From 08045c62a42bdba5ed7548b778360d8340c74b03 Mon Sep 17 00:00:00 2001
From: Daniel Knittl-Frank <knittl89+git@googlemail.com>
Date: Sun, 26 Jun 2011 11:25:49 +0200
Subject: [PATCH] initial commit of fuzzy functions in javascript

---
 linguistics.js | 12 ++++++++++++
 membership.js  | 37 +++++++++++++++++++++++++++++++++++++
 modifiers.js   | 15 +++++++++++++++
 operators.js   | 37 +++++++++++++++++++++++++++++++++++++
 4 files changed, 101 insertions(+)
 create mode 100644 linguistics.js
 create mode 100644 membership.js
 create mode 100644 modifiers.js
 create mode 100644 operators.js

diff --git a/linguistics.js b/linguistics.js
new file mode 100644
index 0000000..1b7db6f
--- /dev/null
+++ b/linguistics.js
@@ -0,0 +1,12 @@
+/* simple linguistic terms to modify fuzzy sets */
+
+function very(a) { return Con(a); }
+function more_or_less(a) { return Dil(a); }
+function plus(a) { return PoweredHedge(a, 1.25); }
+function slightly(a) { return Int(and(plus(a), not(very(a)))); }
+function sort_of(a) {
+	return and(Int(more_or_less(a)), Int(more_or_less(not(a))));
+}
+function pretty(a) { return and(Int(a), not(Int(very(a)))); }
+function rather(a) { return Int(very(a)); }
+function minus(a) { return PoweredHedge(a, 0.75); }
diff --git a/membership.js b/membership.js
new file mode 100644
index 0000000..d413bb6
--- /dev/null
+++ b/membership.js
@@ -0,0 +1,37 @@
+/* membership functions for fuzzy sets */
+
+// Γ function
+function T(x, a, b) {
+	if(x < a) return 0;
+	if(x > b) return 1;
+	return (x-a)/(b-a);
+}
+
+// S function
+function S(x, a, b, g) {
+	if(x < a) return 0;
+	if(x > g) return 1;
+	if(x <= b) return _S(x-a, a, g);
+	else return 1-_S(x-g, a, g);
+}
+function _S(q, a, g) {
+	return 2*Math.pow(q/(g-a),2);
+}
+
+// L function
+function L(x, a, b) {
+	return 1-T(x, a, b);
+}
+
+// Δ function
+function D(x, a, b, g) {
+	if(x < a || x > g) return 0;
+	if(x <= b) return (x-a)/(b-a);
+	return (b-x)/(g-b);
+}
+
+// Π function
+function P(x, a, g) {
+	if(x <= g) return S(x, g-a, g-a/2, g);
+	return 1-S(x, g, g+a/2, g+a);
+}
diff --git a/modifiers.js b/modifiers.js
new file mode 100644
index 0000000..1b211d0
--- /dev/null
+++ b/modifiers.js
@@ -0,0 +1,15 @@
+/* modifier functions for fuzzy sets */
+
+function Dilation(mu) { return PoweredHedge(mu, 0.5); }
+var Dil = Dilation;
+
+function Concentration(mu) { return PoweredHedge(mu, 2); }
+var Con = Concentration;
+
+function PoweredHedge(mu, exponent){ return Math.pow(mu, exponent); }
+
+function ContrastIntensification(mu){
+	if(mu < 0.5) return 2*Math.pow(mu, 2);
+	return 1-2*Math.pow((1-mu), 2);
+}
+var Int = ContrastIntensification;
diff --git a/operators.js b/operators.js
new file mode 100644
index 0000000..9cfbe19
--- /dev/null
+++ b/operators.js
@@ -0,0 +1,37 @@
+/* simple operators for fuzzy sets:
+ * complement (not), intersection (and) and union (and) 
+ */
+
+function not_zadeh(x) { return 1-x; }
+function not_sugeno(x, l) { return (1-x)/(1+l*x); }
+function not_yager(x, l) { return Math.pow(1-Math.pow(x, l), 1/l); }
+
+function not(x) {
+	return not_zadeh(x);
+	//return not_sugeno(x, -0.5);
+	//return not_yager(x, 2);
+}
+
+function and_zadeh(a, b) { return Math.min(a, b); }
+function and_zadeh2(a, b) { return a*b; }
+function and_tnorm(a, b, l) {
+	return 1 - Math.min(1, Math.pow(Math.pow(1-a, l) + Math.pow(1-b, l), 1/l));
+}
+
+function and(a, b) {
+	return and_zadeh(a, b);
+	//return and_zadeh2(a, b);
+	//return and_tnorm(a, b, 2);
+}
+
+function or_zadeh(a, b) { return Math.max(a, b); }
+function or_zadeh2(a, b) { return a+b - a*b; }
+function or_snorm(a, b, l) {
+	return Math.min(1, Math.pow(Math.pow(a, l) + Math.pow(b, l), 1/l));
+}
+
+function or(a, b) {
+	return or_zadeh(a, b);
+	//return or_zadeh(a, b);
+	//return or_snorm(a, b, 2);
+}
-- 
2.11.4.GIT