Connectives and fuzziness for classical effects

Abstract

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 ⊓ and its dual connective ⊓ 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.