Is fuzzy logic invalid?

Fuzzy logic would seem to be wrong because it contradicts fundamental principles in nature:

A thing can be either small or tall. A bird can either fly or not. If the bird is in the air, it is flying, and if he is on the ground, then it is walking. This kind of distinction is natural.

What Fuzzy logic is trying to imagine is the opposite. It doesn't seem to make sense to use fuzzy logic to explain phenomena in the natural world.

A possible argument against Fuzzy logic is to show that it wasn't invented as a mathematical theory but as a non-scientific concept. Quote:

“Fuzzy set theory [...] has its roots in the social nature of human understanding. Fuzzy sets approach directly relates to practical applications of [...] creative misunderstanding” Dimitrov, Vladimir. "Fuzzy logic in service to a better world: The social dimensions of fuzzy sets." IMAC/IEEE CSCC’90 conference, Athens,(Greece). 1999. pdf

So the papers says basically, that Fuzzy logic is the opposite of a mathematical understanding of a world. Are more examples available which disprove Fuzzy logic?

• I'm afraid you are misinterpreting the paper you quote. It is about how fuzzy logic can aid understanding, as binary logic is not sufficient for the modern world: $A$ and $\neg A$ need to be linked, in the authors' words. They strongly support fuzziness as a concept. – Oliver Mason Apr 30 '19 at 13:39

Fuzzy Logic for a bird flying could model gliding creatures, and birds with poor flying ability (if either of these things were important to the use of the logic model), or a situation where you are not sure whether a creature can fly or whether it is an important observation currently.

Most apparent step functions in nature, if inspected closely, have some slope, or more complexity at the boundary than an absolute classification system can cover. The question is then whether this complexity is important in the context of whatever you want to investigate or solve. In many scenarios it might just be some super-rare edge case, in others it can be the main driver for looking at some trait or other in the first place. When looking at the evolution of flight, classifying into "flying" and "not flying" is too crude.

In my opinion the concept just sits in the "all models are wrong, some models are useful" category. And Fuzzy Logic has been useful, for example when in making control systems that would suffer from brittleness using classical Boolean logic. Like all practical AI approaches to problem solutions, Fuzzy Logic solutions have advantages and disadvantages.

I don't see that there is any strong philosophical attack on Fuzzy Logic to be had. It is self-consistent mathematically, and can be used to make working systems.

The foundation of fuzzy logic is quite simple--essentially that a truth value can be between 1 and 0 (between 100% and 0%.)

And easy way to demonstrate this is a scoring game, where players accumulate points. The outcome of the game (it's truth value) is the ratio of points accumulated by the opposing player. Thus, in a game where player 1 scores 60 points, and player 2 scores 40 points, the truth value is .6

This is really a matter of boolean values vs. real numbers, and their application.

Sometimes boolean values (T/F) are suitable to produce adequate results, sometimes they are insufficient. Where classical truth values are insufficient, fuzzy values may have applicability.

(See Neil's answer for a breakdown of how this relates to the real world.)

Tall vs. Not Tall

This is entirely relative. A thing is tall only compared to a thing that is short, otherwise the term has no meaning. Skyscrapers are accounted to be tall, but not compared to mountains. Mt. Everest is tall, but not compared to Olympus Mons on Mars!