Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence
Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on -algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...