Lotfi Zadeh and the Birth of Fuzzy Logic
The denunciations were sometimes extreme.
“Fuzzy theory is wrong, wrong, and pernicious,” said William Kahan, a highly regarded professor of computer sciences and mathematics at the University of California at Berkeley in 1975. “The danger of fuzzy theory is that it will encourage the sort of imprecise thinking that has brought us so much trouble.”
Another berated the theory’s scientific laxity. “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, who is now a professor at Florida State University in Tallahassee. “Fuzzification is a kind of scientific permissiveness, it tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work.”
This article was first published as “Lotfi A. Zadeh.” It appeared in the June 1995 issue of IEEE Spectrum. A PDF version is available on IEEE Xplore. The photographs appeared in the original print version.
A multitude of other outspoken critics also disputed the theory of fuzzy logic, developed by Lotfi A. Zadeh in the mid-1960s. Some 20 years were to pass before the theory became widely accepted—capped by this year’s award of the IEEE Medal of Honor to Zadeh “for pioneering development of fuzzy logic and its many diverse applications.” Even today some critics remain. But Zadeh never wavered. He had found himself alone in his scientific opinions on several earlier occasions.
“There is a picture of me in my study, taken when I was a student at the University of Tehran,” Zadeh told IEEE Spectrum. “I sit at a table, and above the table is a sign in Russian. ODIN, which means ‘alone.’ It was a proclamation of my independence.”
Child of Privilege
Perhaps the confidence Zadeh had in his judgment despite some tough opposition, and his willingness to stand apart from the crowd, originated in a childhood of privilege. He was born in 1921 in Azerbaijan, then part of the Soviet Union, and moved to Iran at age 10. His parents—his father a businessman and newspaper correspondent, his mother a doctor—were comfortably well off. As a child, Zadeh was surrounded by governesses and tutors, while as a young adult, he had a personal servant.
His career goal, for as long as he can remember, was to be an engineering professor. He never considered going into industry, he said, because money was no problem. Rather, he thought of scientific and engineering research as a type of religion, practiced at universities.
Zadeh received an electrical engineering degree from the University of Tehran in 1942. But instead of taking the comfortable route—becoming a professor in Iran—he emigrated to the United States.
“I could have stayed in Iran and become rich, but I felt that I could not do real scientific work there,” he told Spectrum. “Research in Iran was nonexistent.”
Lotfi A. Zadeh
Date of Birth
Feb. 4, 1921
Wife, Fay; children, Stella and Norman
BSEE, University of Tehran, 1942; MSEE, Massachusetts Institute of Technology, 1946; PhD, Columbia University, 1949
Design and analysis of defense systems, International Electronics Corp., New York City, summer of 1944
One U.S. patent, two Iranian patents.
“I made a conscious decision to stop reading fiction at age 15, when I was a voracious reader. I now read scientific books and other nonfiction only.”
Four newspapers daily (The New York Times, San Francisco Chronicle, San Francisco Examiner, The Wall St. Journal or San Jose Mercury News), Business Week, The Economist
Favorite kind of music
Classical and electronic
Sergey Prokofiev, Dimitry Shostakovich
A Hewlett-Packard workstation, which is used “only to print my e-mail; I dictate all my answers to my secretary.”
Favorite television show
Least favorite food
Any kind of shellfish
Three Cs Café, an inexpensive crêperie in Berkeley, Calif.
“No matter what you are told, take it as a compliment.”
Portrait photography (has photographed U.S. Presidents Richard Nixon and Harry Truman, as well as other notables), high-fidelity audio, garage sales
Nissan Quest Minivan
English, Russian, Iranian, French
Two million miles in past 10 years on American and United Airlines alone, uncounted mileage on other airlines
Key organizational memberships
The IEEE, Association for Computing Machinery, International Fuzzy Systems Association, American Association for Artificial Intelligence
The IEEE Medal of Honor (1995) and the Japan Honda Prize (1989)
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.
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.
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.
Once the issue of classification had been solved, Zadeh could develop the theory of fuzzy sets quickly. Two weeks later he had a fairly fleshed-out group of concepts to present to his collaborator at Rand, Richard Bellman. “His response was enthusiastic,” Zadeh said, “and that was a source of encouragement to me-though had he been very critical, I wouldn’t have changed my mind.”
