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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