# Lotfi Zadeh, Father of Mathematical ‘Fuzzy Logic,’ Dies at 96

In academic circles, Professor Zadeh’s work was controversial and sometimes ridiculed, in part because it challenged other forms of mathematics and in part because of his terminology. “Fuzzy logic” seemed to make fun of itself.

But the logic itself was not fuzzy, said Professor Timothy Ross of the University of New Mexico. It was a way of dealing with “fuzzy sets,” collections of information whose boundaries were vague or imprecise. Over the years it proved to be an enormously influential idea.

According to the website Google Scholar, Mr. Zadeh’s 1965 paper, titled “Fuzzy Sets,” has been cited by more than 90,000 scholarly works, and his mathematical concepts have provided practical new ways to build consumer electronics, trade stocks, forecast weather and more.

Lotfi Asker Zadeh was born on Feb. 4, 1921, in Baku, Azerbaijan, which was then a part of the Soviet Union. His father was a journalist, and his mother, born in Russia, was a doctor.

After the family moved across the Soviet border to Iran, Mr. Zadeh graduated with a science degree from the University of Tehran. During World War II he sold goods to the American Army, earning enough money to continue his education in the United States, his son said. He received a master’s degree in electrical engineering from the Massachusetts Institute of Technology in 1946 and a Ph.D. from Columbia in 1949.

As a professor at Columbia, working alongside John Ragazzini, Mr. Zadeh developed a mathematical method called z-transformations, which became a standard means of processing digital signals inside computers and other equipment. He moved to Berkeley in 1959.

Elijah Polak, a professor emeritus at Berkeley, recalled in an interview that Professor Zadeh’s theory of fuzzy sets emerged during their walks across the campus. Professor Zadeh began noticing that when people parked their cars, they would intuitively turn their wheels slightly to the left and then slightly to the right before pulling into a parking space.

“But how much is slightly?” he would ask.

Fuzzy sets began as an effort to use mathematics to define “slightly” — or “tall” or “fast” or “beautiful” or any other concept that has ambiguous boundaries.