07 — Inference And Settings

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Four Stages

1. Fuzzification. Each crisp input is evaluated against all of its sets.
2. Rule evaluation. The statements' degrees are combined, NOT and the WITH weight are applied.
3. Implication and aggregation. The rule's strength shapes part of the output set, and all parts are combined.
4. Defuzzification. The aggregated shape is converted into a crisp number.

System Settings

Setting	Options	Effect
And Operator	Minimum, Product	T-norm for AND
Or Operator	Maximum, Probabilistic Sum	S-norm for OR
Implication	Clip, Scale	Applying rule strength to the consequence
Aggregation	Maximum, Probabilistic Sum, Bounded Sum	Combining rule consequences
Defuzzification Method	six methods below	Converting the result into a number
Sample Count	11…4001, default 201	Resolution of the output curve

The defaults Minimum, Maximum, Clip, Maximum, Centroid, 201 correspond to a typical Mamdani system.

T-Norms and S-Norms

Minimum makes the weakest condition the limiting factor. Product gradually reduces strength for every incomplete condition.

Maximum lets the strongest alternative determine OR. Probabilistic Sum = a + b - ab reinforces several partially true alternatives.

Implication

• Clip cuts off the consequence's membership function at the height of the rule strength. This is classic Mamdani.
• Scale multiplies the entire function by the rule strength and preserves its shape. This approach is often called Larsen implication.

Aggregation

• Maximum takes the largest activation at each point.
• Probabilistic Sum smoothly reinforces agreeing rules.
• Bounded Sum adds activations and caps the sum at one.

Under Maximum, duplicate rules don't increase the peak. Under the summing methods they do, so watch for repeats.

Defuzzification Methods

Method	Result	Typical use
Centroid	Center of gravity of the area under the curve	Smooth continuous control; the default choice
Bisector	The point that splits the area in half	Less sensitive to a long thin tail
Mean of Maxima	Average of all maximum points	Selecting the most-supported result
Smallest of Maxima	Smallest maximum point	Conservative tie-breaking
Largest of Maxima	Largest maximum point	Aggressive tie-breaking
Weighted Average	Weighted average of the consequences' representative values	The fastest method, especially for Singleton

Weighted Average doesn't discretize the output surface and ignores Sample Count. In the editor, its aggregated curve is marked as illustrative.

When No Rule Fires

When no rule activates a particular output, the system returns the midpoint of the range and adds a Warning diagnostic (No rule fired for output '…'). This is a predictable fallback, but not a real decision. Check the coverage of the input sets and the presence of rules for the output.

The warning is produced by every defuzzification method, Weighted Average included, so a fallback is never mistaken for a decision whichever strategy a system is set to.

Sample Count

201 suits most gameplay tasks. Increase the value when the output range is wide, the shapes are narrow, or higher numeric precision is needed. Decrease it only after profiling. Cost scales with the number of outputs, rules, and samples.