Since he was Berkeley’s electrical engineering department chairman at the time and engaged in his struggle over the place of computer science at the university, Zadeh had little time to work on his new theory of fuzzy sets. He published his first paper in 1965, convinced that he was onto something important, but wrote only sparingly on the topic until after he left the department chairmanship in 1968. Since then, fuzzy sets have been his full-time occupation.
“I continue to be an active player,” he said. “I am not merely an elder statesman who rests on his laurels. I give many talks, and this puts me under pressure. I must constantly think of new ideas to talk about and keep up with what others are doing.”
The Golden Fleece
Acceptance of fuzzy set theory by the technical community was slow in coming. Part of the problem was the name—“fuzzy” is hardly proper terminology. And Zadeh knew it.
“I was cognizant of the fact that it would be controversial, but I could not think of any other, respectable term to describe what I had in mind, which was classes that do not have sharp boundaries, like clouds,” he said. “So I decided to do what I thought was right, regardless of how it might be perceived. And I’ve never regretted the name. I think it is better to be visible and provocative than to be bland.”
And, as expected, fuzzy theory did cause controversy. Some people rejected it outright because of the name, without knowing the content. Others rejected it because of the theory’s focus on imprecision.
“I’ve never regretted the name. I think it is better to be visible and provocative than to be bland.”
In the late 1960s, it even garnered the passing attention of Congress as a prime example of the waste of government funds (much of Zadeh’s research was being funded by the National Science Foundation). Former Senator William Proxmire (D-Wis.), the force behind the Golden Fleece Awards that honored such government boondoggles as $600 toilet seats, sent a letter to the foundation suggesting that such “fuzzy” garbage they were supporting should earn a Golden Fleece nomination. A flurry of correspondence from Zadeh and the foundation emerged in defense of the work.
Zadeh remembers the challenge of developing his theories “in the face of opposition, even hostility. Someone with a thinner skin would have been traumatized,” he said.
And Cox remarked, “He meets people who have written some really nasty things, and he’s nice to them.”
But, observed Berkeley’s Whinnery, “I do think this lack of acceptance bothered him, although he now describes it with some humor.”
Eventually, fuzzy theory was taken seriously—by the Japanese.
Eventually, fuzzy theory was taken seriously—by the Japanese. And their implementations of it surprised even Zadeh.
He at first had expected fuzzy sets to apply to fields in which conventional analytic techniques had been ineffectual, for work outside of the hard sciences, for work in philosophy, psychology, linguistics, biology, and so on. He also thought that the theory might apply to control systems, in engine control, for example. But he never expected it to be used in consumer products, which today is perhaps its biggest application, thanks to Japanese electronics companies.
Matsushita Electric Industrial Co. was the first to apply fuzzy theory to a consumer product, a shower head that controlled water temperature, in 1987. Now numerous Japanese consumer products—dishwashers, washing machines, air conditioners, microwave ovens, cameras, camcorders, television sets, copiers, and even automobiles—quietly apply fuzzy technology.
These products make use of fuzzy logic combined with sensors to simplify control. For example, cameras have several focusing spots and use fuzzy’s IF-THEN rules to calculate the optimal focus; camcorders use fuzzy logic for image stabilization; and washing machines use sensors to detect how dirty the water is and how quickly it is clearing to determine the length of wash cycles.
The introduction of fuzzy products by the Japanese riveted press attention on this apparently “new” technology (some two decades after Zadeh had developed the theory). Growing acknowledgment of the theory by his colleagues followed, although some still reject it.
Acceptance, colleagues say, has somewhat changed Zadeh. “Since fuzzy logic has turned into something with so much panache, and he has finally come into his own after being ignored for so many years, I think Lotfi has come out of his shell,” said Cox.
“Had I not launched that theory, I would fall into the same category as many professors—be reasonably well known… but not have made a long-lasting impact.”
To date, hundreds of books have been published on the topic, and some 15 000 technical papers have been written (most, it seems, piled around his office, where stacks of papers leave only a narrow path from the door to his desk). Zadeh is now known as the Father of Fuzzy.
“Had I not launched that theory,” said Zadeh, “I would fall into the same category as many professors—be reasonably well known, have attained a certain level of recognition, and written some books and papers, but not have made a long-lasting impact. So I consider myself to have been lucky that this thing came about.”
“The important criterion of your impact is: has what you have done generated a following? With fuzzy sets, I can definitely say, ‘Yes.’”
Editor’s note: Lotfi Zadeh died in 2017 at the age of 96.