Julie Sungsoon Hwang & Jean-Claude ThillDepartment of GeographyState University of New York at BuffaloU.S.A.

August 24, 200411th Int’l Symposium of Spatial Data Handling

Empirical study on location indeterminacy of localities

Research question

How can we represent vague concepts of spatial object in a (discrete) computing environment (e.g. GIS)?

Nearness in localities

Mental maps of localities

Indeterminate boundaries of localities

Research scope

Mental maps Generals: f (distance, relation, scale) Specifics : f (preferences, experience, …)

Localities Official recognition: eg. administrative unit Unofficial recognition: eg. vernacular region

Research objective [1]

Building the model of locality boundary using fuzzy regions (egg-yolk model) and some rules regarding nearness

0

1

BA

A

B

2-Dimensional Geographic Space

x: 1-Dimensional Geographic SpaceY: Degree of Membership

Research objective [2]

Examining any difference in location indeterminacy between urban and rural settings

BuffaloBuffalo

Urban

WilsonWilson

Rural

Example: identifying localities…

Accident location?

Which city?

Task 1: theoretical

Building the model of locality boundary using fuzzy region and rules of nearness

Fuzzy regions

Core

Exterior

Boundary

Nearness

= Fuzzy set membership of belonging to “Syracuse”

Near “Syracuse”?

What determines the fuzzy set membership What determines the fuzzy set membership function value?function value?

Euclidean distanceEuclidean distance Spatial qualitative relationSpatial qualitative relation Scale-dependentScale-dependent

Locality as a fuzzy region

Exterior

Core

Boundary1stOrderGr2ndOrderGr

Computing fuzzy set membership value in GIS: work steps

1. Delineate boundaries

2. Assign membership values

3. Create TINs 4. Interpolate values on TINs

Computing fuzzy set membership value in GIS: results

ELMA

AMHERST

BUFFALO

CLARENCE

ALDEN

NEWSTEAD

WALESHAMBURG AURORA

LANCASTER

MARILLA

ROYALTON

ORCHARD PARK

PENDLETON

GRAND ISLAND

DARIEN

WHEATFIELD

BENNINGTON

CHEEKTOWAGA

SHELDON

ALABAMA

TONAWANDA

WEST SENECA

LOCKPORT

PEMBROKE

NIAGARA FALLS

NIAGARA

EVANS

NORTH TONAWANDA

LACKAWANNA

SHELBY

EDEN

Legend

County Boundary

TownorCity Boundary (PLACE_PL)

WaterBody

FuzzySet Membership of Locality

Value

High : 1

Low : 0

¯

0 7,500 15,0003,750 Meters

Lake Erie

Comparison to other proximity measures

core exterior0.5-cut boundary

0.5-cut boundary

0.5

1

0.5

1

coreexterior0.5-cut boundary

core

Distance Buffer Fuzzy proximity

Task 2: empirical

Examining any difference in location indeterminacy between urban and rural settings

Georeferencing traffic accident data

We considered 5460 out of 8631 cases from NYS ‘96-’01Of these, 246 urban, and 298 rural localities are compared

Computing location indeterminacy index of localities

i = 1 - (Σi)/n

78% sure

95% sure

58% sure

Comparing location indeterminacy index of urban versus rural localities

Average number of fatal crashes in rural areas is 2 whereas those in urban areas is 16

To work around small number problem, we compute Bayesian estimates of both groups adjusted for within-group distributions

People are 94% (or somewhere between 93% and 95%) sure in identifying urban localities while they are 88% (or somewhere between 86% and 90%) sure in identifying rural localities

ANOVA

Analysis of variance conducted on Bayesian estimates of location indeterminacy confirms the difference between urban versus rural locality is significant in terms of location indeterminacy

Neighborhood types may affect the degree of certainty to which the boundary of locality is perceived

Interpretation of results

• Mental maps of urban settings may be less error-prone than those of rural settings

• Spatial knowledge acquisition: city provides more landmark or route upon which judgment on indeterminate boundaries of localities can be based

• Scale factor: dense urban settings provide a reasonable scale in which humans can conceptualize localities without much difficulty

Conclusions

Fuzzy set theory provides a reasonable mechanics to represent vague concept of geospatial objects

Neighborhood types affect the way humans acquire spatial knowledge and forge mental representations of it