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

Information Flow Model for Commercial Security

Information flow in Discretionary Access Control (DAC) is a well-known difficult problem. This paper formalizes the fundamental concepts and establishes a theory of information flow security. A DAC system is information flow secure (IFS), if any data never flows into the hands of owner’s enemies (explicitly denial access list.

Knowledge Engineering from Data Perspective: Granular Computing Approach

The concept of rough set theory is a mathematical approach to uncertainly and vagueness in data analysis, introduced by Zdzislaw Pawlak in 1980s. Rough set theory assumes the underlying structure of knowledge is a partition. We have extended Pawlak’s concept of knowledge to coverings. We have taken a soft approach regarding any generalized subset as a basic knowledge. We regard a covering as basic knowledge from which the theory of knowledge approximations and learning, knowledge dependency and reduct are developed

Una comparación de algoritmos basados en trayectoria granular para el problema de localización y ruteo con flota heterogénea (LRPH)

Indexación: Scopus.We consider the Location-Routing Problem with Heterogeneous Fleet (LRPH) in which the goal is to determine the depots to be opened, the customers to be assigned to each open depot, and the corresponding routes fulfilling the demand of the customers and by considering a heterogeneous fleet. We propose a comparison of granular approaches of Simulated Annealing (GSA), of Variable Neighborhood Search (GVNS) and of a probabilistic Tabu Search (pGTS) for the LRPH. Thus, the proposed approaches consider a subset of the search space in which non-favorable movements are discarded regarding a granularity factor. The proposed algorithms are experimentally compared for the solution of the LRPH, by taking into account the CPU time and the quality of the solutions obtained on the instances adapted from the literature. The computational results show that algorithm GSA is able to obtain high quality solutions within short CPU times, improving the results obtained by the other proposed approaches.https://revistas.unal.edu.co/index.php/dyna/article/view/55533/5896