Lotfi Zadeh and the Birth of Fuzzy Logic

After graduation, Zadeh had a business association with the US. Army Persian Gulf Command. That enabled him to be financially independent when he came to the United States to enroll in graduate school at the Massachusetts Institute of Technology (MIT) in Cambridge. “MIT didn’t have many graduate students at the time,” Zadeh recalled, “so it was fairly easy to get in, even though the University of Teheran had no track record.”

“No doubt professor Zadeh’s enthusiasm for fuzziness has been reinforced by the prevailing political climate in the United States—one of unprecedented permissiveness,” said R. E. Kalman in 1972

MIT, it turned out, was an easy ride after the demanding course work Zadeh had faced in Tehran.

His choice of subject for his master’s thesis, though, marked one of the first times he would sail against the prevailing technical winds. He chose to study helical antennas, a subject deemed unreasonable by the professor who had taught him antenna theory. Undaunted, Zadeh found another professor to supervise his work.

“I felt that my judgment was correct, and the judgment of people who supposedly knew much more about the subject than I did was not correct,” Zadeh said. “This was one of many such situations. Helical antennas came into wide use in the ‘40s and OS, and my judgment was vindicated.”

By the time Zadeh received his master’s degree in 1946, his parents had moved from Tehran to New York City. So instead of continuing at MIT, he searched out a post as an instructor at New York City’s Columbia University and began his Ph.D. studies there. His thesis on the frequency analysis of time-varying networks considered ways of analyzing systems that change in time.

“It was not a breakthrough,” he recalled, “but it did make an impact and opened a certain direction in its field.”

What he views as his first technical breakthrough came in 1950, when, as an assistant professor at Columbia, he coauthored a paper with his doctoral thesis advisor, John R. Ragazzini, on “An extension of Wiener’s theory of prediction.” This analysis of prediction of time series is often cited as an early classic in its field. This thesis introduced the use of a finite, rather than an infinite, preceding time interval of observation for subsequent smoothing and prediction in the presence of multiple signals and noises. This, and Zadeh’s other work while he was at Columbia, made him a well-known figure in the analysis of analog systems.

Berkeley Beckons

As Zadeh was pretty much entrenched at Columbia, he surprised his colleagues when he packed up in 1959 and moved to the University of California at Berkeley.

“I had not been looking for another position,” Zadeh said, “so the offer from Berkeley was unexpected.’’ It came from electrical engineering department chairman John Whinnery, who called him at home over the weekend and offered him a position. “If my line had been busy, I believe l would still be at Columbia,” Zadeh told Spectrum.

Whinnery recalls it slightly differently. He had heard from a colleague that Zadeh had been toying with the idea of leaving Columbia. Minutes later, Whinnery picked up the phone and called him, arranged to meet him in New York City for dinner, and soon afterward hired him. Berkeley was then growing rapidly, and Whinnery was on the lookout for young scholars who were considered brilliant in their fields. Zadeh fit the bill.

For Zadeh, moving to Berkeley was a simple decision to make: “I was happy at Columbia, but the job was too soft. It was a comfortable, undemanding environment; I was not challenged internally. I realized that at Berkeley my life would not be anywhere near as comfortable, but I felt that it would be good for me to be challenged.” Zadeh has never regretted the decision. To this day he remains at Berkeley, although by now as professor emeritus.

A number of departmental colleagues felt that the trend toward computer science was a fad.

At Berkeley, Zadeh initially continued his work in linear, nonlinear, and finite state systems analysis. But before long he became convinced that digital systems would grow in importance. Appointed as chairman of the electrical engineering department, he decided to act on that conviction, and immediately set about strengthening the role of computer science in the department’s curriculum. He also lobbied the electrical engineering community nationwide to recognize the importance of computer science.

Once again, he found himself fighting conventional wisdom. A number of departmental colleagues felt that the trend toward computer science was a fad, and that computer science should not be assigned a high departmental priority. ‘They accused me of being an Yves St. Laurent,” Zadeh recalled, “a follower of fads.” Elsewhere, professors in the mathematics department, along with the head of the computer center, were lobbying to set up their own computer science department.

Zadeh fought this battle as he has fought others, with polite persistence, his former chairman recollected. “We had many differences of opinion when he was chairman,” Whinnery said. “When he couldn’t convince people, he would get upset, but [even now] you can only tell this by the expression on his face. He doesn’t yell or scream. Then he goes ahead and does what he was going to do anyway. And mostly he’s been right, particularly about the importance of computers in electrical engineering.”

Said Earl Cox, chief executive officer of the Metus Systems Group, Chappaqua, N.Y., who has known Zadeh since the ’70s: “I’ve never seen him anger anybody, even though he prides himself in going his own way, in thinking his own thoughts.” (Zadeh is also known for encouraging others to be independent. He insists his graduate students publish in their own name, noted former student Chin L. Chang, who is now president of Nicesoft Corp., Austin, Texas. That practice goes against custom.)

Zadeh finally got his way in 1967: the name of the department was changed to electrical engineering and computer science (EECS). A separate computer science department was also established in Berkeley’s College of Letters, but after a few years it folded and became absorbed into EECS.

Fuzzy is Born

While he was focusing on systems analysis, in the early 1960s, Zadeh began to feel that traditional systems analysis techniques were too precise for real-world problems. In a paper written in 1961, he mentioned that a new technique was needed, a “fuzzy” kind of mathematics. At the time, though, he had no clear idea how this would work.

That idea came in July 1964. Zadeh was in New York City visiting his parents and planned to leave soon for Southern California, where he would spend several weeks at Rand Corp working on pattern recognition problems. With this upcoming work on his mind, his thoughts often turned to the use of imprecise categories for classification.

“One night in New York,” Zadeh recalled, “I had a dinner engagement with some friends It was canceled, and I spent the evening by myself in my parents’ apartment 1 remember distinctly that the idea occurred to me then to introduce the concept of grade of membership [concepts that became the backbone of fuzzy set theory]. So it is quite possible that if that dinner engagement had not been canceled, the idea would not have occurred to me.”

Fuzzy technology, Zadeh explained, is a means of computing with words—bigger, smaller, taller, shorter. For example, small can be multiplied by a few and added to large, or colder can be added to warmer to get something in between.