DRDODDS Web Page in M/X

"Usuality, Regularity, and Fuzzy Set Logic"
Thomas Whalen and Brian Schott
International Journal of Approximate Reasoning, 6:4
(June 1992) pages 481-504

Fuzzy Expert Systems
Edited by Abraham Kandel
ISBN 0-8493-4297-X
CRC Press, Inc.
2000 Corporate Blvd., NW
Boca Raton FL USA 33431
FAPR Invited Talk

The Role of Fuzzy Logic in Commonsense Reasoning and Knowledge Representation

Lotfi Zadeh

Within AI, it has long been recognized that commonsense reasoning plays a pivotal role in human reasoning and decision making. Significant progress in modeling commonsense reasoning has been achieved through the use of circumscription, non-monotonic reasoning, default reasoning and related techniques. A substantially different direction is suggested in our paper.

The point of departure in our approach is the assumption that, in general, commonsense knowledge consists of a collection of dispositions, that is, propositions which are usually but not necessarily always true. Such propositions are said to be usuality-qualified.

To deal with dispositions, a branch of fuzzy logic referred to as dispositional logic, is developed. In this logic, syllogistic rules of inference play an important role. In addition, the methodology of computing with words (CW) is employed to draw conclusion from data which are expressed in linguistic rather than numerical form. This leads to the concept of a dispositional theorem -- a concept which may lead to a reorientation of methods of inference which apply when the premises are dispositional rather than categorical in nature.

Lotfi Zadeh
Computer Science Division and the Electronics Research Laboratory,
Department of EECS,
University of California,
Berkeley, CA 94720;
USA
PHONE: ..1 510-642-4959
FAX: ..1 510-642-1712 or ..1 510-642-5775
EMAIL: zadeh@cs.berkeley.edu

http://ilpsoft.eecs.berkeley.edu:9636/~ilpsoft/abstracts/zadeh.4.html
Computing With Words--A Paradigm Shift

(Professor Lotfi A. Zadeh)
(ARO) DAAH04-96-1-0341, BISC, (LLNL) B-291525, (NASA) NCC 2-275, and (ONR) N00014-96-1-0556

Computing, in its traditional sense, involves for the most part manipulation of numbers. By contrast, humans employ words in computing and reasoning, arriving at conclusions expressed as words from premises expressed in a natural language.

By their nature, words are less precise than numbers. For this reason, computing with words is generally less precise than computing with numbers. This raises the question: what is the point of computing with words in preference to computing with numbers? There are two major imperatives. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers. And second, computing with words is advantageous when there is a tolerance for imprecision that can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality.

In our approach, the point of departure in computing with words (CW) is a collection of propositions expressed in a natural language, with a proposition viewed as an implicit constraint on a variable. The variables and the associated constraints are assumed to be expressed as composite words, with a constraining word viewed as a label of a granule, that is, a fuzzy set of points drawn together by similarity. Through a process of explicitation based on test-score semantics, the constrained variable and the constraining relation in a proposition are identified, leading to what is called a canonical form. The primary function of canonical forms is to place in evidence the fuzzy constraints that are implicit in the premises. The constraints can assume a variety of forms, among which are possibilistic, probabilistic, conjunctive, and random-set types. For purposes of computation, the rules of inference in fuzzy logic are employed to propagate the constraints from premises to conclusions. Finally, the fuzzy constraints in conclusions are retranslated into propositions expressed in a natural language.

As a methodology, computing with words has wide-ranging implications on both basic and applied levels. In many ways, CW represents a sharp departure from the deep-seated tradition of according more respect to numbers than to words. The role model for CW is the human mind.

Send mail to : (zadeh@cs.berkeley.edu)
October 15, 1996
The Key Roles of Fuzzy Information Granulation in Human Reasoning, Fuzzy Logic and Computing with Words
Lotfi A. Zadeh*

Abstract

*Computer Science Division and the Electronics Research
Laboratory, Department of EECS, University of California, Berkeley, CA
94720-1776; Telephone: 510-642-4959; Fax: 510-642-1712; E-mail:
zadeh@cs.berkeley.edu. Research supported in part by NASA Grant NCC 2-275,
ONR Grant N00014-96-1-0556, LLNL Grant 442427-26449, and the BISC Program of UC Berkeley.

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 whole.

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 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 which 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.

view a Lotfi Zadeh presentation, on the Computing with Words Methodology, to NASA