Fuzzy Logic Truthfulness Demonstration

Question

I'm creating a simplistic example demonstrating fuzzy logic truthfulness. The problem is with determining result truthfulness.

My first concern: By testing a value for truth between a high and low target, is this really using fuzzy logic?

My second concern: Truthfulness % seems incorrect for target/threshold hits.

Results:

Miss: 30
 Hit: 40 at 100% true ( should be 80% ? )
 Hit: 50 at 80% true  ( should be 100% ? )
 Hit: 60 at 66% true  ( should be 80% ? )
Miss: 70

Class:

public class FuzzyTest {

class Result {    
    int value;
    int truthfullness;
}

Result evaluate(final int valueIn, final int target, final int threshold) {
    Result result = null;
    final boolean truth = (((target - threshold) <= valueIn) && (valueIn <= (target + threshold)));
    if (truth) {
        result = new Result();
        result.value = valueIn;
        result.truthfullness = (int) (100.0 - (100.0 * (valueIn - Math.abs(target - threshold)) / valueIn));
    }
    return result;
}

public static void main(final String[] args) {
    final int[] arrayIn = new int[] { 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 };
    final int threshold = 10;
    final int target = 50;
    final FuzzyTest fuzzy = new FuzzyTest();
    for (final int x : arrayIn) {
        final Result result = fuzzy.evaluate(x, target, threshold);
        if (result == null) {
            System.out.println("Miss: " + x);
        }
        else {
            System.out.println("Hit: " + x + " at " + result.truthfullness + "% true");
        }
    }
}
}

Answer 1

By testing a value for truth between a high and low target, is this really using fuzzy logic?

No. It still the same boolean logic. To really get a fuzzy value, you must get the Fuzzy values from a Fuzzy function for your input variables.

A Fuzzy function is a function that receives an real value and returns a value between 0 and 1. Its states a degree of truth of that variable. For example, in the image below (taken from the wikipedia article about Fuzzy), a real value temperature will have a degree of 'cold', 'warm' and 'hot'. These values are your truthfulness.

Truthfulness % seems incorrect for target/threshold hits.

Yes, it is incorrect. First because your threshold is actually between 0 and 1 in the Fuzzy definition (so, you already have a percentage). Second because, if you are defining a threshold of [0, 100], its not Fuzzy.

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If you are using Java to create a Fuzzy system (even a simple one), may I suggest a good framework to do it? Try to use jFuzzyLogic. It will help you to program your Fuzzy system and to understand how Fuzzy works.

Answer 2

Try this to get the values you wanted:

result.truthfullness = (int) (100.0 - (100.0 * Math.abs(target - valueIn)) / target);

It gives this result:

Miss: 30
Hit: 40 at 80% true
Hit: 50 at 100% true
Hit: 60 at 80% true
Miss: 70