@thi.ng/fuzzy/shapes.d.ts

Fuzzy logic operators & configurable rule inferencing engine

import type { FnN2, FnU, FnU2, FnU3, FnU4 } from "@thi.ng/api";
import type { FuzzyFn } from "./api.js";
/**
 * HOF {@link FuzzyFn} always yielding given `x` (should be in `[0,1]`
 * interval).
 *
 * @param x -
 */
export declare const constant: (x: number) => FuzzyFn;
/**
 * HOF {@link FuzzyFn} which takes a value `p` and tolerance `eps`, then yields
 * a discrete window function: `|p - x| <= eps ? 1 : 0`
 *
 * @param p -
 * @param eps -
 */
export declare const point: (p: number, eps?: number) => FuzzyFn;
/**
 * HOF {@link FuzzyFn} yielding a rising ramp in `[a,b]` interval, clamped to
 *`[0,1]`outputs. Returns 0.0 for inputs <= `a` and 1.0 for inputs >= `b`.
 *
 * @param a -
 * @param b -
 */
export declare const ramp: FnU2<number, FuzzyFn>;
/**
 * HOF {@link FuzzyFn} yielding a triangle in the input range `[a..b..c]` with
 * `b` defining the position of the peak value (1.0). Returns 0.0 for inputs
 * outside the `[a,c]` interval.
 *
 * @param a -
 * @param b -
 * @param c -
 */
export declare const triangle: FnU3<number, FuzzyFn>;
/**
 * Similar to {@link triangle}, but yielding a trapezoid for the input range
 * `[a..b..c..d]` with `b` and `c` defining the peak value range (with 1.0
 * outputs). Returns 0.0 for inputs < `a` or > `d`.
 *
 * @param a -
 * @param b -
 * @param c -
 * @param d -
 */
export declare const trapezoid: FnU4<number, FuzzyFn>;
/**
 * HOF {@link FuzzyFn}, yielding sigmoid curve with configurable `steep` and
 * positioned such that `f(bias) = 0.5`.
 *
 * @param bias -
 * @param steep -
 */
export declare const sigmoid: FnU2<number, FuzzyFn>;
/**
 * HOF {@link FuzzyFn}, yielding gaussian bell curve with its peak at `bias` and
 * width defined by `sigma`.
 *
 * @param bias -
 * @param sigma -
 */
export declare const gaussian: FnU2<number, FuzzyFn>;
/**
 * Higher-order function: Takes an existing {@link FuzzyFn} `fn` and returns
 * a new one producing its negated outcome aka `1 - fn(x)`.
 *
 * @param fn -
 */
export declare const negate: FnU<FuzzyFn>;
/**
 * Inverse of {@link ramp}, i.e. a falling slope from `a` -> `b`.
 *
 * @param a -
 * @param b -
 */
export declare const invRamp: FnU2<number, FuzzyFn>;
/**
 * Inverse of {@link sigmoid}.
 *
 * @param bias -
 * @param steep -
 */
export declare const invSigmoid: FnU2<number, FuzzyFn>;
/**
 * Higher-order function: Takes an existing {@link FuzzyFn} `fn` and `weight`
 * factor. Returns new function which computes: `weight * fn(x)`.
 *
 * @param fn -
 * @param weight -
 */
export declare const weighted: (fn: FuzzyFn, weight: number) => FuzzyFn;
/**
 * Higher order function. Returns new function which selects subset of given
 * fuzzy set where `fn(x) > alpha`, or else returns 0.
 *
 * @param fn -
 * @param alpha -
 */
export declare const alphaCut: (fn: FuzzyFn, alpha?: number) => FuzzyFn;
/**
 * Higher order function. Returns new function which selects subset of given
 * fuzzy set where `fn(x) < alpha`, or else returns 0.
 *
 * @param fn -
 * @param alpha -
 */
export declare const invAlphaCut: (fn: FuzzyFn, alpha?: number) => FuzzyFn;
/**
 * Higher order function, complex shape generator. Takes a T-norm (or S-norm) as
 * reduction function `op` and any number of {@link FuzzyFn}s. Returns new
 * `FuzzyFn` which evaluates all given `fns` and combines/reduces their results
 * with `op`.
 *
 * @remarks
 * Depending on the use case and choice of `op`, the `initial` value should
 * either be set to:
 *
 * - T-norm like function: 1.0
 * - S-norm like function: 0.0
 *
 * References:
 *
 * - [Interactive graph](https://www.desmos.com/calculator/pnq6kqzfb5)
 * - https://en.wikipedia.org/wiki/T-norm
 * - https://github.com/thi-ng/umbrella/blob/develop/packages/fuzzy/src/tnorms.ts
 *
 * @example
 * ```ts
 * import { compose, tnormMin, triangle } from "@thi.ng/fuzzy";
 *
 * const f = compose(tnormMin, 1, triangle(0,2,4), triangle(1,3,5));
 * f(1); // 0
 * f(2); // 0.5
 * f(3); // 0.5
 * f(4); // 0
 * ```
 *
 * @example
 * ```ts
 * import { compose, triangle } from "@thi.ng/fuzzy";
 *
 * // M-like shape w/ peaks at 3 & 5
 * const M = compose(
 *   Math.max,
 *   0,
 *   triangle(1,3,5),
 *   triangle(3,5,7)
 * )
 *
 * M(3) // 1
 * M(4) // 0.5
 * M(5) // 1
 * ```
 *
 * @param op -
 * @param initial -
 * @param fns -
 */
export declare const compose: (op: FnN2, initial: number, ...fns: FuzzyFn[]) => FuzzyFn;
/**
 * Syntax sugar for {@link compose} with an initial value of 1.0. The `op` is
 * supposed to be a T-norm.
 *
 * @param op -
 * @param fns -
 */
export declare const intersect: (op: FnN2, ...fns: FuzzyFn[]) => import("@thi.ng/api").FnN;
/**
 * Syntax sugar for {@link compose} with an initial value of 0.0. The `op` is
 * supposed to be a S-norm.
 *
 * @param op -
 * @param fns -
 */
export declare const union: (op: FnN2, ...fns: FuzzyFn[]) => import("@thi.ng/api").FnN;
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