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This question covers in detail, what fuzzy logic is and how it relates to other math fields, such as boolean algebra and sets theory.

This question is also very related, but the answers are focused more on general intuition and potential applicability. The only working system based on fuzzy logic, mentioned there, is MYCIN, which goes back to the early 70s. This quote from wiki summarizes my impression of it:

MYCIN was never actually used in practice.

From my experience in AI, the best tool to deal with uncertainty is Bayesian probability and inference. It allows to apply not only a wide range of probabilistic tools, such as expectation, MLE, cross-entropy, etc, but also calculus and algebra.

Can you call fuzzy logic a "pure theoretical" concept, which only played its role in the early development of AI? Are there real practical applications of fuzzy logic? What problem would you recommend to solve and to code using fuzzy logic?

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Fuzzy logic seems to have multiple of applications historically in Automotive Engineering.

I found an interesting article on the subject from 1997. This excerpt provides an interesting rationale:

The key reason for fuzzy logic’s success in automotive engineering lies in the implications of its paradigm shift. Previously, engineers spent much time creating mathematical models of mechanical systems. More time went to real-world road tests that tuned the fudge factors of the control algorithms. If they succeeded, they ended up with a control algorithm of mathematical formulas involving many experimental parameters. Modifying or later optimizing such a solution is very difficult because of its lack of transparency. Fuzzy logic makes this design process faster, easier, and more transparent. It can implement control strategies using elements of everyday language. Everyone familiar with the control problem can read the fuzzy rules and understand what the system is doing and why. It also works for control systems with many control parameters. Designers can build innovative control systems that would have been intractable using traditional design techniques.
SOURCE: Fuzzy Logic in Automotive Engineering, 1997


Here are some papers and patents for automatic transmission control in motor vehicles. One of them is fairly recent:

Automatic Transmission Shift Schedule Control Using Fuzzy Logic
SOURCE: Society of Automotive Engineers, 1993

Fuzzy Logic in Automatic Transmission Control
SOURCE: International Journal of Vehicle Mechanics and Mobility, 2007

Fuzzy Logic Based Controller For Automated Gear Control in Vehicles
SOURCE: International Journal of Computer Science, 2014

Fuzzy control system for automatic transmission | Patent | 1987

Transmission control with a fuzzy logic controller | Patent | 1992


Likewise with fuzzy logic anti-lock breaking systems (ABS):

Antilock-Braking System and Vehicle Speed Estimation using Fuzzy Logic
SOURCE: FuzzyTECH, 1996

Fuzzy Logic Anti-Lock Break System
SOURCE: International Journal of Scientific & Engineering Research, 2012

Fuzzy controller for anti-skid brake systems | Patent | 1993


This method seems to have been extended to aviation:

A Fuzzy Logic Control Synthesis for an Airplane Antilock-Breaking System
SOURCE: Proceedings of the Romanian Academy, 2004

Landing gear method and apparatus for braking and maneuvering | Patent | 2003


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You've obviously never heard of fuzzy logic washing machines.

● Typically, fuzzy logic controls the washing process, water intake,water temperature, wash time, rinse performance, and spin speed. This optimises the life span of the washing machine. More sophisticated machines weigh the load (so you can’t overload the washing machine), advise on the required amount of detergent, assess cloth material type and water hardness, and check whether the detergent is in powder or liquid form. Some machines even learn from past experience,memorising programs and adjusting them to minimise running costs.

Fuzzy logic is used in a variety of control applications. If your furnace can only be on or off, for example, you might use a probabilistic function of temperature to determine when to turn it on and off, rather than having fixed high and low temperatures activate your thermostat. In some applications, that's been found to improve perceived comfort or efficiency.

For more sophisticated AI applications, you could use fuzzy logic for activations in a neural net, but I don't think it's offering much improvement over fixed, weighted activations.

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    $\begingroup$ Actually, I have heard of them, but I never believe smart terms in marketing. It's possible that Samsung developers implemented some "smart" logic, but sales people decided that "fuzzy logic" sounds too cool in washing machines. If there's evidence that the implementation really uses Zadeh's fuzzy logic, I'd be happy to call it a real practical application. $\endgroup$ – Maxim Oct 4 '17 at 13:16
  • $\begingroup$ @Maxim-- It's real-- the concept was eagerly embraced by Japanese engineers going back to the 70s : en.wikipedia.org/wiki/Fuzzy_logic#Early_applications $\endgroup$ – antlersoft Oct 4 '17 at 21:10
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The site FuzzyTECH lists an array of applications:

Industrial Automation
Monitoring Glaucoma
Coal Power Plant
Complex Chilling Systems
Refuse Incineration Plant
Fuzzy Logic Design
Practical Design
Water Treatment System
Truck Speed Limiter
Medical Shoe
Fuzzy in Appliances
Automotive Engineering
Antilock Braking System
Aircraft Flight Path
Nucluar Fusion
Motorla 68HC12 MCU
Traffic Control
Sonar Systems

Most of the linked articles have good bibliographies citing numerous papers, although it's notable that most of the material is a few decades old.

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