Lab 10: Suitability Mapping using Fuzzy Logic

• Define Goal – Create a Habitat Suitability Map for Nests • Define Potential Factors

– Vegetation– Water – Roads

• Determine the Relationship Between Factors and Nests• Preprocess Data.

– Compute Distance from Water and Roads– Reclass Distances Into Distance Zones???

• Convert Data to Relative Value – Fuzzy Logic Membership Function (0-1 scoring scheme)

• Combine Factors– Weighted Sum– AND– OR

Advantages of the Fuzzy Logic Approach

• Ability to account for uncertainty

• Relationships can be developed with minimum data

• Relatively simple approach

• Robust, handle missing data, uncertainty

• Easy to interpret and communicate results

• Promote and facilitate user participation

Fuzzy Logic Approach

In classical set theory, membership in a given set is defined aseither true or false (i.e. 1 or 0).

However, membership in a fuzzy set is expressed on a continuousscale from 1 (full membership) to 0 (full non-membership), soindividual measurements of an environmental factor may be defined according to their degree of membership in the set between1 and 0.

Many watershed assessment problems can be viewed as ranking watersheds as either being in the “Very Good Condition” set (1) or “Very Bad Condition set (0), with most of the watershed somewhere in between to two extremes (partial membership).

Landfill Site Selection

Fuzzy membership function related to an environmental factor

Potential range of values

A3

1

xB1 B2Vm

Fuzzy membership function related to an environmental factor

Transformed Fuzzy Scoring Function

A2

A1

0 xB1

FMS

Vo Vx

f(x)

01

f(x)

g(x)

Fuzzy Membership Score:

FMSi = ƒ(Environment Factor Xi) Weighted FMSi = [A1 + ((A3 – A1)/2)] + [A2 – ((A3 – A1)/2) – A1] We will not be doing this step in our Lab.

Composite Fuzzy Score:

nCFS = ∑ (Wi * FMSi) i = 1

Wi = weighting factor for environmental factor i

Other Ways to Combine

• Fuzzy OR (Maximum function) - Increasive• Fuzzy AND (Minimum function) - Decreasive • Fuzzy Product (multiply FMSs) - Decreasive• Fuzzy Sum: CFS = 1 – Π (1 – FMSi) – Increasive

• Gamma: CFS = Fuzzy_sumY * Fuzzy_product1-Y

Lab 9 Results

veg type count frac obs exp x^2

1 9821 0.303117 20 9.093519 13.08089

2 14718 0.454259 9 13.62778 1.57152

3 1922 0.059321 0 1.77963 1.77963

4 1390 0.042901 0 1.287037 1.287037

5 3846 0.118704 1 3.561111 1.841922

6 703 0.021698 0 0.650926 0.650926

sum 32400 1 30 30 20.21193

Vegetation

V = 0.58

Roads

water dist count frac obs exp x^2

1 10135 0.312818 12 9.384549 0.72892

2 9423 0.290842 15 8.725269 4.512439

3 7367 0.227384 3 6.821507 2.140863

4 3891 0.120096 0 3.602889 3.602889

5 1583 0.04886 0 1.465786 1.465786

sum 32399 1 30 30 12.4509

Water

V = 0.46

Model Testing You should perform additional tests to assess model performance.

Chi-square and K-S can be used.Relative indices.If possible use an independent data set for testing.

Model Strength