Search results for "Stone's representation theorem for Boolean algebras"
showing 4 items of 4 documents
On Rough Sets in Topological Boolean Algebras
1994
We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.
Conditioning on MV-algebras and additive measures —I
1997
Abstract We present a lattice-ordered semigroup approach for the foundation of conditional events which covers the special situations where the underlying (unconditional) events are Boolean or fuzzy, respectively. Our proposal is quite different from other, ring theoretical, approaches. The problem of extending additivity of uncertainty measures from unconditional to conditional events will be discussed.
Rough Set Algebras as Description Domains
2009
Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓ is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.
Equivalence Relations on Stonian Spaces
1996
Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.