Visualizing the Uncertainty of Urban Ontology Terms

1. Visualizing the Uncertainty of Urban Ontology Terms Hyowon Ban and Ola Ahlqvist Department of Geography, The Ohio State University 1049B Derby Hall, 154 N Oval Mall Columbus, OH 43210, USA. {ban.11, ahlqvist.1}@osu.edu COST C21: The 1st Towntology Workshop Geneva, Swiss Nov. 6~7, 2006

2. Introduction • Ontology in Urban Civil Engineering & Geography • For a better communication about urban environment • The differences in understanding concepts of an ontology • Ex) ontology of an urban area type: urban, suburban, exurban, and rural areas • An articulation of these differences is important

3. Exurban boundary issue • Recently exurban areas have fast growth • Separate definitions to call exurbanization but little consensus • Few research on the uncertainty of the boundaries in exurban areas • Only crisp boundaries in existing studies

4. The research purposes • To compare the spatial implications of different ontological commitments from different definitions of exurban areas • To demonstrate the relevance of representing exurban areas as vague objects • Comparing the traditional crisp representation Vs. a vague, graded representation • Representing the different theoretical boundaries of exurban areas: crisp membership Vs. fuzzy membership • Visualizing them in maps: standard GIS techniques

5. Uncertainty in exurban boundaries • The concept of urban, suburban, exurban, and rural zones • Urban zone: within an urbanized area or an urban cluster (Fig. 1) • Suburban zone: a non-central county, metropolitan (Fig. 2) • Exurban zone: metropolitan counties outside this ring of suburban counties (Fig. 2) • Rural zone: outside of an urbanized area (Fig. 2) • No clear boundary between them Fig. 1. Idealized spatial configuration of urban and rural area concepts Fig. 2. Simple spatial distribution of urban, suburban, exurban, and rural areas

6. Uncertainty: error, vagueness, and ambiguity • Error • Represented with probability • Vagueness • No unique allocation of individual objects to a class • Or, no precise spatial extent of the objects • Ambiguity • More than one definition for a term • One clearly defined object is a member of different classes

7. The idea of fuzzy membership functions • Fuzzy and rough extensions of traditional set theory • To represent semantic uncertainty of concept definitions • A rough fuzzy set • Semantic imprecision * vagueness • “closed” as a crisp and artificial definition“closed” as a continuous function (set of %)μF:U→[0, 1]

8. Implementation of fuzzy membership functions with the exurban definition of Nelson (1992) • “Counties being those within 50 miles of the boundary of the central city of a Metropolitan Statistical Area (MSA) with a population of between 500,000 and less than 2 million, or within 70 miles of the boundary of the central city of an MSA with a population of more than 2 million” Fig. 3. Membership function of distance in Delaware County based on Nelson’s (1992) definition

9. Implementation of fuzzy membership functions with the exurban definition of Daniels (1999) • “10 to 50 miles away from a major urban center of at least 500,000 people, or 5 to 30 miles from a city of at least 50,000 people,population density less than 500/mile2 ,commute distance at 25 minutes or more” Fig. 4. Membership function of distance(left) and population(right) in Delaware County based on Daniels’s (1999) definition

10. Conceptually synthesized definitions of exurban areas Fig. 5. Differences between existing definitions of exurbanization of Daniels (1999) and Nelson (1992)

11. Results: definition of Nelson • Difference between crisp membership & fuzzy membership representations • Geometric + non-geometric representation Fig. 6. Exurban areas based on Nelson’s (1992) definition with crisp membership (left) and fuzzy membership (right)

12. Results: definition of Daniels • The fuzzy membership: a more specific spatial pattern of sprawl than the crisp membership Fig. 7. Exurban areas based on Daniel’s (1999) definition with crisp membership (left) and fuzzy membership (right)

13. Concluding discussion • A clear difference between crisp membership Vs. fuzzy membership representations in defining exurban boundaries • Uncertainty reveals the heterogeneity of exurban areas in a location specific context • The crisp classification of exurban area may miss the graded phenomena

14. Suggested ontology representation and prevailing approaches • The standard first-order logic representation with a fuzzy set • To explicitly recognize the vagueness of terms • To admit partial belonging to several possible categories • Comparison of different notions of exurban areas • Using standard descriptive properties(i.e. population, distance, and etc) • To compare across heterogeneous terminologies • To look for similarities and differences in a flexible manner

15. Future extensions • Negotiated definition with 3D geovisualization (Fig. 8) • Incorporation of the dynamic character of urbanization processes • Category descriptions with time dependent characteristics • A weighted fuzzy membership function • Comparison of the difference between definitions MOUNTGILEAD MANSFIELD DELAWARE COLUMBUS Fig. 8. 3D visualization of the ‘negotiated’ average of fuzzy membership of Daniels and Nelson

16. Questions and answers