Spatial Fuzzy Sets Research Articles

Spatial fuzzy topological space

The concept of spatial fuzzy set is introduced in this article. We have established some fundamental conclusions on the spatial fuzzy set and the spatial fuzzy topological space. Because fuzziness is an internal feature of spatial objects, we used topological relations to build internal properties and relationships between them.

H∞ control for 2-D T-S fuzzy FMII model with stochastic perturbation

This paper deals with the problem of H∞ control for 2-D non-linear system with stochastic perturbation. Based on spatial fuzzy set and inference mechanism, 2-D T-S fuzzy FMII model with stochastic perturbation is established first. Then the results for stability analysis and bounded real lemma are obtained. Moreover, an H∞ fuzzy controller is designed. In order to reduce the computational demand of the conditions for the existence of H∞ fuzzy controller, the control inputs are regarded as the variables independent of the states, and some free matrices are introduced to reduce the conservatism of this method. Then, a new H∞ fuzzy controller is derived. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

Multiobjective evolutionary algorithms to identify highly autocorrelated areas: the case of spatial distribution in financially compromised farms

Local Indicators of Spatial Aggregation (LISA) can be used as objectives in a multicriteria framework when highly autocorrelated areas (hot-spots) must be identified and geographically located in complex areas. To do so, a Multi-Objective Evolutionary Algorithm (MOEA) based on SPEA2 (Strength Pareto Evolutionary Algorithm v.2) has been designed to evaluate three different fitness functions (fine-grained strength, the weighted sum of objectives and fuzzy evaluation of weighted objectives) and three LISA methods. MOEA makes it possible to achieve a compromise between spatial econometric methods as it highlights areas where a specific phenomenon shows significantly high autocorrelation. The spatial distribution of financially compromised olive-tree farms in Andalusia (Spain) was selected for analysis and two fuzzy hot-spots were statistically identified and spatially located. Hot-spots can be considered to be spatial fuzzy sets where the spatial units have a membership degree that can also be calculated.

Defuzzification of spatial fuzzy sets by feature distance minimization

We present a novel defuzzification method, i.e., a mapping from the set of fuzzy sets to the set of crisp sets, and we suggest its application to image processing. Spatial fuzzy sets are, e.g., useful as information preserving representations of objects in images. Defuzzification of such a spatial fuzzy set can be seen as a crisp segmentation procedure. With the aim to provide preservation of selected quantitative features of the fuzzy set, we define the defuzzification of a fuzzy set to be a crisp set which is as close as possible to the fuzzy set, where the distance measure on the set of fuzzy sets, that we propose for defuzzification, incorporates selected local and global features of the fuzzy sets. The distance measure is based on the Minkowski distance between feature representations of the sets. The distance minimization, performed in the suggested defuzzification method, provides preservation of the selected quantitative features of the fuzzy set. The method utilizes the information contained in the fuzzy representation for defining a mapping from the set of fuzzy sets to the set of crisp sets. If the fuzzy set is a representation of an unknown crisp original set, such that the selected features of the original set are preserved in the fuzzy representation, then the defuzzified set may be seen as an approximate reconstruction of the crisp original. We present four optimization algorithms, exhibiting different properties, for finding the crisp set closest to a given discrete fuzzy set. A number of examples, using both synthetic and real images, illustrate the main properties of the proposed method. An evaluation of both theoretical aspects of the method, and its results, is given.

INTERVAL-VALUED FUZZY LOGIC CONTROL FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process.

What is Where? Type-2 Fuzzy Sets for Geographical Information [Research Frontier

Until recently, most research has been done on type-1 fuzzy sets but it is also possible to identify and model type-2 fuzzy sets, and possibly type-n fuzzy sets. Until recently, the question of type-n fuzzy sets has not emerged in the consideration of spatial fuzzy sets. In this short summary, I will present some recent research that has explored the generation of type-2 spatial fuzzy sets, and discuss some consequences of using this type of analysis

Where is Helvellyn? Fuzziness of multi‐scale landscape morphometry

The landscape in which people live is made up of many features, which are named and have importance for cultural reasons. Prominent among these are the naming of upland features such as mountains, but mountains are an enigmatic phenomenon which do not bear precise and repeatable definition. They have a vague spatial extent, and recent research has modelled such classes as spatial fuzzy sets. We take a specifically multi‐resolution approach to the definition of the fuzzy set membership of morphometric classes of landscape. We explore this idea with respect to the identification of culturally recognized landscape features of the English Lake District. Discussion focuses on peaks and passes, and the results show that the landscape elements identified in the analysis correspond to well‐known landmarks included in a place name database for the area, although many more are found in the analysis than are named in the available database. Further analysis shows that a richer interrogation of the landscape can be achieved with Geographical Information Systems when using this method than using standard approaches.

Representation and fusion of heterogeneous fuzzy information in the 3D space for model-based structural recognition—Application to 3D brain imaging

We present a novel approach to model-based pattern recognition where structural information and spatial relationships have a most important role. It is illustrated in the domain of 3D brain structure recognition using an anatomical atlas. Our approach performs segmentation and recognition of the scene simultaneously. The solution of the recognition task is progressive, processing successively different objects, and using different pieces of knowledge about the object and about relationships between objects. Therefore, the core of the approach is the knowledge representation part, and constitutes the main contribution of this paper. We make use of a spatial representation of each piece of information, as a spatial fuzzy set representing a constraint to be satisfied by the searched object, thanks in particular to fuzzy mathematical morphology operations. Fusion of these constraints allows us to select, segment and recognize the desired object.