IA-ENI/FuzzyLogic/FuzzyLogicPCL/FuzzySets/FuzzySet.cs

using System;
using System.Collections.Generic;
using System.Linq;

namespace FuzzyLogicPCL.FuzzySets
{
    /// <summary>
    /// Fuzzy set class : general methods
    /// </summary>
    public class FuzzySet
    {
        /// <summary>
        /// List of points describing the fuzzy set
        /// </summary>
        protected List<Point2D> Points;

        /// <summary>
        /// Minimal value of the fuzzy set
        /// </summary>
        protected double Min {get;set;}

        /// <summary>
        /// Maximal value of the fuzzy set
        /// </summary>
        protected double Max { get; set; }

        /// <summary>
        /// Simple constructor
        /// </summary>
        /// <param name="min">Min. value</param>
        /// <param name="max">Max. value</param>
        public FuzzySet(double min, double max)
        {
            this.Points = new List<Point2D>();
            this.Min = min;
            this.Max = max;
        }

        /// <summary>
        /// Add a point to the fuzzy set. It will be sorted to be at the good place
        /// </summary>
        /// <param name="pt">New point to add</param>
        public void Add(Point2D pt)
        {
            Points.Add(pt);
            Points.Sort();
        }

        /// <summary>
        /// Add a point to the fuzzy set. It will be sorted to be at the good place
        /// </summary>
        /// <param name="x">New point x coordinate</param>
        /// <param name="y">New point y coordinate (degree)</param>
        public void Add(double x, double y)
        {
            Point2D pt = new Point2D(x, y);
            Add(pt);
        }

        /// <summary>
        /// Truth degree at a special x value. It is a simple line interpolation.
        /// </summary>
        /// <param name="XValue">The x coordinate</param>
        /// <returns>The truth degree at this point</returns>
        public double DegreeAtValue(double XValue)
        {
            // Check value in range (else, degree is null)
            if (XValue < Min || XValue > Max)
            {
                return 0;
            }

            // Compute value from interpolation : we locate the before and after point
            Point2D before = Points.LastOrDefault(pt => pt.X <= XValue);
            Point2D after = Points.FirstOrDefault(pt => pt.X >= XValue);
            if (before.Equals(after))
            {
                // x is the coordinate of a defined point
                return before.Y;
            }
            else
            {
                // x is between two points, we compute the interpolated value
                return (((before.Y - after.Y) * (after.X - XValue) / (after.X - before.X)) + after.Y);
            }
        }

        /// <summary>
        /// Compute the centroid (or x coordinate of the center of gravity) of a fuzzy set. Used for defuzzification
        /// </summary>
        /// <returns>The centroid x value</returns>
        public double Centroid()
        {
            // Less than two points : no area, so no centroid
            if (Points.Count < 2)
            {
                return 0;
            }
            else
            {
                // We compute the total area, and the ponderated one
                double ponderatedArea = 0;
                double totalArea = 0;
                double localArea;
                Point2D oldPt = null;
                foreach (Point2D newPt in Points)
                {
                    if (oldPt != null)
                    {
                        // Centroids computation
                        if (oldPt.Y == newPt.Y)
                        {
                            // For a rectangle : at the center value
                            localArea = oldPt.Y * (newPt.X - oldPt.X);
                            totalArea += localArea;
                            ponderatedArea += ((newPt.X - oldPt.X) / 2 + oldPt.X) * localArea;
                        }
                        else
                        {
                            // We have two geometric shapes : a rectangle (at half) and a triangle (at 1/3 or 2/3 depending on the slope)
                            // For the rectangle
                            localArea = Math.Min(oldPt.Y, newPt.Y) * (newPt.X - oldPt.X);
                            totalArea += localArea;
                            ponderatedArea += ((newPt.X - oldPt.X) / 2 + oldPt.X) * localArea;
                            // For the triangle
                            localArea = (newPt.X - oldPt.X) * (Math.Abs(newPt.Y - oldPt.Y)) / 2;
                            totalArea += localArea;
                            if (newPt.Y > oldPt.Y)
                            {
                                ponderatedArea += (2.0 / 3.0 * (newPt.X - oldPt.X) + oldPt.X) * localArea;
                            }
                            else
                            {
                                ponderatedArea += (1.0 / 3.0 * (newPt.X - oldPt.X) + oldPt.X) * localArea;
                            }
                        }
                    }
                    oldPt = newPt;
                }
                // Return the centroid, that is the division of the two areas
                return ponderatedArea / totalArea;
            }
        }

