79,957 research outputs found
High Granular Operator Spaces, and Less-Contaminated General Rough Mereologies
Granular operator spaces and variants had been introduced and used in
theoretical investigations on the foundations of general rough sets by the
present author over the last few years. In this research, higher order versions
of these are presented uniformly as partial algebraic systems. They are also
adapted for practical applications when the data is representable by data
table-like structures according to a minimalist schema for avoiding
contamination. Issues relating to valuations used in information systems or
tables are also addressed. The concept of contamination introduced and studied
by the present author across a number of her papers, concerns mixing up of
information across semantic domains (or domains of discourse). Rough inclusion
functions (\textsf{RIF}s), variants, and numeric functions often have a direct
or indirect role in contaminating algorithms. Some solutions that seek to
replace or avoid them have been proposed and investigated by the present author
in some of her earlier papers. Because multiple kinds of solution are of
interest to the contamination problem, granular generalizations of RIFs are
proposed, and investigated. Interesting representation results are proved and a
core algebraic strategy for generalizing Skowron-Polkowski style of rough
mereology (though for a very different purpose) is formulated. A number of
examples have been added to illustrate key parts of the proposal in higher
order variants of granular operator spaces. Further algorithms grounded in
mereological nearness, suited for decision-making in human-machine interaction
contexts, are proposed by the present author. Applications of granular
\textsf{RIF}s to partial/soft solutions of the inverse problem are also
invented in this paper.Comment: Research paper: Preprint: Final versio
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
Dialectics of Counting and the Mathematics of Vagueness
New concepts of rough natural number systems are introduced in this research
paper from both formal and less formal perspectives. These are used to improve
most rough set-theoretical measures in general Rough Set theory (\textsf{RST})
and to represent rough semantics. The foundations of the theory also rely upon
the axiomatic approach to granularity for all types of general \textsf{RST}
recently developed by the present author. The latter theory is expanded upon in
this paper. It is also shown that algebraic semantics of classical \textsf{RST}
can be obtained from the developed dialectical counting procedures. Fuzzy set
theory is also shown to be representable in purely granule-theoretic terms in
the general perspective of solving the contamination problem that pervades this
research paper. All this constitutes a radically different approach to the
mathematics of vague phenomena and suggests new directions for a more realistic
extension of the foundations of mathematics of vagueness from both foundational
and application points of view. Algebras corresponding to a concept of
\emph{rough naturals} are also studied and variants are characterised in the
penultimate section.Comment: This paper includes my axiomatic approach to granules. arXiv admin
note: substantial text overlap with arXiv:1102.255
A Novel Rough Set Reduct Algorithm for Medical Domain Based on Bee Colony Optimization
Feature selection refers to the problem of selecting relevant features which
produce the most predictive outcome. In particular, feature selection task is
involved in datasets containing huge number of features. Rough set theory has
been one of the most successful methods used for feature selection. However,
this method is still not able to find optimal subsets. This paper proposes a
new feature selection method based on Rough set theory hybrid with Bee Colony
Optimization (BCO) in an attempt to combat this. This proposed work is applied
in the medical domain to find the minimal reducts and experimentally compared
with the Quick Reduct, Entropy Based Reduct, and other hybrid Rough Set methods
such as Genetic Algorithm (GA), Ant Colony Optimization (ACO) and Particle
Swarm Optimization (PSO).Comment: IEEE Publication Format,
https://sites.google.com/site/journalofcomputing
A Framework for Intelligent Medical Diagnosis using Rough Set with Formal Concept Analysis
Medical diagnosis process vary in the degree to which they attempt to deal
with different complicating aspects of diagnosis such as relative importance of
symptoms, varied symptom pattern and the relation between diseases them selves.
Based on decision theory, in the past many mathematical models such as crisp
set, probability distribution, fuzzy set, intuitionistic fuzzy set were
developed to deal with complicating aspects of diagnosis. But, many such models
are failed to include important aspects of the expert decisions. Therefore, an
effort has been made to process inconsistencies in data being considered by
Pawlak with the introduction of rough set theory. Though rough set has major
advantages over the other methods, but it generates too many rules that create
many difficulties while taking decisions. Therefore, it is essential to
minimize the decision rules. In this paper, we use two processes such as pre
process and post process to mine suitable rules and to explore the relationship
among the attributes. In pre process we use rough set theory to mine suitable
rules, whereas in post process we use formal concept analysis from these
suitable rules to explore better knowledge and most important factors affecting
the decision making.Comment: 22 page
Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples
This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology
Rough sets and three-valued structures
In recent years, many papers have been published showing relationships
between rough sets and some lattice theoretical structures. We present here
some strong relations between rough sets and three-valued {\L}ukasiewicz
algebras.Comment: 10 page
Unuploaded experiments have no result
The aim of this note is to attract once again attention of the quantum
community to statistical analysis of data which was reported as violating
Bell's inequality. This analysis suffers of a number of problems. And the main
problem is that rough data is practically unavailable. However, experiments
which are not followed by the open access to the rough data have to be
considered as with no result. The absence of rough data generates a variety of
problems in statistical interpretation of the results of Bell's type
experiment. One may hope that this note would stimulate experimenters to create
the open access data-base for, e.g., Bell tests. Unfortunately, recently
announced experimental loophole-free violation of a Bell inequality using
entangled electron spins separated by 1.3 km was not supported by open-access
data. Therefore in accordance with our approach "it has no result." The
promising data after publication is, of course, a step towards fair analysis
quantum experiments. May be this is a consequence of appearance of this
preprint, v1. But there are a few questions which would be interesting to
clarify before publication (and which we shall discuss in this note).Comment: comments on the recently announced "experimental loophole-free
violation of a Bell inequality using entangled electron spins separated by
1.3 km.
Learning Fuzzy {\beta}-Certain and {\beta}-Possible rules from incomplete quantitative data by rough sets
The rough-set theory proposed by Pawlak, has been widely used in dealing with
data classification problems. The original rough-set model is, however, quite
sensitive to noisy data. Tzung thus proposed deals with the problem of
producing a set of fuzzy certain and fuzzy possible rules from quantitative
data with a predefined tolerance degree of uncertainty and misclassification.
This model allowed, which combines the variable precision rough-set model and
the fuzzy set theory, is thus proposed to solve this problem. This paper thus
deals with the problem of producing a set of fuzzy certain and fuzzy possible
rules from incomplete quantitative data with a predefined tolerance degree of
uncertainty and misclassification. A new method, incomplete quantitative data
for rough-set model and the fuzzy set theory, is thus proposed to solve this
problem. It first transforms each quantitative value into a fuzzy set of
linguistic terms using membership functions and then finding incomplete
quantitative data with lower and the fuzzy upper approximations. It second
calculates the fuzzy {\beta}-lower and the fuzzy {\beta}-upper approximations.
The certain and possible rules are then generated based on these fuzzy
approximations. These rules can then be used to classify unknown objects.Comment: hi thanks for attentio
Covering matroid
In this paper, we propose a new type of matroids, namely covering matroids,
and investigate the connections with the second type of covering-based rough
sets and some existing special matroids. Firstly, as an extension of
partitions, coverings are more natural combinatorial objects and can sometimes
be more efficient to deal with problems in the real world. Through extending
partitions to coverings, we propose a new type of matroids called covering
matroids and prove them to be an extension of partition matroids. Secondly,
since some researchers have successfully applied partition matroids to
classical rough sets, we study the relationships between covering matroids and
covering-based rough sets which are an extension of classical rough sets.
Thirdly, in matroid theory, there are many special matroids, such as
transversal matroids, partition matroids, 2-circuit matroid and
partition-circuit matroids. The relationships among several special matroids
and covering matroids are studied.Comment: 15 page
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