192 research outputs found
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
Homomorphisms between fuzzy information systems revisited
Recently, Wang et al. discussed the properties of fuzzy information systems
under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms
between fuzzy information systems, Applied Mathematics Letters 22 (2009)
1045-1050], where homomorphisms are based upon the concepts of consistent
functions and fuzzy relation mappings. In this paper, we classify consistent
functions as predecessor-consistent and successor-consistent, and then proceed
to present more properties of consistent functions. In addition, we improve
some characterizations of fuzzy relation mappings provided by Wang et al.Comment: 10 page
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
- …