feat(math): add more parametric T-norms

packages/math/src/tnorms.ts

@@ -3,73 +3,115 @@ import { norm } from "./fit";
 
 // https://en.wikipedia.org/wiki/T-norm
 
-export const tnormMin: FnN2 = (a, b) => Math.min(a, b);
+export const tnormMin: FnN2 = (x, y) => Math.min(x, y);
 
-export const tnormProduct: FnN2 = (a, b) => a * b;
+export const tnormProduct: FnN2 = (x, y) => x * y;
 
-export const tnormLukasiewicz: FnN2 = (a, b) => Math.max(0, a + b - 1);
+export const tnormLukasiewicz: FnN2 = (x, y) => Math.max(0, x + y - 1);
 
-export const tnormDrastic: FnN2 = (a, b) => (a === 1 ? b : b === 1 ? a : 0);
+export const tnormDrastic: FnN2 = (x, y) => (x === 1 ? y : y === 1 ? x : 0);
 
-export const tnormNilpotent: FnN2 = (a, b) => (a + b > 1 ? Math.min(a, b) : 0);
+export const tnormNilpotent: FnN2 = (x, y) => (x + y > 1 ? Math.min(x, y) : 0);
 
 /**
  * HOF T-norm. Parametric Hamacher with `p` controlling curvature.
  *
  * @remarks
- * Interactive graph: https://www.desmos.com/calculator/rklntdutlt
+ * Interactive graph: https://www.desmos.com/calculator/4bneccqs3p
  *
- * @param p - curve param (default: 2)
+ * @param p - curve param [0..∞], default: 2
  */
-export const tnormHamacher = (p = 2): FnN2 => (a, b) =>
-    a === 0 && b === 0 ? 0 : (a * b) / (p + (1 - p) * (a + b - a * b));
+export const tnormHamacher = (p = 2): FnN2 => (x, y) =>
+    x === 0 && y === 0 ? 0 : (x * y) / (p + (1 - p) * (x + y - x * y));
 
+/**
+ * HOF T-norm. Parametric Yager with `p` controlling curvature.
+ *
+ * @remarks
+ * Interactive graph: https://www.desmos.com/calculator/4bneccqs3p
+ *
+ * @param p - curve param [0..∞], default: 2
+ */
+export const tnormYager = (p = 2): FnN2 =>
+    p === 0
+        ? () => 0
+        : (x, y) => Math.max(0, 1 - ((1 - x) ** p + (1 - y) ** p) ** (1 / p));
+
+/**
+ * HOF T-norm. Parametric Dombi with `p` controlling curvature.
+ *
+ * @remarks
+ * Interactive graph: https://www.desmos.com/calculator/4bneccqs3p
+ *
+ * @param p - curve param [0..∞], default: 2
+ */
+export const tnormDombi = (p = 2): FnN2 =>
+    p === 0
+        ? () => 0
+        : (x, y) =>
+              x === 0 || y === 0
+                  ? 0
+                  : 1 /
+                    (1 + (((1 - x) / x) ** p + ((1 - y) / y) ** p) ** (1 / p));
+
+/**
+ * HOF T-norm. Parametric Aczél–Alsina with `p` controlling curvature.
+ *
+ * @remarks
+ * Interactive graph: https://www.desmos.com/calculator/4bneccqs3p
+ *
+ * @param p - curve param [0..∞], default: 2
+ */
+export const tnormAczelAlsina = (p = 2): FnN2 => (x, y) =>
+    Math.exp(
+        -((Math.abs(Math.log(x)) ** p + Math.abs(Math.log(y)) ** p) ** (1 / p))
+    );
 /**
  * S-norm (T-conorm), dual of {@link tnormMin}.
  *
- * @param a
- * @param b
+ * @param x
+ * @param y
  */
-export const snormMax: FnN2 = (a, b) => Math.max(a, b);
+export const snormMax: FnN2 = (x, y) => Math.max(x, y);
 
 /**
  * S-norm (T-conorm), dual of {@link tnormProduct}, probabilistic sum:
  * `a + b - a * b`
  *
- * @param a
- * @param b
+ * @param x
+ * @param y
  */
-export const snormProbabilistic: FnN2 = (a, b) => a + b - a * b;
+export const snormProbabilistic: FnN2 = (x, y) => x + y - x * y;
 
 /**
  * S-norm (T-conorm), dual of {@link tnormLukasiewicz}.
  *
- * @param a
- * @param b
+ * @param x
+ * @param y
  */
-export const snormBoundedSum: FnN2 = (a, b) => Math.min(a + b, 1);
+export const snormBoundedSum: FnN2 = (x, y) => Math.min(x + y, 1);
 
 /**
  * S-norm (T-conorm), dual of {@link tnormDrastic}.
  */
-export const snormDrastic: FnN2 = (a, b) => (a === 0 ? b : b === 0 ? a : 1);
+export const snormDrastic: FnN2 = (x, y) => (x === 0 ? y : y === 0 ? x : 1);
 
 /**
  * S-norm (T-conorm), dual of {@link tnormNilpotent}.
  *
- * @param a
- * @param b
+ * @param x
+ * @param y
  */
-export const snormNilpotent: FnN2 = (a, b) => (a + b < 1 ? Math.max(a, b) : 1);
+export const snormNilpotent: FnN2 = (x, y) => (x + y < 1 ? Math.max(x, y) : 1);
 
 /**
  * S-norm (T-conorm), dual of {@link tnormHamacher}, iff that T-norm's curve
  * param is `p=2`.
  *
- * @param a
- * @param b
+ * @param x
+ * @param y
  */
-export const snormEinstein: FnN2 = (a, b) => (a + b) / (1 + a * b);
+export const snormEinstein: FnN2 = (x, y) => (x + y) / (1 + x * y);
 
 /**
  * HOF t-norm. Constructs a new t-norm based on given t-norms for disjoint