Lotfi A. Zadeh

Lotfi A. Zadeh ( born February 4, 1921), actually Lotfali Askar -Zadeh is an American mathematician, computer scientist, electrical engineer and professor emeritus of computer science at the University of California, Berkeley. He is the creator of the theory of fuzzy ( fuzzy) sets ( 1965) and the founder of Fuzzy Logic ( 1973).

Life

Lotfi A. Zadeh was born in Baku, Azerbaijan, the son of Iranian journalists, Rahim Aleskerzade of Ardabil, who worked as an Iranian foreign correspondent here, and his Ukrainian- Jewish wife, the pediatrician Fanya Koriman. 1931 the family went back to Iran, where Zadeh grew up, attended high school and university entrance exams (Abitur ) took off as the second best in the country. He studied electrical engineering at the University of Tehran in 1942 he graduated as an electrical engineer from. In the summer of 1943 he went to the USA where he worked in Boston in 1946 acquired the academic degree of Master of Science in Electrical Engineering in 1949 at Columbia University in New York the doctoral degree ( PhD) at MIT. Here he taught ten years - since 1957 as a professor for life - before he in 1959 a professorship at the University of Berkeley, California followed, where he teaches on his retirement in 1991 and also conducts research. Even as a 89- year-old (2010) Lotfi Zadeh lectured around the world and is still (2012 ) involved as a director of the Berkeley Initiative for Soft Computing to ongoing research and active. In addition to numerous honors and memberships in national and international scientific institutions and academies honorary doctorate from around the world ( so far), he was awarded 24 universities.

Services

Zadeh began his research in the field of systems theory, he worked on issues of decision theory and information systems, and pattern recognition. In 1965 he stated in his - by 2014 more than 50,000 -fold cited - article fuzzy sets for the first time his concept of a theory of fuzzy sets is that the nucleus and the base of the rapidly developing fuzzy logic - (content: The logic of blur) - should be with great effect especially through its diverse applications in engineering and linguistic data processing information science.

The basic idea of ​​the precise recording of inaccurate is not to define fuzzy ( fuzzy) amounts through the objects, the element of this set are ( or are not ), but the degree of their belonging to this set. This is done by membership functions uA: X → [ 0,1] that each element of the definition set X = { x} assign a number from the real-valued interval [ 0,1] of the target amount, which the membership degree uA (x ) for each element x as defined fuzzy set A indicates. Thus, each element is the element of each fuzzy set, but with different, a certain subset defining membership degrees. Zadeh said this new set operations that constitute the multi-valued fuzzy logic operations as a new logical calculus and prove them to be a generalization of two-valued classical logic, which is included as a special case in it.

As part of its possibility theory Zadeh developed the concept of the possibility distribution as fuzzy restriction, like a stretchy bondage restricts the values ​​that a variable can have. Be as F, defined by the membership function uF fuzzy subset of the universe of discourse U = { u}. A proposition of the form X is F, where X is a variable that takes values ​​from U, then the induced possibility distribution ПX which equates the possibility of X, u to accept the value, with uF (u). X is in such a blurred ( fuzzy) variable, which is connected with the possibility distribution ПX in a similar manner as is the case in the theory of probability for the connection of a random variable, and the probability distribution. In addition, proposed Zadeh fuzzy numbers before as special fuzzy sets, which - led to the emergence of fuzzy arithmetic - along with the appropriate rules consistent mathematical operations on these numbers.

