Lotfi A. Zadeh

“Lotfi A. Zadeh at cs.berkeley.edu”

“As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics.”

“Conceptual graphs (CGs) (Sowa 1976; 1984) and fuzzy logic (Zadeh 1965; 1975a) are two logical formalisms that emphasize the target of natural language, each of which is focused on one of the two mentioned desired features of a logic for handling natural language. Conceptual graphs, based on semantic networks and Peirce's existential graphs, combine the visual advantage of graphical languages and the expressive power of logic.”

“I can't say that anything has been "exciting". Rather, I would choose the word "interesting". Not too long ago, the Chinese University of Hong Kong conducted a survey to determine which consumer products were using Fuzzy Logic. The result was a thick report, some 150-200 pages long-washing machines, camcorders, microwave ovens, etc. What interested me wasn't the particular applications so much as the breadth of applications-so many products were incorporating Fuzzy Logic.”

“Well, I knew it was going to be important. That much I knew. In fact, I had thought about sealing it in a dated envelope with my predictions and then opening it 20-30 years later to see if my intuitions were right. I realized this paper marked a new direction. I used to think about it this way-that one day Fuzzy Logic would turn out to be one of the most important things to come out of our Electrical Engineering Computer Systems Division at Berkeley. I never dreamed it would become a worldwide phenomenon. My expectations were much more modest.”

“The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very fake, etc.... As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very quite.”

“To what degree is something true or false?”

“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.”

“Essentially, a fuzzy algorithm is an ordered sequence of instructions (like a computer program) in which some of the instructions may contain labels or fuzzy sets, e.g.: Reduce x slightly if y is very large Increase x very slightly if y is not very large and not very small If x is small then stop; otherwise increase x by 2.”

“A linguistic variable is a variable whose values are words or sentences in a natural or synthetic language.”

“[T]he successes of modern control theory in the design of highly accurate space navigation systems have stimulated its use in the theoretical analyses of economic and biological systems. Similarly, the effectiveness of computer simulation techniques in the macroscopic analyses of physical systems has brought into vogue the use of computer-based econometric models for purposes of forecasting, economic planning, arid management.”

“A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language.”

“[ Fuzzy logic is ] a logic whose distinguishing features are (i) fuzzy truth-values expressed in linguistic terms, e.g., true, very true, more or less true, or somewhat true, false, nor very true and not very false, etc2.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact.”

“In general, complexity and precision bear an inverse relation to one another in the sense that, as the complexity of a problem increases, the possibility of analysing it in precise terms diminishes. Thus 'fuzzy thinking' may not be deplorable, after all, if it makes possible the solution of problems which are much too complex for precise analysis.”

“More often than not, the classes of objects encountered in the real physical world do not have precisely defined criteria of membership. For example, the class of animals clearly includes dogs, horses, birds, etc. as its members, and clearly excludes such objects as rocks, fluids, plants, etc. However, such objects as starfish, bacteria, etc. have an ambiguous status with respect to the class of animals. The same kind of ambiguity arises in the case of a number such as 10 in relation to the “class” of all real numbers which are much greater than 1.”

“A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.”