My condolences go out to his family and friends, but he made a small impact on me at least.
Interviewer:Would you say that Fuzzy Logic turns Aristotelian or Classical Logic on its head?
Lotfi:(Laughs). Back in Aristotle's day, people tried to be as precise as possible. That's the Aristotelian tradition, the Cartesian tradition. Looking at things as being entirely black or white stems from such a tradition. But take the example of good and bad. What we're beginning to understand now is that sometimes things that we perceive as bad really turn out to be good, or perhaps, not as bad as we originally thought. Things can serve a purpose. People back in Aristotle's time and even later thought that by perceiving things in black and white (in absolute terms) that they gained alot. And they did. But they lost a great deal in the process. Fuzzy Logic represents a swing in the opposite direction but I would like to stress that there is much more to Fuzzy Logic than multi-valuedness of truth.
Classical logic has erred in devoting so little attention to approximate reasoning and focusing to such a high degree on exact reasoning. So when you take a course in logic, you learn all kinds of things which are of very little use in everyday life. We encounter approximate reasoning all the time. For example, "Where can I park my car?" Where should I have lunch? Should I place this call "person-to person" or "station to station"? Should I buy this house? How do I get from this side of town to the other when I'm in a hurry? Classical logic, operation research, decision analysis-many other disciplines have nothing to say about this topic.
Pretty substantial list here: https://people.eecs.berkeley.edu/~zadeh/papers/index.htm
1) https://www.amazon.com/Fuzzy-Systems-Handbook-Second-Practit... I had the 1st but 2nd is better
2) that list looks pretty complete but it has been some years
Fuzzy logic reminds me Albert Einstein quote about mathematics. "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
So, there is this material that needs to be heated on a curve (time 0 = room temp, 20 minutes = 400C, 120 minutes = room temp - cannot remember after 20 years - it cooled sorta quickly because of fans when heater off). Software package with oven basically turned heaters full blast, the off, then full blast, etc. about half the time material wasn’t cooked properly. I wrote a bunch of rules that computed a % the heater should be at. Worked really well and was an amazingly small program.
Social wise I wrote rules to judge success based on about 20 factors. Never bothered to pursue it beyond my own satisfaction.
Let's say you have are taking a shower with an automated temperature control. The current temperature is set to 28 degrees Celsius, but there is a sudden shift to 24 degrees.
Probability Theory: Based on prior knowledge, I know that a temperature of 24 degrees Celsius is considered "hot" 10% of the time, "warm" 50% of the time, and "cold" 40% of the time. Based on this the current expected value of the probability distribution is still "warm", so I will leave it same until cold > warm.
Fuzzy Theory: Based on my fuzzy set membership, 24 degrees Celsius has 25% membership in the "hot" set, 60% membership in the "warm" set, and 50% membership in the "cold" set. My fuzzy system is setup to maintain a particular relationship between cold and hot (let's say, cold == hot), and therefore increases temperature until balanced.
For example, you can't have a temperature that is 80% hot AND 80% cold. This problem becomes even more apparent as you increase the number of states (lukewarm, warmish, very warm), as each state reduces the probability of another state.
The differences become more profound as you do more complicated set operations, fuzzy relations, fuzzy systems, and such. In fact, there is even fuzzy probability theory, in which you have a probability distribution of different fuzzy sets.
I don't see why this is an issue. You can also define each of the states as its own binary random variable and then the probabilities of two states conditioned on the temperature can add up to more than 1.
I thought your original post was meant to explain a practical application of fuzzy theory and how it differs from probability theory. Perhaps there is another example that better illustrates how fuzzy theory simplifies a problem where using probability theory would be messy / impossible?
Yes, but then you're defining a probability distribution over the space of fuzzy states.
Is one sample of a fuzzy logic based controller of an industrial process. There are many such examples, I have a book here on fuzzy logic that details a whole raft of them.
Dear God, who is going to clean out his office?