When I first was going to college I was going to major in International Affairs. The summer before my freshman year, I read a book about fuzzy logic. (this book - https://www.amazon.com/Fuzzy-Logic-Revolutionary-Computer-Te...
to be exact) and it so captivated me that I changed my major to electrical engineering. RIP Lofti Zadeh, you had a major impact on the course of my life, however indirectly.
I had the pleasure of having lunch with Prof Zadeh my first year in CS right around the corner from Soda Hall. I had my book out studying and he came over and talked to me and it really made me appreciate the program. Not sure about sticks out in my head so much. I think it was just the congeniality, he made me laugh and I was stressed.
My condolences go out to his family and friends, but he made a small impact on me at least.
RIP Lotfi Aliasker Zadeh.Form an interview "Obstinacy and tenacity. Not being afraid to get embroiled in controversy. That's very much a Turkish tradition. That's part of my character, too. I can be very stubborn. That's probably been beneficial for the development of Fuzzy Logic."
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.
I met him once, he came for a conference at my university. During lunch he sat next to him. What had struck me was how kind, humble and considerate he was. Sometimes people of his caliber have the "I am too important or to busy to talk to some no name student like you" attitude but he was the opposite of that.
I was introduced to fuzzy logic by Earl Cox’s book[1] then I read through his papers[2]. I think reading the book helped a lot since it gave practical examples and code.
Would you mind concisely explaining one example and application of it? I've read (for example) about possibility theory, but I hardly understand what it helps us do that probability theory didn't.
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."
Other than some of the stuff on the Wikipedia article and the double inverted pendulum, I used it with a weird heating problem and some social stuff.
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.
Both are ways of dealing with uncertainty, but probability theory is more about the uncertainty around which state a variable has, while fuzzy theory is the uncertainty around the states themselves.
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.
Since they belong to the same probability distribution, the states are not independently defined. A change that increases the probability of hot MUST decrease the probability of cold, since the probability of all states must sum to 100%.
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.
"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"
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?
> 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.
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.
If he were still at MIT, that would be my wife's job; as a curator for the MIT museum she does a lot of cleaning out and cataloging objects from retiring or deceased professors offices. I'm sure she has a counterpart who will be doing the same.
RIP. Set theory has always been an interesting topic but Prof. Zadeh stirred up the pot by proposing and strongly advocating fuzzy sets, which have opened up both new theoretical and practical paths for others to explore.
I am sad to learn Lotfi has died. He was a friend and a frequent speaker in Stanford's EE380 Colloquium. He was a inspiring pragmatist whose fuzzy logic was understandable,explainable,functioned as expected, and quickly became incorporated into real products. The competing technology, knowledge systems, was far less transparent, slow to leave the lab, and often not as effective.
I'm sure that there will be a renissance of fuzzy logic, its sad to know that he will not witness it.
His character will be missed, but his contributions won't be forgotten.
