The Key Roles of Fuzzy Information Granulation in Human Reasoning, Fuzzy Logic
Wed, 8 Jul 1998 05:33:37 +0200 (MET DST)

Subject: Re: Acquiring Knowledge from Text
Date: 1998/07/01
Message-ID: <6nckhq$tno$>
[Subscribe to]
In article <6nant8$iom$>,
"James Chu" <> wrote:
> Please post reference to literature on CW. I am also working on the same
> idea of using text as the knowledge base for a simulated artificial
> intelligence. I will report more to this group as I have more result to
> report.
> james

Here is the first of some postings on topic of Computing With Words (L. Zadeh)
cheers drdodds

(copyrighted material)
The Key Roles of Fuzzy Information Granulation in Human Reasoning, Fuzzy Logic
and Computing with Words

(Professor Lotfi A. Zadeh)
(ARO) DAAH04-96-1-0341, BISC, (LLNL) B-291525, (NASA) NCC 2-275, and (ONR)

The concepts of granulation and organization play fundamental roles in human
cognition. In a general setting, granulation involves a decomposition of whole
into parts. Conversely, organization involves an integration of parts into

In more specific terms, information granulation (IG) relates to partitioning
a class of points (objects) into granules, with a granule being a clump of
points drawn together by indistinguishability, similarity, or functionality.
The concept of a granule is more general than that of a cluster.

Modes of information granulation in which granules are crisp play important
roles in a wide variety of methods, approaches, and techniques. Among them
are: interval analysis, quantization, rough set theory, diakoptics, divide
and conquer, Dempster-Shafer theory, machine learning from examples,
chunking, qualitative process theory, decision trees, semantic networks,
analog-to- digital conversion, constraint programming, cluster analysis, and
many others.

Important though it is, crisp information granulation (crisp IG) has a major
blind spot. More specifically, it fails to reflect the fact that in much--
perhaps most--of human reasoning and concept formation, granules are fuzzy
rather than crisp. For example, fuzzy granules of a human head are the nose,
forehead, hair, cheeks, etc. Each of the fuzzy granules is associated with a
set of fuzzy attributes, e.g., in the case of the fuzzy granule hair, the
fuzzy attributes are color, length, texture, etc. In turn, each of the fuzzy
attributes is associated with a set of fuzzy values. Specifically, in the
case of the fuzzy attribute length (hair), the fuzzy values are long, short,
not very long, etc. The fuzziness of granules, granule attributes, and
attribute values is characteristic of the ways in which human concepts are
formed, organized, and manipulated.

In human cognition, fuzziness of granules is a direct consequence of fuzziness
of the concepts of indistinguishability, similarity, and functionality.
Furthermore, it is entailed by the finite capacity of the human mind to store
information and resolve detail. In this perspective, fuzzy information
granulation (fuzzy IG) may be viewed as a form of lossy data compression.

Fuzzy information granulation underlies the remarkable human ability to make
rational decisions in an environment of imprecision, uncertainty, and partial
truth. And yet, despite its intrinsic importance, fuzzy information
granulation has received scant attention except in the context of fuzzy
logic, in which fuzzy IG underlies the basic concepts of linguistic variable,
fuzzy if-then rule, and fuzzy graph. In fact, the effectiveness and successes
of fuzzy logic in dealing with real-world problems rest in large measure on
the use of the machinery of fuzzy information granulation. This machinery is
unique to fuzzy logic.

Recently fuzzy information granulation has come to play a central role in the
methodology of computing with words. More specifically, in a natural language
words play the role of labels of fuzzy granules. In computing with words, a
proposition is viewed as an implicit fuzzy constraint on an implicit variable.
The meaning of a proposition is the constraint which it represents.

In CW, the initial data set (IDS) is assumed to consist of a collection of
propositions expressed in a natural language. The result of computation--
referred to as the terminal data set (TDS)--is likewise a collection of
propositions expressed in a natural language. To infer TDS from IDS, the rules
of inference in fuzzy logic are used for constraint propagation from premises
to conclusions.

There are two main rationales for computing with words. First, computing with
words is a necessity when the available information is not precise enough to
justify the use of numbers. And second, computing with words is advantageous
when there is a tolerance for imprecision, uncertainty and partial truth that
can be exploited to achieve tractability, robustness, low solution cost, and
better rapport with reality. In coming years, computing with words is likely
to evolve into an important methodology in its own right with wide-ranging
applications on both basic and applied levels.

Inspired by the ways in which humans granulate human concepts, we can proceed
to granulate conceptual structures in various fields of science. In a sense,
this is what motivates computing with words. An intriguing possibility is to
granulate the conceptual structure of mathematics. This would lead to what may
be called granular mathematics. Eventually, granular mathematics may evolve
into a distinct branch of mathematics having close links to the real world.

In the final analysis, fuzzy information granulation is central to human
reasoning and concept formation. It is this aspect of fuzzy IG that underlies
its essential role in the conception and design of intelligent systems. What
is conclusive is that there are many, many tasks that humans can perform with
ease and that no machine could perform without the use of fuzzy information
granulation. This conclusion has a thought-provoking implication for AI:
without the methodology of fuzzy IG in its armamentarium, AI cannot achieve
its goals.

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