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https://github.com/valiot/flex
FLex: Fuzzy Logic for Elixir
https://github.com/valiot/flex
elixir fuzzy-logic
Last synced: about 2 months ago
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FLex: Fuzzy Logic for Elixir
- Host: GitHub
- URL: https://github.com/valiot/flex
- Owner: valiot
- License: mit
- Created: 2019-05-03T05:23:10.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2023-09-02T20:05:34.000Z (over 1 year ago)
- Last Synced: 2024-09-14T12:22:05.567Z (4 months ago)
- Topics: elixir, fuzzy-logic
- Language: Elixir
- Homepage:
- Size: 214 KB
- Stars: 18
- Watchers: 7
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
***
# FLex
A toolkit for fuzzy logic, this library includes functions to make fuzzy sets, variables and rules for creating a Fuzzy Logic System (FLS).
The goal of FLex is to easily design and efficiently operate fuzzy logic controllers without relying on external libraries.
## Index
* [Features](#features)
* [Installation](#installation)
* [Usage](#usage)
* [Sets](#sets)
* [Variables](#variables)
* [Rules](#rules)
* [System](#system)
* [ANFIS](#anfis)
* [Documentation](#documentation)
* [Contributing](#contributing)
* [License](#License)
* [TODO](#todo)
## Features
The following list is the current supported backend for each component of the FLS:
- Linguistic Rules:
- Lambda function syntax
- Tuple syntax
- Membership functions:
- Triangular
- Trapezoidal
- Saturation
- Shoulder
- Gauss
- Generalized Bell
- Sigmoid
- Z-shaped
- S-shaped
- Pi-shaped
- Linear Combination (Takagi-Sugeno, ANFIS only)
- Fuzzy Inference Systems:
- Mamdani:
- Inference:
- Min
- Output Combination:
- Root-sum-square
- Defuzzification:
- Centroid
- Takagi-Sugeno:
- Inference:
- Max
- Product
- Defuzzification:
- Weighted average
- ANFIS:
- Inference:
- Max
- Product
- Defuzzification:
- Weighted average
- Optimization Method:
- Backpropagation.
- Hybrid (Backpropagation, LSE).
**NOTE:** All systems are single output.
## Installation
The package can be installed by adding `flex` to your list of dependencies in `mix.exs`:
```elixir
def deps do
[
{:flex, "~> 0.1.0"}
]
end
```
## Usage
***
### Sets
**Step 1:** Define all fuzzy sets with `Flex.Set.new/1`, the following options are require:
- `mf_type` - (string) Defines which type of membership function uses the set (e.g., "triangle").
- `tag` - (string) defines the linguistic name of the fuzzy set (e.g., "too hot"),
- `mf_params` - The parameters of the membership function, see Membership functions.
```elixir
t_h = Flex.Set.new(tag: "too hot", mf_type: "saturation", mf_params: [-2, 0, -4])
j_r = Flex.Set.new(tag: "just right", mf_type: "triangle", mf_params: [-2, 0, 2])
t_c = Flex.Set.new(tag: "too cold", mf_type: "shoulder", mf_params: [0, 2, 4])
g_h = Flex.Set.new(tag: "getting hotter", mf_type: "saturation", mf_params: [-5, 0, -10])
n_c = Flex.Set.new(tag: "no change", mf_type: "triangle", mf_params: [-5, 0, 5])
g_c = Flex.Set.new(tag: "getting colder", mf_type: "shoulder", mf_params: [0, 5, 10])
co = Flex.Set.new(tag: "cool", mf_type: "saturation", mf_params: [-50, 0, -100])
d_n = Flex.Set.new(tag: "do nothing", mf_type: "triangle", mf_params: [-50, 0, 50])
he = Flex.Set.new(tag: "heat", mf_type: "shoulder", mf_params: [0, 50, 100])
```
### Variables
**Step 2:** Define all fuzzy variables with `Flex.Variable.new/1`, the following options are required:
* `:tag` - (string) Defines the linguistic name of the fuzzy variable (e.g., "error"),
* `:fuzzy_sets` - (list) Defines which type of membership function use the set (e.g., "triangle").
* `:type` - (atom) Defines the type of variable (e.g., :antecedent or :consequent),
* `:range` - (range) The range in which the variable exists.
