He actually said: “What if you ask 10 people if Bill is tall, and 4 of them say yes, but 6 of them say no? Probabilities have no way of representing this.”)
You may have misunderstood what Zadeh was saying. Suppose Bill is 5 feet, 9 inches in height and all ten people know this. I.e. we are not attempting to represent the likelihood that Bill is or is not tall based on the uncertain evidence given by different people. It is not 60% likely that Bill is tall, and 40% likely that he is not. He is 5 feet, nine inches and everyone knows it. No one disagrees on his actual, measured height.
Now we could taboo the word tall, and we wouldn’t lose any information; and in some contexts that might be the right thing to do. However in practical, day-to-day life humans do use words like tall that have fuzzy, non-crisp boundaries. The truth value of a word like “tall” is better expressed as a real number than a boolean value. Fuzzy logic represents the apparent disagreement on whether or not Bill is tall by saying he is 60% tall and 40% not tall.
That isn’t what distinguishes fuzzy logic from probabilities. Both would represent this case with the number 0.6. The distinguishing feature of fuzzy logic is that it uses non-probabilistic functions to compute joint probabilities, to avoid various practical and computational problems.
You may have misunderstood what Zadeh was saying. Suppose Bill is 5 feet, 9 inches in height and all ten people know this. I.e. we are not attempting to represent the likelihood that Bill is or is not tall based on the uncertain evidence given by different people. It is not 60% likely that Bill is tall, and 40% likely that he is not. He is 5 feet, nine inches and everyone knows it. No one disagrees on his actual, measured height.
Now we could taboo the word tall, and we wouldn’t lose any information; and in some contexts that might be the right thing to do. However in practical, day-to-day life humans do use words like tall that have fuzzy, non-crisp boundaries. The truth value of a word like “tall” is better expressed as a real number than a boolean value. Fuzzy logic represents the apparent disagreement on whether or not Bill is tall by saying he is 60% tall and 40% not tall.
That isn’t what distinguishes fuzzy logic from probabilities. Both would represent this case with the number 0.6. The distinguishing feature of fuzzy logic is that it uses non-probabilistic functions to compute joint probabilities, to avoid various practical and computational problems.