A Revised Taxonomy of Overlay Combinations

Abstract

Overlay remains a central part in any rendition of the GIS toolkit. No other operation acts so clearly to integrate diverse sources of information. Over a number of years, a number of different schemes have been articulated to explain the overlay operation, most notably a 1975 paper by Hopkins and the map algebra advanced by Tomlin. These frameworks do not provide an adequate explanation of how overlay serves to integrate and what limits should be imposed on its application. This paper presents a new taxonomy of overlay combinations based on three groupings of operators: dominance rules, contributory rules and interaction rules. Each rule operates in the environment prescribed by an overlay: the geometric procedure collects a number of distinct attribute values from separate source material. With a dominance rule, one of these values become the result based on some external rule, such as the highest value for ordinal sources. A contributory rule uses all the source values to construct a composite value where each value contributes to the result equally. Addition is the simplest model, though far from universally applicable. An interaction rule uses all the values, but relies on the relationships between the values, not just their numerical values. This new taxonomy offers an improved explanation of GIS operations for education, training and an analytical critique of GIS practice.

Outline of Presentation

• Why care about rules of combination?
  • Review of literature on overlay in GIS
  • Multi-Criteria Decisionmaking literature
• A New Approach
  • Motivation from overlay problem (suitability)
  • 3 classes of rules
    Dominance, Contributory, Interaction
• Connection to transformations
  • Overlay as simple case of transformation
  • Role of attribute combination in
    a generalized theory of transformations

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Previous Literature on Overlay Combinations

• Lewis Hopkins (1977)
  Methods for generating land suitability maps: A comparative evaluation. AIP Journal
  Taxonomy based on level of measurement:
  Gestalt, Ordinal, Linear, Factor Combination, etc.
  Strong caution about interpendence of factors
• Larz Anderson (1987)
  Seven methods for calculating land capability/suitability Planning Advisory Service Report 402
  Pass/Fail screening, graduated screening, weighted factors, penalty point assignment, composite rating, weighted compostie rating, direct assignment
• Dana Tomlin (1982/ 90)
  Map Algebra: open­ended rules of combination

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Multi-Criteria Methods

For example: Benjamin Hobbs (1985) Choosing how to choose (Env. Impact Ass. Rev. 5: 301-319)
"Amalgamation" (purpose to commensurate the incommensurable)
Defends commingling of attributes, but recognizes requirements:
1) "attributes" (variables/factors/maps) completely describe impacts and characteristics of alternatives while avoiding redundancy; values (importance) or prob. dist. known
2) all relevant alternatives be included (to be considered)
3) decision makers have stable preferences and can voice them

Steps:

1) attribute scaling: value-based ­ midpoints/ tradeoffs (conjoint measurement)/"holistic" scaling OR utility-based ­ indifference between midvalue OR p (better) · (1-p) (worse)
2) attribute weighting: how much of one attribute to trade for another
3) decision rule (procedure) from simple weighted addition to fancy methods (ELECTRE)
Issue of "preference independence": are tradeoffs between pairs of variables independent of third variables?

Applied in GIS:

Carver and Openshaw (IJGIS) Nuclear waste sites for UK

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What is missing

• Students get lost in details
• Assumptions (axioms) not clearly stated as such
• Hidden assumption that "level of measurement" or some other simple feature determines "correct" approach

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A New Approach

Presented in Chrisman (1997) Exploring GIS [Wiley]

• Dominance rules
  one value wins
• Contributory rules
  each attribute contributes to result
  (without regard for other values)
• Interaction rules
  pairs of attribute values determine result

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Examples of Combination Rules

Dominance Rules (one value wins)

• Exclusionary screening One strike and you're out.
  Ex: WA Growth Management Critical Areas; PA initial phases of screening
• Exclusionary ranking Extreme value from rankings (usually worst wins)
  USDA/ FAO site evaluations (slight, moderate, severe limitations)
• Highest bid Extreme value from continuous data
  maximum profit at that site (best alternative); could be worst ­ highest risk
• Highest bidder Records identity of extreme value
  Crop result from Thünen model

Independent Rules (all values contribute without regard for the others)

• Voting tabulation Sum of binary exclusions
  PA low-level waste siting process
• Linear combination Sum of 'ratings' (mean, etc.)
  Dane County Solid Waste Plan (added up ordinal values...); METLAND added $
• Weighted linear combination Weighting and rating game
  LESA, Kansas
  "Linear Combination" - the Weighting and Rating Game Vj = Sum (wi rij) / Sum ( wi )
  ­ influence of roundoff (integer values) on ratings and weights
  ­ standardized ratings make weights easier to understand
  ­ Independence of factors
  When the variables are continuous, suitability might have some functional form; total cost, elapsed time, ... which is not simply an average; it could be a total.
• Product Multiplication of factors

Interaction Rules (pairs [or more] of values are consulted to yeild the result)

• Gestalt (Integrated Survey) Informal judgement
• Factor Combination Rank with conjoint measurement
• Rules of combination Formal interaction tables
• Threshold formulae Divided phase space

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Three Classes of Rules

Connection to transformations

• Overlay as special case
  Geometric procedure assembles all the attributes for a given location.
  Rules of combination produce a composite result.
• Framework for transformations:
  Combination of neighborhood (geometry)
  and rule of combination (attribute)
  Handles buffers, interpolation, iterative procedures, etc.