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I need to create a regular grid containing attributes from other thematic data from ecological data. I am in effect creating a homogenous polygon raster and adding information from another dataset which contains irregular-shaped polygons to the regular shaped raster cells . I need to therefore clip or union the fishnet with the thematic data - but the only problem is that inside the fishnet cell only one value is permitted (because this will eventually become a raster-formated dataset most likely a geotif. How do I decide which value the cell obtains? - some features are more important than others and should be weighted, other cells would just obtain the value from the polygon with the largest area inside the cell or possibly because it is location centrally inside the cell.

Below is an illustration of the data in ArcGIS.

enter image description here

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I believe this answer:

How to calculate a percentage of an area covered by polygons ArcGIS 10.1

will help you get a table showing the distribution of land cover types (or whatever your thematic dataset is) for each fishnet square. Essentially, it's Union followed by some Summary Statistics to get one row for each square, with a column for each land cover type.

Once you have that, you could use expressions in Field Calculator to obtain the desired code for each one, for example using IF statements to pick out the more desirable types first, and then a codeblock like getMaxField described in this answer on Esri GeoNet:

https://geonet.esri.com/message/322307#322307

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