153 research outputs found
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
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
Taming Wild High Dimensional Text Data with a Fuzzy Lash
The bag of words (BOW) represents a corpus in a matrix whose elements are the
frequency of words. However, each row in the matrix is a very high-dimensional
sparse vector. Dimension reduction (DR) is a popular method to address sparsity
and high-dimensionality issues. Among different strategies to develop DR
method, Unsupervised Feature Transformation (UFT) is a popular strategy to map
all words on a new basis to represent BOW. The recent increase of text data and
its challenges imply that DR area still needs new perspectives. Although a wide
range of methods based on the UFT strategy has been developed, the fuzzy
approach has not been considered for DR based on this strategy. This research
investigates the application of fuzzy clustering as a DR method based on the
UFT strategy to collapse BOW matrix to provide a lower-dimensional
representation of documents instead of the words in a corpus. The quantitative
evaluation shows that fuzzy clustering produces superior performance and
features to Principal Components Analysis (PCA) and Singular Value
Decomposition (SVD), two popular DR methods based on the UFT strategy
Multialgebraic Systems in Information Granulation
In different fields a conception of granules is applied both as a group of elements defined by internal
properties and as something inseparable whole reflecting external properties. Granular computing may be
interpreted in terms of abstraction, generalization, clustering, levels of abstraction, levels of detail, and so on. We
have proposed to use multialgebraic systems as a mathematical tool for synthesis and analysis of granules and
granule structures. The theorem of necessary and sufficient conditions for multialgebraic systems existence has
been proved
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