Top

Journal of Geographical Systems

Published in:

22-01-2024 | Original Article

Deriving fuzzy topological relations from incomplete observations

Authors: Subhankar Jana, Anjali Patel, Juthika Mahanta

Published in: Journal of Geographical Systems | Issue 1/2024

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Spatial objects in a geographical information system are often vague. Fuzzy topology-based intersection methods were introduced to obtain the topological relation between such vague objects by considering the objects as fuzzy sets. The elements of the intersection matrices express the nature of the intersections between topological parts of the objects. In reality, it may only be possible to calculate some of the required intersections due to the unavailability of data. This paper introduces a method to construct a fuzzy 9-intersection matrix under incomplete observations. Further, it computes the possible fuzzy topological relation using a quantitative fuzzy 9-intersection method based on fuzzy similarity measure. Some special cases of the incomplete observations and fuzzy topological relation under such situations are discussed. Finally, few applications are presented, where the proposed method is used to obtain relation between two uncertain objects under the condition that the topological properties of the objects are partially known.

previous article Geovisualization: an optimization algorithm of viewpoint generation for 3D cadastral property units

next article CHTopoNER model-based method for recognizing Chinese place names from social media information

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Azad KK (1981) On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity. J Math Anal Appl 82(1):14–32CrossRefMathSciNet

Bai L, Zhu L, Zhao Y (2018) Determining topological relations of fuzzy spatiotemporal regions over time in xml. IEEE Access 6:65620–65634CrossRef

Bjørke JT (2004) Topological relations between fuzzy regions: derivation of verbal terms. Fuzzy Sets Syst 141(3):449–467CrossRefMathSciNet

Bloch I (2020) Modeling imprecise and bipolar algebraic and topological relations using morphological dilations. Math Morphol Theory Appl 5(1):1–20

Burrough PA (1996) Opportunities and limitations of GIS-based modeling of solute transport at the regional scale. Appl GIS Model Non-point Source Pollut Vadose Zone 48:19–38

Burrough PA, Frank AU (1995) Concepts and paradigms in spatial information: are current geographical information systems truly generic? Int J Geogr Inf Syst 9(2):101–116CrossRef

Carniel AC, Schneider M (2016) A conceptual model of fuzzy topological relationships for fuzzy regions. In: 2016 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 2271–2278

Carniel AC, Schneider M (2018) Spatial plateau algebra: an executable type system for fuzzy spatial data types. In: 2018 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 1–8

Chang C-L (1968) Fuzzy topological spaces. J Math Anal Appl 24(1):182–190CrossRefMathSciNet

Carniel AC, Schneider M (2017) Coverage degree-based fuzzy topological relationships for fuzzy regions. In: Flexible query answering systems: 12th international conference, FQAS 2017, London, UK, June 21–22, 2017, Proceedings 12. Springer, pp 112–123

Cheng T, Molenaar M, Lin H (2001) Formalizing fuzzy objects from uncertain classification results. Int J Geogr Inf Sci 15(1):27–42CrossRef

Clementini E, Di Felice P (1996) An algebraic model for spatial objects with indeterminate boundaries. Geogr Objects Indeterminate Boundaries 2:155–169

Cohn AG, Gotts M (1996) The ‘egg-yolk’ representation of regions with indeterminate. Geogr Objects Indeterminate Boundaries 2:171–187

Das R (2022) Spatial fuzzy topological space. Proyecciones (Antofagasta) 41(4):999–1013CrossRefMathSciNet

Dilo A (2006) Representation of and reasoning with vagueness in spatial information: a system for handling vague objects. Wageningen University and Research, Wageningen

Dilo A, De By RA, Stein A (2007) A system of types and operators for handling vague spatial objects. Int J Geogr Inf Sci 21(4):397–426CrossRef

Du S, Qin Q, Wang Q, Li B (2005a) Fuzzy description of topological relations i: a unified fuzzy 9-intersection model. In: International conference on natural computation. Springer, pp 1261–1273

Du S, Wang Q, Qin Q, Yang Y (2005b) Fuzzy description of topological relations ii: computation methods and examples. In: International conference on natural computation. Springer, pp 1274–1279

Egenhofer MJ, Franzosa RD (1991) Point-set topological spatial relations. Int J Geogr Inf Syst 5(2):161–174CrossRef

Egenhofer MJ, Herring J (1990) Categorizing binary topological relations between regions, lines, and points in geographic databases. Santa Barbara CA Natl Center Geogr Inf Anal Tech Rep 9(94–1):76–105

Egenhofer MJ, Sharma J, Mark DM et al (1993) A critical comparison of the 4-intersection and 9-intersection models for spatial relations: formal analysis. pp 47–68

Fisher P (1996) Boolean and fuzzy regions. Geogr Objects Indeterminate Boundaries 2:87–94

Freeman J (1975) The modelling of spatial relations. Comput Graphics Image Process 4(2):156–171CrossRef

Guang-qing W, Chong-you Z (1991) Fuzzy boundary and characteristic properties of order-homomorphisms. Fuzzy Sets Syst 39(3):329–337CrossRefMathSciNet

Guo J, Shao X, Mo X (2018) Qualitative topological relations between interval type-2 fuzzy spatial objects. Trans GIS 22(6):1596–1631CrossRef