```elixir
fuzzy_sets = [t_h, j_r, t_c]
error = Flex.Variable.new(tag: "error", fuzzy_sets: fuzzy_sets, type: :antecedent, range: -4..4)
fuzzy_sets = [g_h, n_c, g_c]
dt_error = Flex.Variable.new(tag: "dt_error", fuzzy_sets: fuzzy_sets, type: :antecedent, range: -10..10)
fuzzy_sets = [co, d_n, he]
output = Flex.Variable.new(tag: "output", fuzzy_sets: fuzzy_sets, type: :consequent, range: -100..100)
```
### Rules
Currently there are two types of syntax for defining the rules `statement`:
* Anonymous function syntax:
```elixir
r1 = fn [at1, at2, con] ->
(at1 ~> "too hot" &&& at2 ~> "getting colder") >>> con ~> "cool"
end
```
* Tuple syntax:
```elixir
r1 = {{{{"error", "too hot", "~>"}, {"dt_error", "getting colder", "~>"}, "&&&"}, "output",
">>>"}, "cool", "~>"}
```
**Step 3:** Define all Linguistic rules with `Flex.Rule.new/1`, the following options are required:
- `:statement` - Defines the rule behavior.
- `:antecedent` - (list) Defines the input variables.
- `:consequent` - Defines the output variable.
```elixir
import Flex.Rule
r1 =
{{{{"error", "too hot", "~>"}, {"dt_error", "getting colder", "~>"}, "&&&"}, "output",
">>>"}, "cool", "~>"}
r2 =
{{{{"error", "just right", "~>"}, {"dt_error", "getting colder", "~>"}, "&&&"}, "output",
">>>"}, "heat", "~>"}
r3 =
{{{{"error", "too cold", "~>"}, {"dt_error", "getting colder", "~>"}, "&&&"}, "output",
">>>"}, "heat", "~>"}
r4 =
{{{{"error", "too hot", "~>"}, {"dt_error", "no change", "~>"}, "&&&"}, "output", ">>>"},
"cool", "~>"}
r5 =
{{{{"error", "just right", "~>"}, {"dt_error", "no change", "~>"}, "&&&"}, "output", ">>>"},
"do nothing", "~>"}
r6 =
{{{{"error", "too cold", "~>"}, {"dt_error", "no change", "~>"}, "&&&"}, "output", ">>>"},
"heat", "~>"}
r7 =
{{{{"error", "too hot", "~>"}, {"dt_error", "getting hotter", "~>"}, "&&&"}, "output",
">>>"}, "cool", "~>"}
r8 =
{{{{"error", "just right", "~>"}, {"dt_error", "getting hotter", "~>"}, "&&&"}, "output",
">>>"}, "cool", "~>"}
r9 =
{{{{"error", "too cold", "~>"}, {"dt_error", "getting hotter", "~>"}, "&&&"}, "output",
">>>"}, "cool", "~>"}
rule1 = Flex.Rule.new(statement: r1, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule2 = Flex.Rule.new(statement: r2, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule3 = Flex.Rule.new(statement: r3, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule4 = Flex.Rule.new(statement: r4, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule5 = Flex.Rule.new(statement: r5, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule6 = Flex.Rule.new(statement: r6, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule7 = Flex.Rule.new(statement: r7, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule8 = Flex.Rule.new(statement: r8, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rule9 = Flex.Rule.new(statement: r9, consequent: output.tag, antecedent: [error.tag, dt_error.tag])
rules = [rule1, rule2, rule3, rule4, rule5, rule6, rule7, rule8, rule9]
```
**Note**: You need to `import Flex.Rule` module.
### System
**Step 4:** Define FLS with `Flex.System.start_link/1` or `Flex.System.start_link/2` if you want to overwrite the GenServer options; the following options are require:
- `:rules` - Defines the behavior of the system based on a list of rules.
- `:antecedent` - (list) Defines the input variables.
- `:consequent` - Defines the output variable.
- `:engine_type` - Defines the inference engine behavior (default: Mamdini).
```elixir
{:ok, s_pid} = Flex.System.start_link(antecedent: [error, dt_error], consequent: output, rules: rules)
```
**Step 5:** Fit the FLS with a input vector using `Flex.System.compute/2`.
```elixir
result = Flex.System.compute(s_pid, [-1, -2.5])
#result ~= -63.4 aprox
```
In `test/system_test.exs` there is an example of use, that is based on this [example](http://robotics.ee.uwa.edu.au/courses/faulttolerant/notes/FT5.pdf).
### ANFIS
An adaptive network-based fuzzy inference system (ANFIS) is a kind of artificial neural network that is based on Takagi–Sugeno fuzzy inference system, this implementation use backpropagation, only Gaussian & Generalized Bell Membership functions are allowed. In `examples/anfis_demo1.exs` there is an example of use.
## Documentation
The docs can be found at [https://hexdocs.pm/flex](https://hexdocs.pm/flex).
## Contributing
* Fork our repository on github.
* Fix or add what is needed.
* Commit to your repository.
* Issue a github pull request (fill the PR template).
## License
See [LICENSE](https://github.com/valiot/flex/blob/master/LICENSE).
## TODO
* Add more membership functions.
* Add more inference methods.
* Add more defuzzification methods.
* Add helper functions.
* Add metaprogramming for linguistic rules.