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 structure, knowledge granulation and knowledge distance in a knowledge base

AbstractOne of the strengths of rough set theory is the fact that an unknown target concept can be approximately characterized by existing knowledge structures in a knowledge base. Knowledge structures in knowledge bases have two categories: complete and incomplete. In this paper, through uniformly expressing these two kinds of knowledge structures, we first address four operators on a knowledge base, which are adequate for generating new knowledge structures through using known knowledge structures. Then, an axiom definition of knowledge granulation in knowledge bases is presented, under which some existing knowledge granulations become its special forms. Finally, we introduce the concept of a knowledge distance for calculating the difference between two knowledge structures in the same knowledge base. Noting that the knowledge distance satisfies the three properties of a distance space on all knowledge structures induced by a given universe. These results will be very helpful for knowledge discovery from knowledge bases and significant for establishing a framework of granular computing in knowledge bases

A GIS-based multi-criteria evaluation framework for uncertainty reduction in earthquake disaster management using granular computing

One of the most important steps in earthquake disaster management is the prediction of probable damages which is called earthquake vulnerability assessment. Earthquake vulnerability assessment is a multicriteria problem and a number of multi-criteria decision making models have been proposed for the problem. Two main sources of uncertainty including uncertainty associated with experts‘ point of views and the one associated with attribute values exist in the earthquake vulnerability assessment problem. If the uncertainty in these two sources is not handled properly the resulted seismic vulnerability map will be unreliable. The main objective of this research is to propose a reliable model for earthquake vulnerability assessment which is able to manage the uncertainty associated with the experts‘ opinions. Granular Computing (GrC) is able to extract a set of if-then rules with minimum incompatibility from an information table. An integration of Dempster-Shafer Theory (DST) and GrC is applied in the current research to minimize the entropy in experts‘ opinions. The accuracy of the model based on the integration of the DST and GrC is 83%, while the accuracy of the single-expert model is 62% which indicates the importance of uncertainty management in seismic vulnerability assessment problem. Due to limited accessibility to current data, only six criteria are used in this model. However, the model is able to take into account both qualitative and quantitative criteria

The Sun's Supergranulation

Supergranulation is a fluid-dynamical phenomenon taking place in the solar photosphere, primarily detected in the form of a vigorous cellular flow pattern with a typical horizontal scale of approximately 30--35~megameters, a dynamical evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow component and a much weaker 20--30~m/s vertical component. Supergranulation was discovered more than sixty years ago, however, explaining its physical origin and most important observational characteristics has proven extremely challenging ever since, as a result of the intrinsic multiscale, nonlinear dynamical complexity of the problem concurring with strong observational and computational limitations. Key progress on this problem is now taking place with the advent of 21st-century supercomputing resources and the availability of global observations of the dynamics of the solar surface with high spatial and temporal resolutions. This article provides an exhaustive review of observational, numerical and theoretical research on supergranulation, and discusses the current status of our understanding of its origin and dynamics, most importantly in terms of large-scale nonlinear thermal convection, in the light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new theoretical, numerical and observational developments. All sections, including discussion, revised extensively. Also includes previously unpublished results on nonlinear dynamics of convection in large domains, and lagrangian transport at the solar surfac