Wikimore

This article is definitively not a tutorial on fuzzy logic. It's simply refers a category of usefull images to help writing wiki articles on fuzzy logic operators. Only, very short comments are thus provided here.

Fuzzyfication

linear

one segment
two segments

non linear

one segment
5,15,45... 3645
$two segments 10 − 5 {\displaystyle 10^{-5}} to 10 3 {\displaystyle 10^{3}}$
two segments
$10^{-5}$ to $10^{3}$
$two segments − 10 3 {\displaystyle -10^{3}} to 10 7 {\displaystyle 10^{7}}$
two segments
$-10^{3}$ to $10^{7}$

Monadic Operators

NOP, NOT

NOP
(2D view)
NOP
(3D view)
NOT
(2D view)
NOT
(3D view)

CONCENTRATE, DILATE

CONCENTRATE
(2D view)
CONCENTRATE
(3D view)
DILATE
(2D view)
DILATE
(3D view)

Something AND its Contrary

A AND (NOT A)
(2D view)
A AND (NOT A)
(3D view)

Zadeh Dyadic Operators

The standard fuzzy operators are given the name of Prof. Dr. Lofti A. Zadeh archive copy at the Wayback Machine

These operators use very few resources and are thus suitable a.o. for embedded intelligent systems.

Zadeh AND
Zadeh OR
Zadeh XOR
(exclusive OR)
Zadeh IMPLIES

Zadeh NAND
(NOT AND)
Zadeh NOR
(NOT OR)
Zadeh NXR
(NOT XOR)
Zadeh NOT IMPLIES

Dyadic Operators based on a Hyperbolic Paraboloid

HyperbolicParaboloid
(by Mathematica)
fuzzy NXR
(NOT XOR)

With the increasing power of computers, these operators become usable.

AND
(Hyperbolic Paraboloid)
OR
(Hyperbolic Paraboloid)
XOR
(Hyperbolic Paraboloid)
IMPLIES
(Hyperbolic Paraboloid)

NAND
(Hyperbolic Paraboloid)
NOR
(Hyperbolic Paraboloid)
NXR
(Hyperbolic Paraboloid)
NOT IMPLIES
(Hyperbolic Paraboloid)

Yager Dyadic Operators

The images are related to the Yager-2 operators (with exponent = 2).

The operators are given the name of Prof. Dr. Ronald R. Yager

Yager-2 AND
(with exponent=2)
Yager-2 OR
(with exponent=2)

Ternary Operators

Some applications of these operators may need important computer power.

Ternary Operator applied to fuzzy values

MEAN
50%, 50%
WEIGHTED
75%, 25%
WEIGHTED
(french: pondération)

Ternary Operator applied to fuzzy operations

These operators and similar surfaces are developed by Prof. Marc W.F. Meurrens (User:Marc.M)

AND-OR
75%, 25%

Search Oriented

Such fuzzy operators may be usefull a.o. for fuzzy searches. Mind that such operators may be time comsuming.

MEAN-AND-OR
MEAN-OR-AND
WEIGHTED-AND-OR
75%, 25%
WEIGHTED-OR-AND
75%, 25%

Miscellaneous

The representation of these (generally unused) operators are provided here for the completeness of the Ternary section.

AND-OR-AND
(a.k.a. AND)
OR-AND-OR
(a.k.a. AND)
XOR-OR-AND
(a.k.a. AND)
XOR-AND-OR
(a.k.a. AND)

AND-AND-OR
(a.k.a. OR)
OR-OR-AND
(a.k.a. OR)

The 10 basic Operations

NOP [0 1] => [0 1]

NOP
(2D view)
NOP
(3D view)

NOT [0 1] => [1 0]

NOT
(2D view)
NOT
(3D view)

[0 0 1 1] AND [0 1 0 1] => [0 0 0 1]

Zadeh AND
Hyperbolic Paraboloid
AND
Yager-2 AND

compare
fzX == fzY
compare
fzY == (1 - fzX)
compare
fzX == 75%
compare
fzY == 25%

[0 0 1 1] OR [0 1 0 1] => [0 1 1 1]

Zadeh OR
Hyperbolic Paraboloid
OR
Yager-2 OR

compare
fzX == fzY
compare
fzY == (1 - fzX)

[0 0 1 1] XOR [0 1 0 1] => [0 1 1 0] (UNEQUAL)

Zadeh XOR
Hyperbolic Paraboloid
XOR

[0 0 1 1] IMPLIES [0 1 0 1] => [1 1 0 1]

Boolean IMPLIES
Zadeh IMPLIES
Hyperbolic Paraboloid
IMPLIES

[0 0 1 1] NAND [0 1 0 1] => [1 1 1 0]

Zadeh NAND
Hyperbolic Paraboloid
NAND

[0 0 1 1] NOR [0 1 0 1] => [1 0 0 0]

Zadeh NOR
Hyperbolic Paraboloid
NOR

[0 0 1 1] NXR [0 1 0 1] => [1 0 0 1] (EQUAL)

Zadeh NXR
Hyperbolic Paraboloid
NXR

[0 0 1 1] NOT_IMPLIES [0 1 0 1] => [0 0 1 0]

Boolean NOT_IMPLIES
Zadeh NOT_IMPLIES
Hyperbolic Paraboloid
NOT_IMPLIES

Category:Fuzzy operator#%20