Zadeh was best known for proposing fuzzy mathematics consisting of these fuzzy-related concepts: fuzzy sets, fuzzy logic, fuzzy algorithms, fuzzy semantics, fuzzy languages, fuzzy control, fuzzy systems, fuzzy probabilities, fuzzy events, and fuzzy information.
In 1931, when Zadeh was ten years old, his family moved to Tehran in Iran, his father's homeland. Zadeh was enrolled in Alborz College, which was a Presbyterianmissionary school, where he was educated for the next eight years, and where he met his future wife, Fay. Zadeh says that he was "deeply influenced" by the "extremely decent, fine, honest and helpful" missionaries from the United States who ran the college. "To me they represented the best that you could find in the United States – people from the Midwest with strong roots. They were really 'Good Samaritans' – willing to give of themselves for the benefit of others. So this kind of attitude influenced me deeply. It also instilled in me a deep desire to live in the United States." During this time, Zadeh was awarded several patents.
Despite being more fluent in Russian than in Persian, Zadeh sat for the national university exams and placed third in the entire country. As a student, he ranked first in his class in his first two years. In 1942, he graduated from the University of Tehran with a degree in electrical engineering, one of only three students in that field to graduate that year, due to the turmoil created by World War II, when the United States, Britain and the Soviet Union invaded Iran, whose ruler, Reza Shah, was pro-German. Over 30,000 American soldiers were based there, and Zadeh worked with his father, who did business with them as a contractor for hardware and building materials.
In 1943, Zadeh decided to emigrate to the United States, and traveled to Philadelphia by way of Cairo after months of delay waiting for the proper papers or for the right ship to appear. He arrived in mid-1944, and entered the Massachusetts Institute of Technology (MIT) as a graduate student later that year. While in the United States, he changed his name to Lotfi Asker Zadeh.
He received an MS degree in electrical engineering from MIT in 1946, and then applied to Columbia University, as his parents had settled in New York City. Columbia admitted him as a doctoral student, and offered him an instructorship as well. He received his Ph.D. in electrical engineering from Columbia in 1949, and became an assistant professor the next year.
Zadeh was called "quick to shrug off nationalism, insisting there are much deeper issues in life", and was quoted as saying in an interview: "The question really isn't whether I'm American, Russian, Iranian, Azerbaijani, or anything else. I've been shaped by all these people and cultures and I feel quite comfortable among all of them." He noted in the same interview: "Obstinacy and tenacity. Not being afraid to get embroiled in controversy. That's very much a Turkish tradition. That's part of my character, too. I can be very stubborn. That's probably been beneficial for the development of Fuzzy Logic." He described himself as "an American, mathematically oriented, electrical engineer of Iranian descent, born in Russia."
Zadeh was married to Fay Zadeh and had two children, Stella Zadeh and Norman Zada.
Zadeh died in his home in Berkeley, California, on September 6, 2017, at the age of 96. He is buried in the first Alley of Honor in Baku, Azerbaijan, where he was born. His funeral was well attended by "highly respected people", including the president of Azerbaijan. A month previous to his death, the University of Tehran had released an erroneous report that Zadeh had died, but withdrew it several days later.
According to Google Scholar, as of September 2017, Zadeh's work has been cited about 180,000 times in scholarly works, with the 1965 "Fuzzy Sets" paper receiving about 90,000 citations.
Fuzzy sets and systems
Zadeh, in his theory of fuzzy sets, proposed using a membership function (with a range covering the interval [0,1]) operating on the domain of all possible values. He proposed new operations for the calculus of logic and showed that fuzzy logic was a generalisation of classical and Boolean logic. He also proposed fuzzy numbers as a special case of fuzzy sets, as well as the corresponding rules for consistent mathematical operations (fuzzy arithmetic).
Zadeh is also cred, along with John R. Ragazzini, in 1952, with having pioneered the development of the z-transform method in discrete time signal processing and analysis. These methods are now standard in digital signal processing, digital control, and other discrete-time systems used in industry and research. He was an or of the International Journal of Computational Cognition.
1965. "Fuzzy sets". Information and Control. 1965; 8: 338–353.
1965. "Fuzzy sets and systems". In: Fox J, or. System Theory. Brooklyn, NY: Polytechnic Press, 1965: 29–39.
1972. "A fuzzy-set-theoretical interpretation of linguistic hedges". Journal of Cybernetics 1972; 2: 4–34.
1973. "Outline of a new approach to the analysis of complex systems and decision processes". IEEE Trans. Systems, Man and Cybernetics, 1973; 3: 28–44.
1974. "Fuzzy logic and its application to approximate reasoning". In: Information Processing 74, Proc. IFIP Congr. 1974 (3), pp. 591–594.
1975. "Fuzzy logic and approximate reasoning". Synthese, 1975; 30: 407–428.
1975. "Calculus of fuzzy restrictions". In: Zadeh LA, Fu KS, Tanaka K, Shimura M, ors. Fuzzy Sets and their Applications to Cognitive and Decision Processes. New York: Academic Press, 1975: 1–39.
1975. "The concept of a linguistic variable and its application to approximate reasoning", I-III, Information Sciences 8 (1975) 199–251, 301–357; 9 (1976) 43–80.
2002. "From computing with numbers to computing with words — from manipulation of measurements to manipulation of perceptions". International Journal of Applied Math and Computer Science, pp. 307–324, vol. 12, no. 3, 2002.
2012. Computing With Words. Principal Concepts and Ideas. Berlin: Springer, 2012.
^Zadeh, L. A. (1997). "Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic". Fuzzy Sets and Systems. 90 (2): 111–127. doi:10.1016/S0165-0114(97)00077-8.
Seising, Rudolf: The Fuzzification of Systems. The Genesis of Fuzzy Set Theory and Its Initial Applications – Developments up to the 1970s (Studies in Fuzziness and Soft Computing, Vol. 216) Berlin, New York, [et al.]: Springer 2007.