On the first look, fuzzy logic is an efficient way in dealing with uncertainty. It allows to store vague information into a float variable which allows similar to a color gradient a realistic description of the world. The problem is, that in a concrete example, Fuzzy logic has the tendency to become a subjective opinion panel which makes it a bad idea for practical applications.

In the example, two people are asked if the glass of water is full or not. The answer is different and not predictable. Person1 will judge, that the glass is empty, because he has a pessimistic membership function. But Person2 has a different opinion and will say “yes, the glass is full”.

The example was mentioned to show, that Fuzzy logic doesn't solve the problem with uncertain knowledge, but it will result into an unreliable system. Is there a way to make the concept more trustworthy and judge objective about the content of the bottle?

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There's no particularly good reason that fuzzy logic needs to be subjective.

Fuzzy logic merely involves representing concepts as a degree of membership in a fuzzy set, rather than a binary membership function.

In many applications, like, say, cooking rice, fuzzy logic can give us a way to capture the fact that agents have subjective preferences about a concept with an objective membership function.

To continue with the rice cooking example, two individuals may disagree about whether a particular pot of rice is "done" or not, because they have different notions of what "done" means. If we ask many individuals for their opinions, we can elicit a representative membership function for the group as a whole. Our cooker can then measure the humidity of the rice and decide that the "doneness" of the right is 60%, corresponding to a level of "doneness" that 60% of people would call "done", and 40% call "not done" if asked to make a binary estimate. The function is objective, because it describes the degree to which a typical person is likely to say the rice is done (an objective quantity we can measure), and not the subjective views of one individual.

This is not really very different from working with probabilities, but your intuition is right in that two agents with fuzzy logic beliefs do not necessarily have a clear way to combine those beliefs into an objective function. That is one of Cheeseman's classic critiques of non-probabilistic approaches to dealing with uncertainty.

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