IEEE Systems, Man and Cybernetics Magazine - July 2018 - 53

Remembering Lotfi Zadeh (continued from page 52)
resulting from a set of imprecise linguistic rules describing

language, reasoning, and creativity, and, according to

the behavior of a dynamic system and an observed fact

my understanding, what would help to do so would

thereof). The second was fundamental for extending the

be to develop a type of physics for these three natural

arithmetic operations of addition, rest, multiplication, and

phenomena [S6].

division to fuzzy numbers for computing, e.g., "around four"

Just as physics deals with matter, energy, and movement,

plus "around nine," and so on. It also allowed an arithmetic

CWP should address an experimentally based theoretic

of fuzzy numbers to be established as well as linguistic

science that, up until now, has not existed. To attain such

expressions such as "the probability that John is young is

a science, significant experiments would need to be

tall" to be addressed. The Extension Principle is widely used in

designed and conducted by searching for the actual

problems that concern CWP, along with the extensive use of

uses of linguistic connectives, hedges, quantifiers, relations

linguistic variables and generalized constraints.

of inference and analogy, and so on, on the Internet
[S2]. This, at least, would serve to refine the use of the

Conclusion

mathematical operations usually employed to design

ET: The most remarkable thing in Prof. Zadeh's post-1965 work

them. Since the meaning of words in plain language is

is that it meant something like the opening of a door toward

always context dependent and purpose driven, fuzzy sets

scientific analysis and the technological exploitation of

are not only a matter of degree but, at least with regard

linguistic imprecision. This is work that allows representation

to their application to reality, a matter of design. Badly

through sets, attained thanks to the work on which George

designing the membership functions representing fuzzy

Boole embarked in the mid-19th century, to be extended to

terms could easily lead to solving a problem other than the

other fields.

one currently posed.

Language is permeated by such a large amount of

AS: I don't believe that there will ever be a single

imprecise words that the impossibility of their mathematical

calculus of language, but who knows if there could be

representation through the Boolean algebra of classical

a family of calculus for each specific part of language?

or crisp sets, based in its specification axiom, is a powerful

Ultimately, Boolean algebras are useful for representing

limitation (even if it is not the only one) on the possibility of,

precise reasoning, with either random or possibilistic

first, mechanizing plain language, and, second, common

types of uncertainty; orthomodular lattices serve for the

sense or ordinary reasoning. Without fuzzy sets and fuzzy

uncertain case of quantum physics; standard algebras

relations, it is not actually possible to make machines

of fuzzy sets take care of several cases of imprecise and

think like people with precisely used terms. This limitation

uncertain reasoning, and so on. A calculus of language

is too strong to capture many of the nuances of plain

would require a combination of logics, but at the present,

language. Ortholattices, De Morgan algebras, and even

that challenge would seem to be a chimera. In any case, a

the weaker typical standard algebras of fuzzy sets are

good deal of the history of science and technology lies in

successful for some parts of language but are endowed

the pursuit of utopias.

with laws and properties that cannot always be supposed

ET: Fundamentally, Prof. Zadeh poses an intriguing problem

in plain language and ordinary reasoning. In addition,

to researchers, concerning not only the modeling and

it is not evident that Kolmogorov's theory of probability is

representation of plain language and ordinary reasoning

applicable to the not-always-random uncertainty appearing

[S13], [S14] but also its exploitation for arriving at machines

in linguistic statements, owing essentially to the impossibility

that will actually think like people. That is, he confronts us with

in many cases of assuming the additive law, even though

the ultimate problem of AI.

imprecise events may admit perfect classifications or

AS: AI has to address that ascribed to Seymour Papert's

partitions. Often, with imprecise events, a totality is not

superhuman human fallacy [S1], which says that a machine

recognizable as a sum of disjoint parts. For instance, Prof.

does not think unless it shows superhuman skills. But human

Zadeh's measures of possibility are not additive. The loss and

intelligence is characterized by providing, through the

gain of imprecise information cannot be seen as it can be

processes of trial and error, partial, revisable, and provisional

with precise information.

solutions to problems that are frequently unsharp. In this

Without the possibility of representing plain language and

task, tolerant and robust systems will be desirable, and Prof.

ordinary reasoning, it will be very difficult, if not impossible,

Zadeh's fuzzy logic provides interesting tools that contribute

to untie the famous Gordian Knot of AI. The true future

to this aim.

for such a goal lies in continuing along the lines of CWP
established by Prof. Zadeh. Nonetheless, beforehand, we
will need to learn more about the natural phenomena of

(continued on page 54)

Ju ly 2018

IEEE SyStEmS, man, & CybErnEtICS magazInE

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