4,412 research outputs found
Information completeness in Nelson algebras of rough sets induced by quasiorders
In this paper, we give an algebraic completeness theorem for constructive
logic with strong negation in terms of finite rough set-based Nelson algebras
determined by quasiorders. We show how for a quasiorder , its rough
set-based Nelson algebra can be obtained by applying the well-known
construction by Sendlewski. We prove that if the set of all -closed
elements, which may be viewed as the set of completely defined objects, is
cofinal, then the rough set-based Nelson algebra determined by a quasiorder
forms an effective lattice, that is, an algebraic model of the logic ,
which is characterised by a modal operator grasping the notion of "to be
classically valid". We present a necessary and sufficient condition under which
a Nelson algebra is isomorphic to a rough set-based effective lattice
determined by a quasiorder.Comment: 15 page
Defining rough sets as core-support pairs of three-valued functions
We answer the question what properties a collection of
three-valued functions on a set must fulfill so that there exists a
quasiorder on such that the rough sets determined by coincide
with the core--support pairs of the functions in . Applying this
characterization, we give a new representation of rough sets determined by
equivalences in terms of three-valued {\L}ukasiewicz algebras of three-valued
functions.Comment: This version is accepted for publication in Approximate Reasoning
(May 2021
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