By Lotfi A. Zadeh

In essence, Computing with phrases (CWW) is a process of computation during which the gadgets of computation are predominantly phrases, words and propositions drawn from a usual language. CWW relies on fuzzy good judgment. In technological know-how there's a deep-seated culture of in accordance even more appreciate to numbers than to phrases. In a primary approach, 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 wide selection of functions starting from electronic cameras and family home equipment to fraud detection structures, biomedical instrumentation and subway trains.

CWW deals a different capability—the potential to precisiate typical language. Unprecisiated (raw) average language can't be computed with. A key inspiration which underlies precisiation of that means is that of the which 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 suggestions of computational difficulties that are acknowledged in a ordinary language. conventional arithmetic doesn't have this capability.

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**Example text**

The meaning postulate, MP, may be expressed as: MP: p = restriction on X z The meaning postulate is the point of departure in precisiation of meaning in CWW. 82/263 45 46 Phase 1—Precisiation THE CONCEPT OF A RESTRICTION— A CLOSER LOOK z I am asked: What is the value of a realvalued variable X? My answer is: I do not know the value precisely but I have a perception which I can express as a restriction (generalized constraint) (Zadeh 2006a) on the values which X can take. 83/263 EXAMPLES 8 ≤ X ≤ 10 z X is small z Usually X is small z X is normally distributed with mean 9 and variance 2.

Indeed, in retrospect, the unconventional ideas suggested by me may well be viewed as self-evident to the point of triviality. Thank you. 60/263 KEY POINT z What Kalman and other critics of CWW did not realize is that precisiation of meaning opens the door to construction of a system of computation which offers an important capability that traditional systems of computation do not have— the capability to compute and reason with information described in a natural language. 61/263 What Is Computing with Words (CWW)?

A special case of a combination of possibilistic and probabilistic restrictions is a Z-restriction (r=z) (Zadeh 2011) 86/263 47 48 Phase 1—Precisiation EXAMPLES z Possibilistic restriction (r=blank): R(X): X is A where A is a fuzzy set in U with the membership function µA. A plays the role of the possibility distribution of X (Zadeh 1978) Poss(X=u)= µA(u) 87/263 PROBABILISTIC RESTRICTION z Probabilistic restriction (r=p): R(X): X isp P where P plays the role of the probability distribution of X.