283 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, Topological, and Mereological Foundations of Existential Granules
In this research, new concepts of existential granules that determine
themselves are invented, and are characterized from algebraic, topological, and
mereological perspectives. Existential granules are those that determine
themselves initially, and interact with their environment subsequently.
Examples of the concept, such as those of granular balls, though inadequately
defined, algorithmically established, and insufficiently theorized in earlier
works by others, are already used in applications of rough sets and soft
computing. It is shown that they fit into multiple theoretical frameworks
(axiomatic, adaptive, and others) of granular computing. The characterization
is intended for algorithm development, application to classification problems
and possible mathematical foundations of generalizations of the approach.
Additionally, many open problems are posed and directions provided.Comment: 15 Pages. Accepted IJCRS 202
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