315 research outputs found
Approximations from Anywhere and General Rough Sets
Not all approximations arise from information systems. The problem of fitting
approximations, subjected to some rules (and related data), to information
systems in a rough scheme of things is known as the \emph{inverse problem}. The
inverse problem is more general than the duality (or abstract representation)
problems and was introduced by the present author in her earlier papers. From
the practical perspective, a few (as opposed to one) theoretical frameworks may
be suitable for formulating the problem itself. \emph{Granular operator spaces}
have been recently introduced and investigated by the present author in her
recent work in the context of antichain based and dialectical semantics for
general rough sets. The nature of the inverse problem is examined from
number-theoretic and combinatorial perspectives in a higher order variant of
granular operator spaces and some necessary conditions are proved. The results
and the novel approach would be useful in a number of unsupervised and semi
supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings,
Springe
Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery
In the context of general rough sets, the act of combining two things to form
another is not straightforward. The situation is similar for other theories
that concern uncertainty and vagueness. Such acts can be endowed with
additional meaning that go beyond structural conjunction and disjunction as in
the theory of -norms and associated implications over -fuzzy sets. In the
present research, algebraic models of acts of combining things in generalized
rough sets over lattices with approximation operators (called rough convenience
lattices) is invented. The investigation is strongly motivated by the desire to
model skeptical or pessimistic, and optimistic or possibilistic aggregation in
human reasoning, and the choice of operations is constrained by the
perspective. Fundamental results on the weak negations and implications
afforded by the minimal models are proved. In addition, the model is suitable
for the study of discriminatory/toxic behavior in human reasoning, and of ML
algorithms learning such behavior.Comment: 15 Pages. Accepted. IJCRS-202
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