# @thi.ng/fuzzy > Fuzzy logic operators & configurable rule inferencing engine Latest version **2.1.144** (published 2026-08-25) · Apache-2.0 license · 0 weekly downloads ## Install ```sh npm install @thi.ng/fuzzy pnpm add @thi.ng/fuzzy yarn add @thi.ng/fuzzy bun add @thi.ng/fuzzy ``` ## Health **Score 70/100 (B)** — status: active. Positive: has types; esm support; no vulnerabilities; recently updated; high maintenance score; high quality score. Warnings: low downloads. ## Facts | | | |---|---| | Version | 2.1.144 | | Published | 2026-08-25 | | First published | 2020-12-22 | | Weekly downloads | 0 | | License | Apache-2.0 | | TypeScript types | bundled | | Module format | ESM | | Node | >=18 | | Dependencies | 2 | | Unpacked size | 60.7 KB | | Known vulnerabilities | 0 | | Install scripts | no | | Author | Karsten Schmidt | | Maintainers | thi.ng | | Keywords | agent, functional, fuzzy, inference, logic, math, rule, t-norm, typescript | ## Links - npm: https://www.npmjs.com/package/@thi.ng/fuzzy - Repository: https://codeberg.org/thi.ng/umbrella - Homepage: https://thi.ng/fuzzy - Funding: https://github.com/sponsors/postspectacular - npm.io page: https://npm.io/package/@thi.ng/fuzzy ## Dependencies (2) - [@thi.ng/api](https://npm.io/package/@thi.ng/api.md) ^8.12.28 - [@thi.ng/math](https://npm.io/package/@thi.ng/math.md) ^5.15.17 ## Alternatives - [@openai/codex-sdk](https://npm.io/package/@openai/codex-sdk.md) — 731.4K weekly downloads - [babel-plugin-transform-react-jsx](https://npm.io/package/babel-plugin-transform-react-jsx.md) — 565.0K weekly downloads - [babel-helper-remove-or-void](https://npm.io/package/babel-helper-remove-or-void.md) — 508.5K weekly downloads - [@pnpm/store-controller-types](https://npm.io/package/@pnpm/store-controller-types.md) — 186.9K weekly downloads - [react-native-signature-canvas](https://npm.io/package/react-native-signature-canvas.md) — 155.6K weekly downloads ## Recent versions - 2.1.144 (latest) — 2026-08-25 - 2.1.143 — 2026-07-02 - 2.1.142 — 2026-06-05 - 2.1.141 — 2026-05-23 - 2.1.140 — 2026-05-20 - 2.1.138 — 2026-05-11 - 2.1.137 — 2026-05-08 - 2.1.136 — 2026-04-26 - 2.1.135 — 2026-04-18 - 2.1.134 — 2026-04-02 - 2.1.133 — 2026-03-19 - 2.1.132 — 2026-03-07 - 2.1.131 — 2026-03-07 - 2.1.130 — 2026-02-07 - 2.1.129 — 2026-01-23 - … 148 more at https://npm.io/package/@thi.ng/fuzzy/versions ## README # ![@thi.ng/fuzzy](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/banners/thing-fuzzy.svg?1e243dac) [![npm version](https://img.shields.io/npm/v/@thi.ng/fuzzy.svg)](https://www.npmjs.com/package/@thi.ng/fuzzy) ![npm downloads](https://img.shields.io/npm/dm/@thi.ng/fuzzy.svg) [![Mastodon Follow](https://img.shields.io/mastodon/follow/109331703950160316?domain=https%3A%2F%2Fmastodon.thi.ng&style=social)](https://mastodon.thi.ng/@toxi) > [!NOTE] > This is one of 217 standalone projects. LLM-free, human-made and > cared for software, maintained as part of the > [@thi.ng/umbrella](https://codeberg.org/thi.ng/umbrella/) ecosystem and > anti-framework. > > 🚀 Please help me to work full-time on these projects by [sponsoring > me](https://codeberg.org/thi.ng/umbrella/src/branch/develop/CONTRIBUTING.md#donations). > Thank you! ❤️ - [About](#about) - [Features](#features) - [References / Further reading](#references--further-reading) - [Status](#status) - [Support packages](#support-packages) - [Installation](#installation) - [Dependencies](#dependencies) - [API](#api) - [Fuzzy set generators & combinators](#fuzzy-set-generators--combinators) - [Linguistic variables](#linguistic-variables) - [Rule creation & inferencing](#rule-creation--inferencing) - [Authors](#authors) - [License](#license) ## About Fuzzy logic operators & configurable rule inferencing engine. ### Features - Entirely declarative & functional approach - Fully type checked - Fuzzy set domain shaping & composition functions (incl. negated / inverse) - Various [T-norms & S-norms](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy/src/tnorms.ts), incl. parametric versions - Rules with multiple inputs/outputs and arbitrary term combinators (i.e. T-norms). Syntax sugar for common `and`/`or` rules. - Defuzzification via customizable strategies and options to balance precision vs. performance - Maxima: First, Last, Mean - Center-of-Gravity (COG) - Linguistic variable creation and term/set classification for given domain values - Fuzzy set visualization (via [@thi.ng/fuzzy-viz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy-viz)) ### References / Further