I hope you don't take this the wrong way, but I do not think you have any idea what you are talking about (EDIT: I mean when it comes to fuzzy logic and how to represent binary numbers for arithmetic in logic systems. I don't really mean "no idea" as you have at least some decent understanding of boolean logic).
" but when it comes to simple arithmetic fuzzy logic is horrible."
In what way do you think this could possibly be true? Exactly what part of it seems horrible to you? Please be specific and do not continue making general statements that hold no information about what you are implying.
"If we where doing probability calculations or something along those lines its super useful"
That is just incorrect, while fuzzy logic deals with uncertainties, those uncertainties are not the same as probability.
A probability deals with likelihood, chances that something may happen while fuzzy logic deals with degrees of truth.
In probability, if you were presented with "This chest has a 0.7 probability of being full" we mean that there is a chance that the chest is full or not. I fuzzy logic, if you are presented with "This chest is 0.7 full" it means that the chest is full by some definition of full. This contrasts deeply with probability where an event's occurrence is uncertain as the only thing that is uncertain is the definition of "full".
"""
Boolean (bit-wise) - 8 AND 1 = 0
Fuzzy (16 state) - 8 AND 1 = 8
suuuurrrreeee...... "equivalent"
its only equivalent when you limit the fuzzy logic to 2 states lol
"""
This is also incorrect. You do not seem to understand what you are representing. There is either one of two possibilities:
1. We are dealing with a single bit(line of redstone indicating a binary signal)
That means your example should be:
Boolean: 1 AND 1 = 1 (A signal strength of 8 in a boolean system is just "ON" or "1")
16 state: 8 AND 1 = 1 (An incorrect way to represent a binary number in 16 state, however in this case it still works as the line is "ON", correctly it should be 15 AND 15 = 15 as you must be able to invert to 0 when dealing with binary)
When you hook these up to a lamp for example, you will see that the lamp turns on in both cases.
2. We are dealing with 4 bits(lines of redstone indicating a binary signal where you are for some reason denoting numerals in decimal while working with binary)
This means your example should be:
Boolean: 1/0/0/0 AND 0/0/0/1 = 0/0/0/0
16 state: 15/0/0/0 AND 0/0/0/15 = 0/0/0/0 (or even with the incorrect representation of state 8 8/0/0/0 AND 0/0/0/8 = 0/0/0/0)
If you hook these to four lamps for example, you will see that none of the lamps turn on.
Binary and boolean are not the same. Boolean is logic dealing with 2 states, binary is a number system which you can represent with absolutely anything that has at least 2 different symbols/states for representation. I am assuming that you were attempting number 2 in this case, sending the binary representation of the decimal number "8" through for a bitwise AND operation. Bitwise implies you are operating on bits (meaning binary digits, not boolean digits), you still have to correctly represent the numbers you are dealing with, no matter what the state limit of the used logic system is.
"In other words hex signal strength arithmetic in redstone is crap. like... really super poopy crap"
Back to my question of "How is it crap?", hoping that you actually explain what your issue with it is.
" but when it comes to simple arithmetic fuzzy logic is horrible."
In what way do you think this could possibly be true? Exactly what part of it seems horrible to you? Please be specific and do not continue making general statements that hold no information about what you are implying.
"If we where doing probability calculations or something along those lines its super useful"
That is just incorrect, while fuzzy logic deals with uncertainties, those uncertainties are not the same as probability.
A probability deals with likelihood, chances that something may happen while fuzzy logic deals with degrees of truth.
In probability, if you were presented with "This chest has a 0.7 probability of being full" we mean that there is a chance that the chest is full or not. I fuzzy logic, if you are presented with "This chest is 0.7 full" it means that the chest is full by some definition of full. This contrasts deeply with probability where an event's occurrence is uncertain as the only thing that is uncertain is the definition of "full".
"""
Boolean (bit-wise) - 8 AND 1 = 0
Fuzzy (16 state) - 8 AND 1 = 8
suuuurrrreeee...... "equivalent"
its only equivalent when you limit the fuzzy logic to 2 states lol
"""
This is also incorrect. You do not seem to understand what you are representing. There is either one of two possibilities:
1. We are dealing with a single bit(line of redstone indicating a binary signal)
That means your example should be:
Boolean: 1 AND 1 = 1 (A signal strength of 8 in a boolean system is just "ON" or "1")
16 state: 8 AND 1 = 1 (An incorrect way to represent a binary number in 16 state, however in this case it still works as the line is "ON", correctly it should be 15 AND 15 = 15 as you must be able to invert to 0 when dealing with binary)
When you hook these up to a lamp for example, you will see that the lamp turns on in both cases.
2. We are dealing with 4 bits(lines of redstone indicating a binary signal where you are for some reason denoting numerals in decimal while working with binary)
This means your example should be:
Boolean: 1/0/0/0 AND 0/0/0/1 = 0/0/0/0
16 state: 15/0/0/0 AND 0/0/0/15 = 0/0/0/0 (or even with the incorrect representation of state 8 8/0/0/0 AND 0/0/0/8 = 0/0/0/0)
If you hook these to four lamps for example, you will see that none of the lamps turn on.
Binary and boolean are not the same. Boolean is logic dealing with 2 states, binary is a number system which you can represent with absolutely anything that has at least 2 different symbols/states for representation. I am assuming that you were attempting number 2 in this case, sending the binary representation of the decimal number "8" through for a bitwise AND operation. Bitwise implies you are operating on bits (meaning binary digits, not boolean digits), you still have to correctly represent the numbers you are dealing with, no matter what the state limit of the used logic system is.
"In other words hex signal strength arithmetic in redstone is crap. like... really super poopy crap"
Back to my question of "How is it crap?", hoping that you actually explain what your issue with it is.