Membership function used in fuzzy singletons: fuzzy sets that have just one point with membership value 1.

Sometimes it is needed to represent crisp (classical) number in the fuzzy domain. Several approaches can be used, like adding some uncertain (fuzziness) in the original number (the number one, for instance, can be seen as a TrapezoidalFunction with -0.5, 1.0 and 0.5 parameters). Another approach is to declare fuzzy singletons: fuzzy sets with only one point returning a none zero membership.

While trapezoidal and half trapezoidal are classic functions used in fuzzy functions, this class supports any function or approximation that can be represented as a sequence of lines.

Sample usage:

// creating the instance SingletonFunction membershipFunction = new SingletonFunction( 10 ); // getting membership for several points for ( int i = 0; i < 20; i++ ) Console.WriteLine( membershipFunction.GetMembership( i ) );
Inheritance: IMembershipFunction
SingletonFunction Class Documentation
Exemple #1
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        private InferenceSystem SetupInferenceSystem(byte minLuma, byte maxLuma, byte meanLuma)
        {
            var lumaIn = new LinguisticVariable("LumaIn", minLuma, maxLuma);
            var lumaOut = new LinguisticVariable("LumaOut", 0, 255);

            var darkFunction = new TrapezoidalFunction(minLuma, meanLuma, TrapezoidalFunction.EdgeType.Right);
            var darkSet = new FuzzySet("Dark", darkFunction);

            var mediumFunction = new TrapezoidalFunction(minLuma, meanLuma, maxLuma);
            var mediumSet = new FuzzySet("Medium", mediumFunction);

            var lightFunction = new TrapezoidalFunction(meanLuma, maxLuma, TrapezoidalFunction.EdgeType.Left);
            var lightSet = new FuzzySet("Light", lightFunction);

            lumaIn.AddLabel(darkSet);
            lumaIn.AddLabel(mediumSet);
            lumaIn.AddLabel(lightSet);

            var whiteFunction = new SingletonFunction(255);
            var whiteSet = new FuzzySet("White", whiteFunction);

            var blackFunction = new SingletonFunction(0);
            var blackSet = new FuzzySet("Black", blackFunction);

            var grayFunction = new SingletonFunction(128);
            var graySet = new FuzzySet("Gray", grayFunction);

            lumaOut.AddLabel(blackSet);
            lumaOut.AddLabel(graySet);
            lumaOut.AddLabel(whiteSet);

            var database = new Database();
            database.AddVariable(lumaIn);
            database.AddVariable(lumaOut);

            var inferenceSystem = new InferenceSystem(database, new CogDefuzzifier());
            inferenceSystem.NewRule("Rule 1", "IF LumaIn IS Dark THEN LumaOut is Black");
            inferenceSystem.NewRule("Rule 2", "IF LumaIn IS Medium THEN LumaOut is Gray");
            inferenceSystem.NewRule("Rule 3", "IF LumaIn IS Light THEN LumaOut is White");

            return inferenceSystem;
        }