Modeling and manipulating fuzzy regions: strategies to define the topological relation between two fuzzy regions (original) (raw)

Some Topological Invariants and a Qualitative Topological Relation Model between Fuzzy Regions

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007), 2007

Topological relations are one of the most fundamental properties of spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalize the topological relations between fuzzy regions needs more investigation. The paper provides a theoretic framework for modeling topological relations between fuzzy regions. A novel topological model is formalized based on fuzzy topological space (FTS). In order to derive disjoint topological parts of a fuzzy set in FTS, the closure of a fuzzy set is decomposed into two novel parts, the core and the fringe. By use of the core, fringe and the outer of a fuzzy set in the FTS, a new 9-intersection matrix is proposed as a qualitative model for identification of topological relations between two simple fuzzy regions. Since all analysis is totally derived from FTS, therefore its results are universally applicable for GIS modeling and applications.

Modeling fuzzy topological predicates for fuzzy regions

Proceedings of the 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL '14, 2014

Spatial database systems and Geographical Information Systems (GIS) are currently only able to handle crisp spatial objects, i.e., objects whose extent, shape, and boundary are precisely determined. However, GIS applications are also interested in managing vague or fuzzy spatial objects. Spatial fuzziness captures the inherent property of many spatial objects in reality that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. While topological relationships have been broadly explored for crisp spatial objects, this is not the case for fuzzy spatial objects. In this paper, we propose a novel model to formally define fuzzy topological predicates for simple and complex fuzzy regions. The model encompasses six fuzzy predicates (overlap, disjoint, inside, contains, equal and meet), wherein here we focus on the fuzzy overlap and the fuzzy disjoint predicates only. For their computation we consider two low-level measures, the degree of membership and the degree of coverage, and map them to high-level fuzzy modifiers and linguistic values respectively that are deployed in spatial queries by end-users.

Topological relations between fuzzy regions in a fuzzy topological space

International Journal of Applied Earth Observation and Geoinformation, 2010

Topological relations are one of the most important aspects in GIS modeling. The topological relations between crisp spatial objects have been well identified. However, the topological relations between fuzzy spatial objects need more investigation. This paper deals with building a special fuzzy topological space for fuzzy sets. Based on it, a formal definition of simple fuzzy region is given. A 4 Â 4-intersection and furthermore a 5 Â 5-intersection approach are proposed for the formalism of topological relations. Finally 152 topological relations between two simple fuzzy regions are identified based on the 4 Â 4intersection approach in R 2 .

Qualified topological relations between spatial objects with possible vague shape

International Journal of Geographical Information Science, 2009

Broad boundaries are generally used to represent objects with fuzzy spatial extents. This concept is typically defined as a polygonal zone that should respect both connectedness and closeness conditions. Therefore, some real configurations, like regions with a partially broad boundary (e.g., a lake with rocker and swamp banks), are considered invalid. The main objective of this paper is to represent different levels of spatial fuzziness and consider these levels during the identification of topological relations. Then, we define a fuzzy spatial object as a minimal extent and a maximal extent. Topological relations are identified by a 4-Intersection matrix that describes four subrelations between the minimal and the maximal extents. For fuzzy regions, 242 relations are distinguished and classified into 40 clusters. This approach permits the representation of partially fuzzy objects as well as the expression of integrity constraints and spatial queries with different levels of fuzziness.

Fuzzy topological simulation for deducing in GIS

Applied Geomatics, 2009

The proposed methodology relies on the fuzzy nine-intersection matrix which is a generalization of the crisp four-intersection matrix for topological similarity computing. The similarity computation between 3D fuzzy matrix and 3D crisp nine-intersection matrix enables the decision variables to be derived. Decision variables, which are used for deducing and drawing conclusion, are consisted of semantic parts and quantifiers (type and strength of relations). Since these variables are dependent on the boundary directly, it is essential to present an efficient method for defining 3D fuzzy boundary. So, in this paper, we complete the information about how we can define fuzzy boundaries between two 3D phenomena and present a new procedure for simulation of 3D spatial topology in a deductive geographic information system (GIS). Therefore, a fuzzy knowledge-base system and an inference engine will be shown results for deduction in GIS environment.

ORIGINAL PAPER Fuzzy topological simulation for deducing in GIS

2009

The proposed methodology relies on the fuzzy nine-intersection matrix which is a generalization of the crisp four-intersection matrix for topological similarity computing. The similarity computation between 3D fuzzy matrix and 3D crisp nine-intersection matrix enables the decision variables to be derived. Decision variables, which are used for deducing and drawing conclusion, are consisted of semantic parts and quantifiers (type and strength of relations). Since these variables are dependent on the boundary directly, it is essential to present an efficient method for defining 3D fuzzy boundary. So, in this paper, we complete the information about how we can define fuzzy boundaries between two 3D phenomena and present a new procedure for simulation of 3D spatial topology in a deductive geographic information system (GIS). Therefore, a fuzzy knowledge-base system and an inference engine will be shown results for deduction in GIS environment.

Topological relations on fuzzy regions: intersection matrices

2006

In traditional geographic databases and geographic information systems, a variety of different models to represent information is used. In geoscience however, many data is inherently vague or prone to uncertainty (i.e. due to limited measurements), yet the current models don’t take this into account. In the paper we examine the topological relations on a conceptual level for use with fuzzy regions, as developed before. The relations at hand stem from the nineintersection model and are presented within the same framework as the fuzzy bitmap and fuzzy tin models for fuzzy regions.

Fuzzy Intersection and Difference Model for Topological Relations

Topological relations have played important roles in spatial query, analysis and reasoning in Geographic Information Systems (GIS) and spatial databases. The topological relations between crisp and fuzzy spatial objects based upon the 9- intersections topological model have been identified. However the formalization of the topological relations between fuzzy regions needs more investigation. The paper provides a theoretical framework for modelling topological relations between fuzzy regions based upon a new fuzzy topological model called the Fuzzy Intersection and Difference (FID) Model. A novel topological model is formalized based on Fuzzy Topological Space (FTS). In order to derive all fuzzy topological relations between two fuzzy spatial objects, the fuzzy spatial object (A) is decomposed in four components: the Interior, the Interior's Boundary, the Object's Boundary, and the Exterior's Boundary of A. By use of this definition of fuzzy spatial object, new 4*4-Int...

Fuzzy Spatial Relations between Vague Regions

2006 3rd International IEEE Conference Intelligent Systems, 2006

Various intelligent systems rely heavily on formalisms for spatial representation and reasoning. However, it is widely recognized that real-world regions are seldom characterized by a precisely defined boundary. This paper proposes a generalization of the Region Connection Calculus (RCC) which allows to define spatial relations between vague regions. To this end, spatial relations are modelled as fuzzy relations. To support spatial reasoning based on these relations, we give some important properties and a transitivity table. Furthermore, we show how imprecise spatial information can be modelled in our approach when vague regions are represented as fuzzy sets.

2D fuzzy spatial relations: New way of computing and representation

2010

In existing methods, fuzzy topological relations are based on computing topological relations between fuzzy objects. These types of fuzzy topological relations are due to the imprecision in observed phenomenon and objects have the weak contour. This imprecision can be found in semantics of relationships or it represents the fuzzy semantics. In such a situation, fuzzy topological relations are needed between crisp objects. These relations are much less developed.