Download Computing with Words: Principal Concepts and Ideas by Lotfi A. Zadeh PDF

By Lotfi A. Zadeh

In essence, Computing with phrases (CWW) is a process of computation within which the gadgets of computation are predominantly phrases, words and propositions drawn from a typical language. CWW relies on fuzzy common sense. In technology there's a deep-seated culture of in accordance even more recognize to numbers than to phrases. In a basic means, CWW is a problem to this practice. what's no longer widely known is that, this day, phrases are utilized in position of numbers in a large choice of functions starting from electronic cameras and family home equipment to fraud detection structures, biomedical instrumentation and subway trains.

CWW bargains a different capability—the potential to precisiate normal language. Unprecisiated (raw) usual language can't be computed with. A key proposal which underlies precisiation of that means is that of the that means postulate: A proposition, p, is a restrict at the values which a variable, X—a variable that's implicit in p—is allowed to take.

CWW has a big ramification for arithmetic. Addition of the formalism of CWW to arithmetic empowers arithmetic to build mathematical options of computational difficulties that are said in a average language. conventional arithmetic doesn't have this capability.

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RATIONALES FOR THE USE OF WORDS use of words A B C necessary advantageous expedient Numbers not known Numbers are known. There is a tolerance for imprecision. Words are good enough. Linguistic summarization 42/263 NOTE z Today, most applications of CWW1, especially in the realm of consumer products, are based on Rationales B and C. A key role is played by linguistic summarization. 43/263 23 24 What Is Computing with Words (CWW)? LINGUISTIC SUMMARIZATION VIA GRANULATION (FUZZY PARTITION) Y f granule L granulation M S 0 0 X Y S medium × large (M×L) *f (fuzzy graph) M L (large) granulation fsummarization*f : if X is small then Y is small *f = if X is medium then Y is large if X is large then Y is small X 0 (For definition of granulation see Slide 94) 44/263 FUZZY LOGIC GAMBIT z Fuzzy Logic Gambit = deliberate imprecisiation through granulation, followed by graduation Y f granulation if X is small then Y is small if X is medium then Y is large summarization if X is large then Y is small 0 z X The Fuzzy Logic Gambit is employed in many applications of fuzzy logic, especially in the realm of consumer products 45/263 What Is Computing with Words (CWW)?

52/263 COMMENT (Kalman 1972) I would like to comment briefly on Professor Zadeh’s presentation. His proposals could be severely, ferociously, even brutally criticized from a technical point of view. This would be out of place here. But a blunt question remains: Is Professor Zadeh presenting important ideas or is he indulging in wishful thinking? 53/263 What Is Computing with Words (CWW)? The most serious objection to fuzzification of system analysis is that lack of methods of system analysis is not the principal scientific problem in the systems field.

RATIONALES FOR THE USE OF WORDS use of words A B C necessary advantageous expedient Numbers not known Numbers are known. There is a tolerance for imprecision. Words are good enough. Linguistic summarization 42/263 NOTE z Today, most applications of CWW1, especially in the realm of consumer products, are based on Rationales B and C. A key role is played by linguistic summarization. 43/263 23 24 What Is Computing with Words (CWW)? LINGUISTIC SUMMARIZATION VIA GRANULATION (FUZZY PARTITION) Y f granule L granulation M S 0 0 X Y S medium × large (M×L) *f (fuzzy graph) M L (large) granulation fsummarization*f : if X is small then Y is small *f = if X is medium then Y is large if X is large then Y is small X 0 (For definition of granulation see Slide 94) 44/263 FUZZY LOGIC GAMBIT z Fuzzy Logic Gambit = deliberate imprecisiation through granulation, followed by graduation Y f granulation if X is small then Y is small if X is medium then Y is large summarization if X is large then Y is small 0 z X The Fuzzy Logic Gambit is employed in many applications of fuzzy logic, especially in the realm of consumer products 45/263 What Is Computing with Words (CWW)?

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