# Spatial Decision Support Layers

A Spatial Decision Support System^{[1]} operates on Layers as input data. Rule based system processes the layers and creates a decision support output (e.g. spatial multi-criteria evaluation and expert knowledge^{[2]}). The output of spatial decision support system can be (among others) a spatial decision support layer again.

## Contents

## Mathematics: Spatial Decision Support Layer as Mapping[edit]

In terms of mathematical definition a spatial decision support layer is a mapping

where is the codomain (target set) of the mapping .

includes the **geographic coordinate system** , the height and the time index . So is a subset of a threedimensional vector space . The geographic coordinate system is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols. In specialized works, "geographic coordinates" are distinguished from other similar coordinate systems, such as geocentric coordinates and geodetic coordinates. See, for example, Sean E. Urban and P. Kenneth Seidelmann^{[3]} The coordinates are often chosen such that one of the numbers represents a vertical position, and two or three of the numbers represent a horizontal position. A common choice of coordinates is latitude, longitude and elevation^{[4]}.

## Computer Science: Spatial Decision Support Layer as UML-Class[edit]

- Learn Unified Modelling Language UML and create a UML Class for a Spatial Decision Support Layer.
- Create a Spatial Fuzzy Layer for Spatial Decision Support Systems in UML. What are additional methods for these sub classes, so that Fuzzy Rules can be applied on Spatial Fuzzy Membership functions.

## Learning Task[edit]

- Learn about Spatial Fuzzy Logic and create a spatial decision support layer for temperature at specific time .

- We use a membership function that maps a temperature into the real number between 0 and 1 (i.e. the interval ) by the following definition

- With definition above the temperature is optimal for mosquitoes () at a temperature . If the temperature is higher than (e.g. ) or lower than the fuzzy value is decreasing for lower and higher temperatures example the domain can be defined as the set of real numbers , so that the membership function could take all temperatures in degrees Celsius as input variable.

- The function maps the the tupel with the longitude , the latitude , the elevation above sealevel and the time index to the temperature at the geolocation at altitude and time index .
- Explain, why the altitude and time index are important input parameters for the temperature layer!
- Composistion defines a spatial decision support layers. Explain the purpose for vector control units working for a Public Health Agency.

## See also[edit]

- Spatial Decision Support Systems
- Improve Trust in Spatial Decision Support Layers by application of Digital Signature

## References[edit]

- ↑ Keenan, P. B. (2002). Spatial decision support systems. Decision Making Support Systems Achievements and Challenges for the New Decade, 28-39.
- ↑ Store, R., & Kangas, J. (2001). Integrating spatial multi-criteria evaluation and expert knowledge for GIS-based habitat suitability modelling. Landscape and urban planning, 55(2), 79-93.
- ↑
*Explanatory Supplement to the Astronomical Almanac, 3rd. ed., (Mill Valley CA: University Science Books, 2013) p. 20–23.* - ↑ A guide to coordinate systems in Great Britain, Mar 2015, D00659 v2.3, access date 2015-06-22, Ordnance Survey, http://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf