Rules
Rules are defined by operators, like AND, OR, EQUALS, etc. While it is easy to understand what these operators do in Boolean Logic, with Fuzzy Logic there are several ways of defining and implementing them, as the result of IF the temperature IS hot AND the temperature IS comfortable is neither true or false, but a veracity in the range [0, 1].
Wikipedia has a nice List of operators with representations of them to easily compare the algorithms.
Implementation
With the veracity x, y and the weight w in the range [0,1] for fuzzy logic, and x,y,w = 0 or 1 for boolean logic.
| Name | JavaScript, C… Boolean | Python Boolean | Fuzzy: Zadeh (linear) | Fuzzy: Hyperbolic Parabloid | Fuzzy: Yager-2 |
|---|---|---|---|---|---|
| NOT(x) | !x |
not x |
1-x |
1-x |
1-x |
| AND(x,y) | x && y |
x and y |
min(x,y) |
xy |
1- min( 1, sqrt( (1-x)² + (1-y)² ) ) |
| OR(x,y) | x || y |
x or y |
max(x,y) |
x+y - xy |
min( 1, (x² + y²)² ) |
| XOR(x,y) | x != y |
x is not y |
x + y - 2min(x,y) |
x+y - 2xy |
|
| NXR(x,y) | x == y |
x is y |
1-x-y + 2*min(x,y) |
1-x-y + (2xy) |
|
| IMPLIES(x,y) | !(x && !y) |
not (x and not y) |
1 - min(x, 1-y) |
1 - x + xy |
|
| DOES_NOT_IMPLY(x,y) | x && !y |
x and not y |
min(x,1-y) |
x*(1-y) |
|
| NAND(x,y) | !(x && y) |
not (x and y) |
1-min(x,y) |
1 - xy |
|
| NOR(x,y) | !(x || y) |
not (x or y) |
1 - max(x,y) |
1-x-y + xy |
|
| WEIGHTED(x,y,w | wx + (1-w)y |
wx + (1-w)y |
wx + (1-w)y |