“Set membership is graduated. Degrees of belonging measured as real numbers between zero and one. Boundaries of the set are soft, not crisp”.

This word salad says almost nothing to majority of people. Let’s make it easier. Take your washing machine. It can, as a human, select the best mode with its duration, pace and temperature regime, according to the volume of laundry. Or, take your auto-focus camera. It selects optimal parameters of shooting with its distance to an object, illumination of a scene and image sharpness, according to camera’s resolution.

These are two examples, among thousands of others, of real-life application of what is called fuzzy logic, which, in turn, is based on fuzzy sets theory. Your home appliances behave themselves in such an intelligent manner because of fuzzy logic-based control systems that do the job for you.
Deviation from entrenched ideas of classical binary (black and white, true or false) logic, stating that a component should unambiguously belong to a set with distinctly fixed boundaries, to the shades of gray (sets have fuzzy boundaries), similar to human reasoning, significantly extends range of options in decision making and problem solving.

In general terms, fuzzy logic plays a role of a connector between strict principles of formal logic and reality, which is often vague and beyond our notion.

Let’s proceed to examples again and take high fashion field. There are principal criteria there in selecting candidate, e.g. a face, a height, age, etc. Face should be symmetrical, without physical defects, preferably with big eyes, full lips and high cheek-bones. A model should be 175 to 181 cm tall with shapely figure.

Fuzzy logic found room in the set of haute couture for a girl with irregular-shaped face, unusually low weight, who measured 169 cm, but had one asset that did not precisely belong to the successful model’s criteria - unsurpassed naturalness and charm. It was one of the world’s most famous supermodels – Kate Moss.

Invention of this concept and its application to different fields of human activities has been a great achievement of Dr. Lotfi A. Zadeh, an outstanding scientist of Azerbaijani origin, who was born and grew in Baku, Azerbaijan, studied Tehran University, and made his world-shaking findings in UC Berkeley, USA.

His 1965 research paper on fuzzy sets theory, which is one of the most cited of the 20th century, and further development of fuzzy logic was an attempt to complete computer logic, operating only with precise data, with human reasoning with its uncertainty and judgment.

For almost two decades fuzzy logic theory faced a dark skepticism from the world’s scientific community. Japanese scientists were the first who perceived the superiority of Zadeh’s new theory. In 1985 Hitachi engineers applied fuzzy computer to control speed of trains by automatic acceleration and braking for 16-station railway of Sendai city, resulting in less electricity consumption. Fuzzy logic-based control systems were then successfully applied in different areas by Nissan, Sony, Ricoh and others.

Since then the theory has been widely accepted and used in a large number of applications ranging from consumer products (washing machines, fridges, air conditioners, cameras), medical equipment, and vehicle transmissions to industrial engineering, industrial process control, autonomous vehicle navigation and NASA advanced piloting techniques.

Lately the focus has shifted to non-engineering applications such as social sciences, policy sciences, fraud detection systems, assessment of credit-worthiness systems, and economics.
Lotfi A. Zadeh received numerous awards for his contribution to science as an inventor of a new field of research called fuzzy logic. Experts say fuzzy logic-based technologies are well on the way to be a multi-billion business.

Lotfi A. Zadeh - a man who really changed the world, died on September 6, 2017, at age 96.
Rest in peace, dear Lotfi, we are proud of you.