4,084 research outputs found
Data granulation by the principles of uncertainty
Researches in granular modeling produced a variety of mathematical models,
such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets,
which are all suitable to characterize the so-called information granules.
Modeling of the input data uncertainty is recognized as a crucial aspect in
information granulation. Moreover, the uncertainty is a well-studied concept in
many mathematical settings, such as those of probability theory, fuzzy set
theory, and possibility theory. This fact suggests that an appropriate
quantification of the uncertainty expressed by the information granule model
could be used to define an invariant property, to be exploited in practical
situations of information granulation. In this perspective, a procedure of
information granulation is effective if the uncertainty conveyed by the
synthesized information granule is in a monotonically increasing relation with
the uncertainty of the input data. In this paper, we present a data granulation
framework that elaborates over the principles of uncertainty introduced by
Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is
possible to apply such principles regardless of the input data type and the
specific mathematical setting adopted for the information granules. The
proposed framework is conceived (i) to offer a guideline for the synthesis of
information granules and (ii) to build a groundwork to compare and
quantitatively judge over different data granulation procedures. To provide a
suitable case study, we introduce a new data granulation technique based on the
minimum sum of distances, which is designed to generate type-2 fuzzy sets. We
analyze the procedure by performing different experiments on two distinct data
types: feature vectors and labeled graphs. Results show that the uncertainty of
the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference
Knowledge Granulation, Rough Entropy and Uncertainty Measure in Incomplete Fuzzy Information System
Many real world problems deal with ordering of objects instead of classifying objects, although most of research in data analysis has been focused on the latter. One of the extensions of classical rough sets to take into account the ordering properties is dominance-based rough sets approach which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this paper, we address knowledge measures and reduction in incomplete fuzzy information system using the approach. Firstly, new definitions of knowledge granulation and rough entropy are given, and some important properties of them are investigated. Then, dominance matrix about the measures knowledge granulation and rough entropy is obtained, which could be used to eliminate the redundant attributes in incomplete fuzzy information system. Lastly, a matrix algorithm for knowledge reduction is proposed. An example illustrates the validity of this method and shows the method is applicable to complex fuzzy system. Experiments are also made to show the performance of the newly proposed algorithm
Modeling of Social Transitions Using Intelligent Systems
In this study, we reproduce two new hybrid intelligent systems, involve three
prominent intelligent computing and approximate reasoning methods: Self
Organizing feature Map (SOM), Neruo-Fuzzy Inference System and Rough Set Theory
(RST),called SONFIS and SORST. We show how our algorithms can be construed as a
linkage of government-society interactions, where government catches various
states of behaviors: solid (absolute) or flexible. So, transition of society,
by changing of connectivity parameters (noise) from order to disorder is
inferred
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