        /// <summary>
        /// ToString method, returns the fuzzy set with the format : [min-max] : list of points
        /// </summary>
        /// <returns>The fuzzy set returns as a string</returns>
        public override String ToString()
        {
            String result = "[" + Min + "-" + Max + "]:";
            foreach (Point2D pt in Points)
            {
                result += pt.ToString(); //"(" + pt.X + ";" + pt.Y + ")";
            }
            return result;
        }

        /// <summary>
        /// ! Operator (NOT) : inverse the fuzzy set (1- original value)
        /// </summary>
        /// <param name="fs">The original fuzzy set</param>
        /// <returns>A new fuzzy set</returns>
        public static FuzzySet operator !(FuzzySet fs) {
            FuzzySet result = new FuzzySet(fs.Min, fs.Max);
            foreach (Point2D pt in fs.Points)
            {
                result.Add(new Point2D(pt.X, 1 - pt.Y));
            }
            return result;
        }

        /// <summary>
        /// Compute the multiplication of a fuzzy set : all y values are "value" times
        /// </summary>
        /// <param name="fs">Original fuzzy set</param>
        /// <param name="value">Number</param>
        /// <returns>New fuzzy set (fuzzy set * value)</returns>
        public static FuzzySet operator *(FuzzySet fs, double value)
        {
            FuzzySet result = new FuzzySet(fs.Min, fs.Max);
            foreach (Point2D pt in fs.Points)
            {
                result.Add(new Point2D(pt.X, pt.Y * value));
            }
            return result;
        }

        /// <summary>
        /// Equality operator
        /// </summary>
        /// <param name="fs1">First fuzzy set</param>
        /// <param name="fs2">Second fuzzy set</param>
        /// <returns>True if the two fuzzy sets have the same range and the same points, false otherwise</returns>
        public static Boolean operator == (FuzzySet fs1, FuzzySet fs2)
        {
            return fs1.ToString().Equals(fs2.ToString());
        }

        /// <summary>
        /// Difference operator
        /// </summary>
        /// <param name="fs1">First fuzzy set</param>
        /// <param name="fs2">Second fuzzy set</param>
        /// <returns>True if the two fuzzy sets have not the same range or not the same points</returns>
        public static Boolean operator != (FuzzySet fs1, FuzzySet fs2)
        {
            return !(fs1 == fs2);
        }

        /// <summary>
        /// Intersection operator : min(fs1, fs2)
        /// </summary>
        /// <param name="fs1">First fuzzy set</param>
        /// <param name="fs2">Second fuzzy set</param>
        /// <returns>New fuzzy set representing the intersection</returns>
        public static FuzzySet operator &(FuzzySet fs1, FuzzySet fs2)
        {
            return Merge(fs1, fs2, Math.Min);
        }

        /// <summary>
        /// Union operator : max(fs1, fs2)
        /// </summary>
        /// <param name="fs1">First fuzzy set</param>
        /// <param name="fs2">Second fuzzy set</param>
        /// <returns>New fuzzy set representing the union</returns>
        public static FuzzySet operator |(FuzzySet fs1, FuzzySet fs2)
        {
            return Merge(fs1, fs2, Math.Max);
        }

