feat(math): add various T-norm functions

thi-ng · Dec 10, 2020 · ab4a810 · ab4a810
1 parent 04f3290
commit ab4a810
Show file tree

Hide file tree

Showing 3 changed files with 92 additions and 0 deletions.
diff --git a/packages/math/package.json b/packages/math/package.json
@@ -67,6 +67,7 @@
         "quadratic",
         "smooth",
         "solver",
+        "t-norm",
         "trigonometry",
         "typescript"
     ],

diff --git a/packages/math/src/index.ts b/packages/math/src/index.ts
@@ -14,3 +14,4 @@ export * from "./ratio";
 export * from "./safe-div";
 export * from "./solve";
 export * from "./step";
+export * from "./tnorms";
diff --git a/packages/math/src/tnorms.ts b/packages/math/src/tnorms.ts
@@ -0,0 +1,90 @@
+import type { FnN2 } from "@thi.ng/api";
+import { norm } from "./fit";
+
+// https://en.wikipedia.org/wiki/T-norm
+
+export const tnormMin: FnN2 = (a, b) => Math.min(a, b);
+
+export const tnormProduct: FnN2 = (a, b) => a * b;
+
+export const tnormLukasiewicz: FnN2 = (a, b) => Math.max(0, a + b - 1);
+
+export const tnormDrastic: FnN2 = (a, b) => (a === 1 ? b : b === 1 ? a : 0);
+
+export const tnormNilpotent: FnN2 = (a, b) => (a + b > 1 ? Math.min(a, b) : 0);
+
+/**
+ * HOF T-norm. Parametric Hamacher with `p` controlling curvature.
+ *
+ * @param p - curve param (default: 2)
+ */
+export const tnormHamacher = (p = 2): FnN2 => (a, b) =>
+    a === 0 && b === 0 ? 0 : (a * b) / (p + (1 - p) * (a + b - a * b));
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormMin}.
+ *
+ * @param a
+ * @param b
+ */
+export const snormMax: FnN2 = (a, b) => Math.max(a, b);
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormProduct}, probabilistic sum:
+ * `a + b - a * b`
+ *
+ * @param a
+ * @param b
+ */
+export const snormProbabilistic: FnN2 = (a, b) => a + b - a * b;
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormLukasiewicz}.
+ *
+ * @param a
+ * @param b
+ */
+export const snormBoundedSum: FnN2 = (a, b) => Math.min(a + b, 1);
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormDrastic}.
+ */
+export const snormDrastic: FnN2 = (a, b) => (a === 0 ? b : b === 0 ? a : 1);
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormNilpotent}.
+ *
+ * @param a
+ * @param b
+ */
+export const snormNilpotent: FnN2 = (a, b) => (a + b < 1 ? Math.max(a, b) : 1);
+
+/**
+ * S-norm (T-conorm), dual of {@link tnormHamacher}, iff that T-norm's curve
+ * param is `p=2`.
+ *
+ * @param a
+ * @param b
+ */
+export const snormEinstein: FnN2 = (a, b) => (a + b) / (1 + a * b);
+
+/**
+ * HOF t-norm. Constructs a new t-norm based on given t-norms for disjoint
+ * subintervals, completing remaining regions via {@link min}.
+ *
+ * @remarks
+ * Reference: https://en.wikipedia.org/wiki/Construction_of_t-norms#Ordinal_sums
+ *
+ * @param specs
+ */
+export const ordinalSum = (
+    specs: { domain: [number, number]; tnorm: FnN2 }[]
+): FnN2 => (x, y) => {
+    for (let s of specs) {
+        const [a, b] = s.domain;
+        if (x >= a && x <= b && y >= a && y <= b) {
+            return a + (b - a) * s.tnorm(norm(x, a, b), norm(y, a, b));
+        }
+    }
+    return Math.min(x, y);
+};