Topological relations between fuzzy regions in a fuzzy topological space

Tang, Xinming; Kainz, Wolfgang; Wang, Hongyan

doi:10.1016/j.jag.2010.01.004

Cited by 30 publications

(35 citation statements)

References 28 publications

(28 reference statements)

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“…The former approaches (Cohn and Gilts, 1996;Smith, 1996;Tang and Kainz, 2002) have introduced the concept of fuzzy topology into GIS. We use the application of fuzzy topology to compute the interior, exterior and boundary of fuzzy spatial objects.…”

Section: Resultsmentioning

confidence: 99%

Application of Fuzzy Topological relation in Flood Prediction

Chamuah¹,

Chetia²

2015

IJCA

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Now a day in GIS application fuzzy spatial objects have become extremely important. There have been many research developments on the conceptual description of topological relation between spatial objects. In this paper a formal definition of the computational fuzzy topology is shown which is based on the interior operator and closure operators. In spatial object modeling the interior and exterior boundary are computed based on computational fuzzy topology. An example for determining interior boundary and exterior boundary of flood affected areas of upper Assam based on data collected from Govt. of Assam GOI Directory Assam Tourism NIC ASHA Districts of India.

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Section: Resultsmentioning

confidence: 99%

Application of Fuzzy Topological relation in Flood Prediction

Chamuah¹,

Chetia²

2015

IJCA

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“…Based upon that, simple metric operations such as the area of a fuzzy region and the length of a fuzzy line were further developed in [23], in which only unary functions were considered. On relationship between fuzzy objects, different models of fuzzy topological predicates, which characterize the relative position of two fuzzy objects toward each other were discussed in [25,28,24]. However, it remains largely untouched to answer more advanced spatial queries such as the nearest neighbor query, which is addressed in this paper.…”

Section: Related Workmentioning

confidence: 99%

“…Although fuzzy objects have long been studied in GIS community [25,28,2,22], common spatial queries such as range and kNN queries still remain uninvestigated at large. In this paper we will address the problem of searching the k nearest objects in Euclidean space over large fuzzy dataset.…”

Section: Introductionmentioning

confidence: 99%

K-nearest neighbor search for fuzzy objects

Zheng

Fung

Zhou

2010

Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data

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The K-Nearest Neighbor search (kNN) problem has been investigated extensively in the past due to its broad range of applications. In this paper we study this problem in the context of fuzzy objects that have indeterministic boundaries. Fuzzy objects play an important role in many areas, such as biomedical image databases and GIS. Existing research on fuzzy objects mainly focuses on modelling basic fuzzy object types and operations, leaving the processing of more advanced queries such as kNN query untouched. In this paper, we propose two new kinds of kNN queries for fuzzy objects, Ad-hoc kNN query (AKNN) and Range kNN query (RKNN), to find the k nearest objects qualifying at a probability threshold or within a probability range. For efficient AKNN query processing, we optimize the basic best-first search algorithm by deriving more accurate approximations for the distance function between fuzzy objects and the query object. To improve the performance of RKNN search, effective pruning rules are developed to significantly reduce the search space and further speed up the candidate refinement process. The efficiency of our proposed algorithms as well as the optimization techniques are verified with an extensive set of experiments using both synthetic and real datasets.

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“…Examples are given by Altman (1994) presenting fuzzy set theoretic approaches for handling imprecision in spatial analysis and introducing fuzzy regions in ℕ 2 , Schneider (1999) providing the foundation of FUSA in terms of fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions together with some fuzzy spatial operations, Dilo, de By & Stein (2007) introducing a similar type system of fuzzy (called "vague") spatial data types with a more comprehensive set of operations, Schneider (2003) proposing a conceptual model and an implementation model of fuzzy spatial objects that are not defined on the Euclidean plane but on a discrete geometric domain called grid partition, and Schneider (2000) presenting metric operations on fuzzy spatial objects like the area of a fuzzy region or the length of a fuzzy line. Different models of fuzzy topological predicates, which are not discussed in this chapter and which characterize the relative position of two fuzzy spatial objects towards each other, are discussed in Petry et al (2002), Schneider (2001aSchneider ( , 2001b, Shi & Guo (1999), Tang & Kainz (2002), and Zhan (1997.…”

Section: A Classification Of Models For Vague Spatial Objectsmentioning

confidence: 99%

Soft Computing Techniques in Spatial Databases

Schneider

2010

Soft Computing Applications for Database Technologies

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Spatial database systems and geographical information systems are currently only able to support geographical applications that deal with crisp spatial objects, that is, objects whose extent, shape, and boundary are precisely determined. Examples are land parcels, school districts, and state territories. However, many new, emerging applications are interested in modeling and processing geographic data that are inherently characterized by spatial vagueness or spatial indeterminacy. Examples are air polluted areas, temperature zones, and lakes. These applications require novel concepts due to the lack of adequate approaches and systems. In this chapter, we show how soft computing techniques can provide a solution to this problem. We give an overview of two type systems or algebras that can be integrated into database systems and utilized for the modeling and handling of spatial vagueness. The first type system, called Vague Spatial Algebra (VASA), is based on well known, general, and exact models of crisp spatial data types and introduces vague points, vague lines, and vague regions. This enables an exact definition of the vague spatial data model since we can build it upon an already existing theory of spatial data types. The second type system, called Fuzzy Spatial Algebra (FUSA), leverages fuzzy set theory and fuzzy topology and introduces novel fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions. This enables an even more fine-grained modeling of spatial objects that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. This chapter provides a formal definition of the structure and semantics of both type systems. Further, we introduce spatial set operations for both algebras and obtain vague and fuzzy versions of geometric intersection, union, and difference. Finally, we describe how these data types can be embedded into extensible databases and show some example queries.

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Topological relations between fuzzy regions in a fuzzy topological space

Cited by 30 publications

References 28 publications

Application of Fuzzy Topological relation in Flood Prediction

Application of Fuzzy Topological relation in Flood Prediction

K-nearest neighbor search for fuzzy objects

Soft Computing Techniques in Spatial Databases

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