ArcGIS Tutorial: How Fuzzy overlays work

The fuzzy Overlay tool can analyze the possibility that a phenomenon belongs to multiple sets during multi-criteria overlay analysis. A fuzzy overlay can not only determine which collection a phenomenon might belong to, but also analyze the relationships between members of multiple collections.

Overlay Types list Some of the methods that are appropriate for merging data based on set theory analysis. Each method can explore the members of each unit that belongs to the various input criteria. The available methods are fuzzy and, fuzzy Or, Fuzzy Product, Fuzzy Sum, and fuzzy Gamma. Each method provides different aspects of the members of each cell to multiple input criteria.

　　Fuzzy and

The Fuzzy and overlay type returns the minimum value of the collection to which the cell position belongs. This method is useful when you need to determine the lowest common denominator for members of all input criteria. For example, in a housing suitability model, you might want to select only those locations that meet the probabilities of all criteria greater than or equal to 0.5.

Fuzzy and uses the following functions during the evaluation process:

Fuzzyandvalue = min (arg1, ..., argn)

　　Fuzzy Or

The Fuzzy Or overlay type returns the maximum value of the collection to which the cell position belongs. This method is useful when you need to determine the maximum classification value for all input criteria. For example, in a housing suitability model, you might want to determine that at least one of the criteria is completely in place within the appropriate set (value 1).

Fuzzy Or uses the following functions during the evaluation process:

Fuzzyorvalue = max (Arg1, ..., argn)

　　Fuzzy Product

For each cell, the fuzzy Product overlay type multiplies each blur value for all input criteria. The resulting product will be less than any input value entered, and the value may be very small when the input is a member of more than one collection. It is difficult to correlate the product of all input criteria with the relative relationship of values. The Fuzzy Product option is not a common option.

Fuzzy Product uses the following functions during the evaluation process:

Fuzzyproductvalue = Product (Arg1, ..., argn)

　　Fuzzy Sum

The Fuzzy Sum overlay type adds the blur value of each collection to which the cell location belongs. The resulting sum is an incremental linear composite function that is based on the number of criteria entered into the analysis.

Fuzzy Sum is not algebraic and should not be confused with weighted overlay and weighting and the additional methods used in the tool. Both of these overlay methods assume that the input is as good as possible. Adding all the categorical values in the fuzzy Sum analysis does not necessarily indicate a more appropriate location. The Fuzzy Sum option is not a common option.

Fuzzy Sum uses the following functions during the evaluation process:

Fuzzysumvalue = 1-product (1-arg1, ..., 1-argn)

　　Fuzzy Gamma

The fuzzy gamma type is the algebraic product of fuzzy product and fuzzy Sum, both of which use Gamma as exponent. The generalization function is as follows:

μ (x) = (fuzzysum) γ* (fuzzyproduct) 1-γ

This is a specific function used by Fuzzy Gamma:

Fuzzygammavalue = POW (1-((1-ARG1) * (1-ARG2) * ...), Gamma) *

Pow (ARG1 * arg2 * ..., 1-gamma)

If the specified gamma equals 1, the output is equal to the fuzzy Sum, and if gamma equals 0, the output is equal to the fuzzy Product. A value in between allows you to combine the evidence raster between these two extrema, and the result may be different from the fuzzy or fuzzy and. Fuzzy Gamma is a tradeoff between fuzzy Sum with incremental effect and fuzzy Product with diminishing effect. The relationship between gamma is defined as the term "fuzzy Sum" and "Fuzzy Product".

　　

Fuzzy Gamma establishes a relationship between multiple input criteria, not just the value of a single member collection, as in fuzzy Or and fuzzy and.

You can use the fuzzy Gamma when you need a value that is greater than fuzzy Product but less than the fuzzy Sum.

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ArcGIS Tutorial: How Fuzzy overlays work