Jana S, Mahanta J (2022a) Boundary of a fuzzy set and its application in GIS: a review. Artif Intell Rev 56(7):6477–6507. https://doi.org/10.1007/s10462-022-10331-0CrossRef

Jana S, Mahanta J (2022b) A method to obtain fuzzy relations between uncertain objects using similarity measure. https://doi.org/10.21203/rs.3.rs-1743983/v1

Jana S, Mahanta J (2022c) Intuitionistic fuzzy 9 intersection matrix for obtaining the relationship between indeterminate objects. In: Intelligent system design. Springer, pp 171–178

Kurata Y (2008) The 9+-intersection: a universal framework for modeling topological relations. In: International conference on geographic information science. Springer, pp 181–198

Lee-Kwang H, Song Y-S, Lee K-M (1994) Similarity measure between fuzzy sets and between elements. Fuzzy Sets Syst 62(3):291–293CrossRefMathSciNet

Liu B, Li D, Ruan J, Zhang L, You L, Huayi W (2015a) A model of fuzzy topological relations for simple spatial objects in GIS. Boletim de Ciências Geodésicas 21:389–408CrossRef

Liu B, Li D, Xia Y, Ruan J, Lili X, Huanyi W (2015b) Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions. PLoS ONE 10(3):e0117379CrossRefPubMedPubMedCentral

Liu K, Shi W (2006) Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology. Int J Geogr Inf Sci 20(8):857–883CrossRef

Liu K, Shi W (2009) Quantitative fuzzy topological relations of spatial objects by induced fuzzy topology. Int J Appl Earth Obs Geoinf 11(1):38–45

Mahanta J, Das PK (2014) On fuzzy boundary. J Fuzzy Math 22(1):197–201MathSciNet

Molenaar M (1996) A syntactic approach for handling the semantics of fuzzy spatial. Geogr Objects Indeterminate Boundaries 2:207

Njila RCN, Mostafavi MA, Brodeur J (2021) A decentralized fuzzy rule-based approach for computing topological relations between spatial dynamic continuous phenomena with vague boundaries using sensor data. Sensors 21(20):6840CrossRefADS

Pal SK, King RA (1981) Image enhancement using smoothing with fuzzy sets. IEEE Trans Syst Man Cybern Part A Syst Hum 11(7):494–501CrossRef

Pao-Ming P, Ying-Ming L (1980) Fuzzy topology. J Math Anal Appl 77(1):20–37CrossRefMathSciNet

Pappis CP, Karacapilidis NI (1993) A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst 56(2):171–174CrossRefMathSciNet

Pauly A, Schneider M (2010) Vasa: an algebra for vague spatial data in databases. Inf Syst 35(1):111–138CrossRef

Raha S, Pal NR, Ray KS (2002) Similarity-based approximate reasoning: methodology and application. IEEE Trans Syst Man Cybern Part A Syst Hum 32(4):541–547CrossRef

Schneider M (1999) Uncertainty management for spatial datain databases: fuzzy spatial data types. In: International symposium on spatial databases. Springer, pp 330–351

Shi W, Liu K (2007) A fuzzy topology for computing the interior, boundary, and exterior of spatial objects quantitatively in GIS. Comput Geosci 33(7):898–915CrossRefADS

Tang X, Kainz W (2002) Analysis of topological relations between fuzzy regions in a general fuzzy topological space. In: Symposium on geospatial theory, processing and applications. Citeseer, pp 1–15

Tang X, Kainz W, Wang H (2010) Topological relations between fuzzy regions in a fuzzy topological space. Int J Appl Earth Obs Geoinf 12:S151–S165

Tao C, Molenaar M, Bouloucos T (1997) Identification of fuzzy objects from field observation data. In: International conference on spatial information theory. Springer, pp 241–259

Wang W-J (1997) New similarity measures on fuzzy sets and on elements. Fuzzy Sets Syst 85(3):305–309CrossRefMathSciNet

Warren RH (1977) Boundary of a fuzzy set. Indiana Univ Math J 26(2):191–197CrossRefMathSciNet

Weiss MD (1975) Fixed points, separation, and induced topologies for fuzzy sets. J Math Anal Appl 50(1):142–150CrossRefMathSciNet

Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRef

Zhan FB (1998) Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries. Soft Comput 2(2):28–34CrossRef

Zhang C, Fu H (2006) Similarity measures on three kinds of fuzzy sets. Pattern Recogn Lett 27(12):1307–1317CrossRefADS

Title: Deriving fuzzy topological relations from incomplete observations
Authors: Subhankar Jana
Anjali Patel
Juthika Mahanta
Publication date: 22-01-2024
Publisher: Springer Berlin Heidelberg
Published in: Journal of Geographical Systems / Issue 1/2024
Print ISSN: 1435-5930
Electronic ISSN: 1435-5949
DOI: https://doi.org/10.1007/s10109-023-00432-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 1/2024

CHTopoNER model-based method for recognizing Chinese place names from social media information

Estimating school provision, access and costs from local pupil counts under decentralised governance

2023 JGS best paper award and the editors’ choice paper volume 26(1)

Synergic effects of meteorological factors on urban form-outdoor exercise relationship: A study with crowdsourced data

Geovisualization: an optimization algorithm of viewpoint generation for 3D cadastral property units

Accelerated multi-hillshade hierarchic clustering for automatic lineament extraction

Premium Partner