reading - [Fuzzy Logic (Wikipedia)](https://en.wikipedia.org/wiki/Fuzzy_logic) - [T-norm (Wikipedia)](https://en.wikipedia.org/wiki/T-Norm) - [Fuzzy Logic - University of Western Australia](https://teaching.csse.uwa.edu.au/units/CITS7212/Lectures/Students/Fuzzy.pdf) - [Introduction to Fuzzy Logic](https://www.researchgate.net/publication/267041266_Introduction_to_fuzzy_logic) - [Defuzzification (Wikipedia)](https://en.wikipedia.org/wiki/Defuzzification) - [Defuzzification methods](https://cse.iitkgp.ac.in/~dsamanta/courses/archive/sca/Archives/Chapter%205%20Defuzzification%20Methods.pdf) - [Comparison of the COG Defuzzification Technique](https://arxiv.org/pdf/1612.00742.pdf) ## Status **STABLE** - used in production [Search or submit any issues for this package](https://codeberg.org/thi.ng/umbrella/issues?q=%5Bfuzzy%5D) ## Support packages - [@thi.ng/fuzzy-viz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy-viz) - Visualization, instrumentation & introspection utils for [@thi.ng/fuzzy](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy) ## Installation ```bash yarn add @thi.ng/fuzzy ``` ESM import: ```ts import * as fuzzy from "@thi.ng/fuzzy"; ``` Browser ESM import: ```html ``` [JSDelivr documentation](https://www.jsdelivr.com/) For Node.js REPL: ```js const fuzzy = await import("@thi.ng/fuzzy"); ``` Package sizes (brotli'd, pre-treeshake): ESM: 1.62 KB ## Dependencies - [@thi.ng/api](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/api) - [@thi.ng/math](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/math) Note: @thi.ng/api is in _most_ cases a type-only import (not used at runtime) ## API [Generated API docs](https://docs.thi.ng/umbrella/fuzzy/) (See [tests](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy/test) for more usage examples). ### Fuzzy set generators & combinators Generators: - `constant()` - `point()` - `ramp()` / `invRamp()` - `triangle()` - `trapezoid()` - `sigmoid()` / `invSigmoid()` - `gaussian()` Combinators: - `negate()` - `weighted()` - `alphaCut()` / `invAlphaCut()` - `compose()` / `intersect()` / `union()` ### Linguistic variables Linguistic variables (short: **L-var**s) are groupings of named (and possibly overlapping) fuzzy sets within a given value domain. The can be used standalone or as inputs/outputs in rules (further below). The [@thi.ng/fuzzy-viz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy-viz) package provides utilities to visualize the fuzzy sets of an L-var. ![fuzzy set visualization of the example l-var](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/fuzzy/temperature-lvar-2.svg) ```ts import { variable, invSigmoid, sigmoid, trapezoid, evaluate, classify } from "@thi.ng/fuzzy"; // temperature sets (in celsius) const temp = variable( // value domain [-20, 40], { freezing: invSigmoid(0, 2), cold: trapezoid(-1, 2, 16, 20), warm: trapezoid(15, 20, 30, 34), hot: sigmoid(32, 2) } ); // evaluate all fuzzy sets for given domain value evaluate(temp, 18) // { // freezing: 2.220446049250313e-16, // cold: 0.5, // warm: 0.6, // hot: 6.914400106935423e-13 // } evaluate(temp, 28) // { // freezing: 0, // cold: 0, // warm: 1, // hot: 0.0003353501304664781 // } // classify temperature (min confidence 33%, default: 50%) classify(temp, 28, 0.33) // "warm" ``` ### Rule creation & inferencing Example taken from Franck Dernoncourt's [Introduction to Fuzzy Logic](https://www.researchgate.net/publication/267041266_Introduction_to_fuzzy_logic): ![fuzzy set illustration from F.Dernoncourt's tutorial](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/fuzzy/fuzzy-matrix-dernoncourt.png) ```ts import { variable, ramp, invRamp, gaussian, triangle, or, defuzz, meanOfMaximaStrategy } from "@thi.ng/fuzzy"; // define fuzzy input variables const inputs = { food: variable([0, 10], { awful: invRamp(1, 3), delicious: ramp(7, 9), }), service: variable([0, 10], { poor: gaussian(0, 1.5), good: gaussian(5, 1.5), excellent: gaussian(10, 1.5), }), }; const outputs = { tip: variable([0, 30], { low: triangle(0, 5, 10), medium: triangle(10, 15, 20), high: triangle(20, 25, 30), }), }; // l-vars, rules and defuzzification are using generics for type safety // we define these 2 type aliases for brevity type I = typeof inputs; type O = typeof outputs; // rule definitions: // if service is poor OR food is awful -> tip is low // if service is normal -> tip is medium // if service is excellent OR food is delicious -> tip is high const rules = [ or({ food: "awful", service: "poor" }, { tip: "low" }), or({ service: "good" }, { tip: "medium" }), or({ food: "delicious", service: "excellent" }, { tip: "high" }), ]; // defuzzification using default center-of-gravity strategy defuzz( inputs, outputs, rules, // input values { food: 7.32, service: 7.83 }, ); // { tip: 22.650000000000034 } // defuzz with custom strategy (note: each has further config options) defuzz( inputs, outputs, rules, // input values { food: 7.32, service: 7.83 }, // custom defuzz strategy meanOfMaximaStrategy() ); // { tip: 25.050000000000043 } ``` Note: The results are slightly different than those in the textbook example, due to different `gaussian` fuzzy sets used for the `service` L-var. Using `instrumentStrategy()` from the upcoming [@thi.ng/fuzzy-viz](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/fuzzy-viz) package, we can also visualize the final, transformed fuzzy sets used to compute crisp results and highlight the position of the crisp result value. Here is the ASCII art output for the [`centroidStrategy`](https://docs.thi.ng/umbrella/fuzzy/functions/centroidStrategy.html) and using `tnormMin` (the default) to transform each rule's output set(s): ```ts import { defuzz, centroidStrategy } from "@thi.ng/fuzzy"; import { instrumentStrategy, fuzzySetToAscii } from "@thi.ng/fuzzy-viz"; // wrap existing strategy const strat = instrumentStrategy(centroidStrategy(), fuzzySetToAscii()); // call defuzz as normal defuzz(inputs, outputs, rules, strat); // obtain secondary results via deref() console.log(strat.deref()[0]); ``` ```text ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅..... .......................................................................▁|██████████████████████▇.... ......................................................................▁█|███████████████████████▇... ....................................▅▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▅....▂██|████████████████████████▇.. ...................................▅█████████████████████████████▅..▂███|██████████████████████████. ..................................▅███████████████████████████████▅▂████|███████████████████████████ ^ 21.52 ``` Different results can be obtained by adjusting the [T-norm](https://en.wikipedia.org/wiki/T-Norm) used to transform each rule's output sets, here using `tnormHamacher(2)`. ```text .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.......................... .........................................................................|.........▃▂............... .........................................................................|.......▃███▆▂............. .........................................................................|....▁▅███████▇▃........... ................................................▁▃▆▃▁....................|.▁▄▇████████████▆▃........ ...........................................▁▂▄▆███████▆▄▂▁..............▂|▇██████████████████▆▃▁.... ...................................▁▂▃▄▅▆▇█████████████████▇▆▅▄▃▂▁..▂▄▆██|███████████████████████▅▃▁ ^ 21.84 ``` ...or using `tnormAczelAlsina(2)` (there're many more available): ```text ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|........................... ........................................................................|.....▂▃▄▅▅▅▅▅▄▄▃▁.......... ........................................................................|.▂▅▇██████████████▆▄....... ........................................................................|▇████████████████████▆▂.... ........................................▁▂▃▄▄▅▅▆▆▆▆▆▆▆▅▅▄▄▃▂▁.........▃█|███████████████████████▆▁.. ....................................▂▄▇███████████████████████▇▄▂....▆██|█████████████████████████▄. ..................................▃▇█████████████████████████████▇▃▂████|██████████████████████████▇ ^ 21.58 ``` Just for illustration purposes (and using a different example), SVG output can be obtained by merely switching to another instrumentation function (here `fuzzySetToSvg()`): ![fuzzySetToSvg() visualization example](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/fuzzy/strategy-viz.svg) ## Authors - [Karsten Schmidt](https://thi.ng) If this project contributes to an academic publication, please cite it as: ```bibtex @misc{thing-fuzzy, title = "@thi.ng/fuzzy", author = "Karsten Schmidt", note = "https://thi.ng/fuzzy", year = 2020 } ``` ## License © 2020 - 2026 Karsten Schmidt // Apache License 2.0 --- _Source: https://npm.io/package/@thi.ng/fuzzy · Machine-readable twin of the npm.io package page. Health data is recomputed on every publish._