Connectives and fuzziness for classical effects

This article investigates various constructs on a set of classical effects (measurable fuzzy sets or fuzzy events). We begin by studying the properties of a connective box with bottom missing and its dual connective box with top missing which seem to have been neglected in the literature. The importance of these connectives for fuzzy probability theory is pointed out. We then introduce and investigate the properties of a commutator which can be employed to define a degree of relative fuzziness. A special case of this commutator defines a degree of fuzziness. The expectation of the commutator provides a relative entropy whose properties are delineated and the expectation of the special case gives an entropy function that has been previously studied as a measure of fuzziness. (C) 1999 Elsevier Science B.V. All rights reserved.