in this study, we offer a general view at the area of fuzzy modeling and fuzzymodels, identify the visible development phases and elaborate on a new and promisingdirections of system modeling by introducing a concept of granular models. granularmodels, especially granular fuzzy models constitute an important generalization of existingfuzzy models and, in contrast to the existing models, generat...

A framework is proposed for studying a particular class of set-theoretic approaches to granular computing. A granule is a subset of a universal set, a granular structure is a family of subsets of the universal set, and relationship between granules is given by the standard set-inclusion relation. By imposing different conditions on the family of subsets, we can define several types of granular ...

A detailed description for the solution of the Landau-Lifshitz-Gilbert equation with the finite element method is given. The use of implicit time integration schemes with proper preconditioning is reported. Simulations of a single phase magnetic nanoelement without surface roughness and a magnetic nanoelement with a granular structure are performed to investigate the influence of the microstruc...

In this paper, from the viewpoint of granular computing, information granule and concept granule are introduced to information systems, and then structure of concept granules and their distance, concept granular entropy and significance degree are presented. The concept of concept granule-based granular lattice is proposed in information systems. The representation and operation rules of comple...

granular media of CoCrPtTa structure (type a) and micromagnetic standard problem #4 has been done. Moreover, an investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations on granular media of Co structure (type b) has been done. The stiffness of the problems ...

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic ...

Physical and chemical transformation processes in reactive granular media involve the reorganization of the structure. In this paper, we study experimentally the rearrangements of a two-dimensional (2D) granular packing undergoing a localized transformation. We track the position and evolution of all the disks that constitute the granular packing when either a large intruder shrinks in size or ...