        /// <summary>
        /// Private method computing the merging of two fuzzy sets
        /// </summary>
        /// <param name="fs1">First fuzzy set</param>
        /// <param name="fs2">Second fuzzy set</param>
        /// <param name="MergeFt">Function for merging (eg min, or max), with two parameters (two double values) and the one to keep (double)</param>
        /// <returns>The resulting fuzzy set</returns>
        private static FuzzySet Merge(FuzzySet fs1, FuzzySet fs2, Func<double, double, double> MergeFt)
        {
            // New Fuzzy set
            FuzzySet result = new FuzzySet(Math.Min(fs1.Min, fs2.Min), Math.Max(fs1.Max, fs2.Max));

            // Creation of iterators on lists + initialization
            List<Point2D>.Enumerator enum1 = fs1.Points.GetEnumerator();
            List<Point2D>.Enumerator enum2 = fs2.Points.GetEnumerator();
            enum1.MoveNext();
            enum2.MoveNext();
            Point2D oldPt1 = enum1.Current;

            // Relative positions of fuzzy sets (to know when they intersect)
            int relativePosition = 0;
            int newRelativePosition = Math.Sign(enum1.Current.Y - enum2.Current.Y);

            // Loop while there are points in the two collections
            Boolean endOfList1 = false;
            Boolean endOfList2 = false;
            while (!endOfList1 && !endOfList2)
            {
                // New x values
                double x1 = enum1.Current.X;
                double x2 = enum2.Current.X;
                // New current position
                relativePosition = newRelativePosition;
                newRelativePosition = Math.Sign(enum1.Current.Y - enum2.Current.Y);

                if (relativePosition != newRelativePosition && relativePosition != 0 && newRelativePosition != 0)
                {
                    // Positions have changed, so we have to compute the intersection and add it
                    // Compute the points coordinates
                    double x = (x1 == x2 ? oldPt1.X : Math.Min(x1, x2));
                    double xPrime = Math.Max(x1, x2);
                    // Intersection
                    double slope1 = (fs1.DegreeAtValue(xPrime) - fs1.DegreeAtValue(x)) / (xPrime - x);
                    double slope2 = (fs2.DegreeAtValue(xPrime) - fs2.DegreeAtValue(x)) / (xPrime - x);
                    double delta = (fs2.DegreeAtValue(x) - fs1.DegreeAtValue(x)) / (slope1 - slope2);
                    // Add point
                    result.Add(x + delta, fs1.DegreeAtValue(x + delta));
                    // Go on
                    if (x1 < x2)
                    {
                        oldPt1 = enum1.Current;
                        endOfList1 = !(enum1.MoveNext());
                    }
                    else if (x1 > x2)
                    {
                        endOfList2 = !(enum2.MoveNext());
                    }
                }
                else if (x1 == x2)
                {
                    // The two points are on the same X, so we take the good value (eg min or max)
                    result.Add(x1, MergeFt(enum1.Current.Y, enum2.Current.Y));
                    oldPt1 = enum1.Current;
                    endOfList1 = !(enum1.MoveNext());
                    endOfList2 = !(enum2.MoveNext());
                }
                else if (x1 < x2)
                {
                    // Fs1 point is first, we add the value (eg min or max) between the enum1 point and the degree for fs2
                    result.Add(x1, MergeFt(enum1.Current.Y, fs2.DegreeAtValue(x1)));
                    oldPt1 = enum1.Current;
                    endOfList1 = !(enum1.MoveNext());
                }
                else
                {
                    // This time, it's fs2 first
                    result.Add(x2, MergeFt(fs1.DegreeAtValue(x2), enum2.Current.Y));
                    endOfList2 = !(enum2.MoveNext());
                }
            }

            // Add end points
            if (!endOfList1)
            {
                while (!endOfList1)
                {
                    result.Add(enum1.Current.X, MergeFt(0, enum1.Current.Y));
                    endOfList1 = !enum1.MoveNext();
                }
            }
            else if (!endOfList2)
            {
                while (!endOfList2)
                {
                    result.Add(enum2.Current.X, MergeFt(0, enum2.Current.Y));
                    endOfList2 = !enum2.MoveNext();
                }
            }

            return result;
        }
    }
}