sets can be generalized to fuzzy relations between elements ; fuzzy Markovian chains, that describe transitions between elements ; fuzzy functions ; fuzzy numbers ; fuzzy reasoning based on fuzzy relations ; fuzzy inclusion ; and fuzzy partitions. The possibility measure is a fuzzy translation of the probability measure: it quantifies the possibility of an event instead of the probability. Three applications of fuzzy sets and possibility measures have been elaborated: fuzzy linear regression, the fuzzy shortest path problem and fuzzy multi-criteria analysis. On the basis of the fuzzy shortest path problem (the interpretations of) the possibility measure and the probability measure are compared.