" In general, complexity and precision bear in inverse relation to one another in the sense that, as the complexity of a problem Increases, The Possibility of analyzing it in precise terms diminishes. [ ... ] From this point of view, the capacity of a human brain to manipulate fuzzy concepts and non- quantitative sensory inputs june well be one of its most important assets. Malthus, ' fuzzy thinking ' june not be deplorable, after all, if it makes possible the solution of problems Which are much too complex for precise analysis. "

Zadeh coined the term Soft Computing, which was not used substantially to the (not always possible ) exact numerical analysis of a complex system in favor of its qualitative characterization and description in natural language terms. Their intrinsic ( extensional as intensional ) vagueness make it possible to carry the empirical inaccuracies and analytical uncertainties into account. It is developed by Zadeh TEST score semantics of natural language expressions in the linguistic variables play a decisive role in the center. His formal meaning representation language PRUF ( Possibilistic Relational Universal Fuzzy ) and the progress on instantiated, explanatory data structures TEST scores take over a knowledge representations ( knowledge representation ) of artificial intelligence comparable function. Critics of this approach that attest to such linguistic characterizations of multi - parameter systems, at best, a black-box modeling of system behavior, overlook mostly that it in not the functional explanation and simulation of such system, but the emulative modeling and control of their possible behavior uncertainty is as able to afford the human assets with comparable efficiency and ease.

Zadeh's ideas proved to be extremely fruitful and experienced in the last two decades of the 20th century a remarkable acceptance and wider reception in the research of neural networks, expert systems, control theory and artificial intelligence. Lately Zadeh's research interests focus on the fuzzy logic, fuzzy ( fuzzy) semantics of natural language, a theory predictable perception ( computational theory of perception ), as well as the computation with words / words ( computing with words ).

Zadeh is the editor or advisory board member of more than 70 scientific journals worldwide, he has published numerous articles (over 200 as a single author) from his wide range of research on different aspects of the design, the design, implementation and analysis of information and decision systems.

In 1966 he was invited speaker at the International Congress of Mathematicians in Moscow ( research on some non-classical regulatory problems in the U.S.).

Writings (selection )

  • Fuzzy sets. Information and Control 8 (1965 ): 338-353.
  • Fuzzy sets and systems. In: J. Fox, editor. System Theory. Brooklyn, NY: Polytechnic Press, 1965, pp. 29-39.
  • The concept of system, aggregate, and state in system theory. In: L. A. Zadeh, E. Polak, editors. System Theory [ Inter- University Electronic Series, Vol 8], New York: McGraw -Hill, 1969, p.3 -42
  • Quantitative Fuzzy Semantics. Information Science 3 (1971 ): 159-176.
  • A fuzzy -set- theoretical interpretation of linguistic hedges. Journal of Cybernetics 2 (1972 ): 4-34.
  • Fuzzy Languages ​​and Their Relation to Human and Machine Intelligence. In: M. Marois, editor. Man and computer. Basel: Karger, 1972, p.130 -165
  • Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Systems, Man and Cybernetics, 3 ( 1973): 28-44.
  • Fuzzy logic and its application to approximate reasoning. In: Information Processing 74, Proc. IFIP Congr. 1974, p 591-594.
  • Fuzzy logic and approximate reasoning. Synthesis 30 (1975): 407-428.
  • Calculus of fuzzy restrictions. In: L. A. Zadeh, K.S. Fu, K. Tanaka, M. Shimura, editors. Fuzzy Sets and their Applications to Cognitive and Decision Processes. New York: Academic Press, 1975, pp. 1-39.
  • The concept of a linguistic variable and its application to approximate reasoning, Part I, Information Sciences 8 (1975 ): 199-251.
  • The concept of a linguistic variable and its application to approximate reasoning, Part II, Information Sciences 8 (1975 ): 301-357.
  • The concept of a linguistic variable and its application to approximate reasoning, Part III, Information Sciences 9 (1976 ): 43-80.
  • PRUF - a meaning representation language for natural languages ​​. Intern. Journal Man-Machine Studies 10 (1978 ): 395-460
  • TEST -Score Semantics for Natural Languages ​​and Meaning Representation via PRUF. In: Burghard B. Rieger, editor: Empirical Semantics I [ Quantitative Linguistics 12], Bochum: Brockmeyer 1981, p 281-349
  • Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90 (1997): 111-127
  • From Computing with Numbers to Computing with Words - from manipulation of Measurement to manipulation of Perception. In: Paul P. Wang, editor: Computing with Words [ Wiley Series on Intelligent Systems 3], New York: Wiley & Sons, 2001, pp.35- 68
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