Wyniki wyszukiwania - BazTech

1

Weak relative pseudocomplements in semilattices

Cirulis J.

Demonstratio Mathematica

|

2011

|

Vol. 44, nr 4

651-672

EN

Weak relative pseudocomplementation on a meet semilattice S is a partial operation * which associates with every pair (x, y) of elements, where (…) an element z (the weak pseudocomplement of x relative to y which is the greatest among elements u such that (…). The element z coincides with the pseudocomplement of x in the upper section [y) and, if S is modular, with the pseudocomplement of x relative to y A weakly relatively pseudomented semilattice is said to be extended, if it is equipped with a total binary operation extending *. We study congruence properties of the variety of such semilattices and review some of its subvarieties already described in the literature.

2

Subtraction-like operations in nearsemilattices

Cirulis J.

Demonstratio Mathematica

|

2010

|

Vol. 43, nr 4

725-738

EN

A nearsemilattice is a poset having the upper-bound property. A binary operation — on a poset with the least element 0 is said to be subtraction-like if x ≤ y if and only if x — y = 0 for all x, y. Associated with such an operation is a family of partial operations lp defined by lp(x) := p— x on every initial segment [0, p]; these operations are thought of as local (sectional) complementations of some kind. We study several types of subtraction-like operations, show that each of these operations can be restored in a uniform way from the corresponding local complementations, and state some connections between properties of a (sufficiently strong) subtraction on a nearsemilattice and distributivity of the latter.

3

Rough Set Algebras as Description Domains

Cirulis J.

Fundamenta Informaticae

|

2009

|

Vol. 90, nr 1-2

27-41

EN

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 ↓α 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.