/*
* Copyright (c) 2012, Søren Atmakuri Davidsen
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package fuzzy4j.sets;
import fuzzy4j.util.SimpleInterval;
/**
* Implementation of an S-shape membershipi function.
*
* Negate the function to create Z-shape.
* @author Soren A. Davidsen <soren@tanesha.net>
*/
public class SFunction implements FuzzyFunction, SupportAware, CenterAware {
private double a;
private double b;
private double ab_middle;
/**
* Creates an S function that goes between [0, 1].
*
* @param a The point where x starts to to grow. f(x) = 0 forall x < a
* @param b The point where x is at 1, f(x) = 1 forall x > b
*/
public SFunction(double a, double b) {
this.a = Math.min(a, b);
this.b = Math.max(a, b);
this.ab_middle = this.a + ((this.b - this.a) / 2);
}
@Override
public double apply(double x) {
if (x <= a) // up to a
return 0;
else if (x <= ab_middle) // a up to ab_middle
return 2.0 * Math.pow(((x - a) / (b - a)), 2);
else if (x <= b) // ab_middle up to b
return 1.0 - (2.0 * Math.pow(((b - x) / (b - a)), 2));
else // more than b
return 1;
}
@Override
public SimpleInterval support() {
return new SimpleInterval(false, a, Double.POSITIVE_INFINITY, true);
}
@Override
public double center() {
return b;
}
public String toString() {
return "S(x, " + a + ", " + ab_middle + ", " + b + ")";
}
}