Fuzzy Logic and AI

1 Introduction

Many industrial applications of fuzzy logic-based intel­ ligent systems have been successfully developed in the past decade. Recent!:-·. Japanese consumer manufactur­ ers such as Sony, Panasonic , Canon, Minolta, Hitachi , and Nissan has introduced a. wide variety of "intelligent consumer products" employing fuzzy logic into the mar­ ket. As a result, there has been an increasing interest in fuzzy logic in general and its relationship with artificial intelligence, in particular .

Fuzzy Logic and AI

John Yen (co-chair)

Department of Computer Science Texas A&::l\'1 University College Station, TX 17843-:3112 U.S. A.

Didier Dubois and Henri Prade

I.R.I.T.- Equipe Intelligence Artificielle et Robotique

Universite Paul Sa.batier 118 route de Narbonne :31062 Toulouse Cedex

France

Enrique H. Ruspini

Piero Bonissone (co-chair)

Genera.! ELectric CRD Buildg I\.1. Room 5C:32 A 1 River Rd.

Schenectady, N\. 12:309 U.S. A.

Christian Freksa

l._!niversitat Hamburg Fa.chbereich Informatik \VSV. Bodenstedstra.Be 16 2000 Hamburg .50 Germany

Ramon Lopez de Mantaras

Artificial Intelligence Center SRI International 33:3 Ravenswood A venue Menlo Park. CA 9402.5 U.S. A.

Lotfi A. Zadeh

Computer Science Division Department of EECS University of California. Berkeley, CA 74720

U.S. A.

This panel on Fu.:;::y Logic and AI has three major ob­ ject.ives . First , it will provide an overview about the state of the art of fuzzy logic technology and its a.pplication in AI. Second. it will offer insights on promising directions of interdisciplinary research that may play a key role in the development of next generation intelligent syst.ems. Third, and most importantly, such a. panel will encour­ age fruitful technical exchanges between the general AI conununity and the fuzzy logic community.

To achieve these objectives, the panelists are asked to respond to the following questions:

1. In what areas in AI has fuzzy logic offered important contributions?
2. What techniques in AI have been successfully inte­ grated with fuzzy logic?
3. \t\'hat techniques in AI can be synergistically inte­ grated with fuzzy logic?
4. What ideas/techniques in AI can contribute to the further advancement of fuzzy logic technology?
5. What role will fuzzy logic play in the next genera-

C.E.A.B (Centre D~Estudis Avancats de Blanes)

Cami de Santa Barbara BLANES (Girona)

Spain In the following sections. we will summarize the position statement of each panelist regardings the issues listed above.

2 Soft Computing Lotfi A. Zadeh

The past few years have witnessed a rapid growth of interests in a cluster of modes of modeling and compu­ tation which collectively may be described as .soft com­ puting.

The distinguishing characteristic of soft computing is that its primary aim is to achieve t.ract.abilit.v. robust­ n.ess, low cost, and high MIQ (machine intelligence quo­ tient) through an exploitation of the tolerance for impre­ cision and uncertainty. Thus, in soft computing what is usually sought is an approximate solution to a precisely formulated problem or. more typically. an approximate solution to an imprecisely formulated problem.

In general. high precision carries a high cost . The challenge. then. is to exploit the tolerance for imprecision by devising methods of computation which lead to an acceptable solution at low cost. This. in essence, is the guiding principle of soft computing. By its nature , soft computing is much closer to human reasoninO' than the traditional modes of computation. 0

At this juncture, the major components of soft com­ puting are fuzzy logic. neural network theory. and prob­ a:bilistic rea.<;oning techniques. including genetic algo­ nthms, chaos theory, and parts of learning theory. In­ crea.<;ingly. these techniques are used in combination t.o achieve significant improvement in performance adapt­ ability. Among the important application area.<; for soft computing are control systems . expert systems. data compression techniques. image processing. and decision support systems.

It may be argued that it is soft computing- rather than the traditional hard computing - that should be viewed a.<; the foundation for artificial intelligence. In the years ahead, this may well become a widely held position .

3 Fuzzy Logic Controllers: An AI Perspective Piero P. Bonissone

A Fuzzy Logic Controller is a knowledge based system in which the knowledge of process operators or prod­ uct engineers has been used to synthesize a closed loop controller for the process. We view fuzzy logic control technology as a high level language in which we can ef­ ficiently define and synthesize non-linear controllers for a given process . We contrast fuzzy Proportional Inte­ gral (PI) controllers with conventional PI and two di­ mensional sliding mode controllers. Then we compare the development. of Fuzzy Logic Controllers (FLC) with that of Knowledge Based System (KBS) applirations.

Traditional controllers are derived from a mathemat­ ical model of the open-loop process to be controlled, following cla.'Ssical control theory techniques. FLCs are typically derived from a knowledge acquisition process

(or are aut.omatically synthesized from a self-organizing control architecture). In either case. the result. of the synthesis is a Knowledge Base (KB). rather than an al­ gorithm. The KB consists of a set of fuzzy-rules (rules and termsets). which is evaluated by an interpreter . The interpreter is composed of a quantification (or fuzzifica­ tion) stage, au inference engine (or fuzzy matcher). and a defuzzification stage.

\Ve a:nalyze FLCs according to three organizing lay­ ers typically used in describing I~nowledge Ba.sed Sys­ tems: knowledge representation. inference. and control. In the knowledge representation layer we will describe fuzzy state vectors. t.erm-set. of linguistic values, and f~zzy product.io.n I:ules. In the inference layer we will pro­ VIde a geometnc mterpretation for the disjunctive case of t.he generalized modus ponens. a.nd describe the in­ ference process based on fuzzy predicate evaluation . rule Left Hand Side ( LHS) evaluation, rule detachment . and rules aggregation. In the control laver we will show three different defuzzification methods a;Id we illustrate meta­ reasoning capabilities (supervisory mode).

FLC interpreters are used during the development phase of a. FLC application to provide inference trace­ ability (transparency) , which facilitates the KB design. implementation. and refinement . However , the use of an interpreter requires the evaluation of all the rules in the KB at every iteration.

Therefore. after a functional validation (stability or robustness aualysis). the KB is compiled like a. program­ ming language or a. traditional knowledge base applica­ tion, and a simpler run-time engine is used for deploy­ ment. The result of this compilation process is a look­ up table that allows for a faster, more efficient execu­ tion that can be performed by simpler processors . This feature enables us to build inexpensive FLCs for cost­ sensitive applications.

In summary, we consider a Fuzzy Logic Controller to be a high level lauguage with its local semantics. inter­ pret.~r , and compiler . which ena.bles us to quickly syn­ thesize non-linear controllers for dvnamic svstems .

Finally we will illustrate an application of Fuzzy Logic Controllers. We will describe the development of a fuzzy logic hierarchical controller for a. recupa.rative Tur­ boshaft engine. The problem consists in developing a hi­ erarchical supervisory controller that governs the use of ten low level controller. Each low-level controller is de­ signed to otpimize the control function for a specific re­ gion of the engine state space or "engine mode''. We will contrast the behavior of a classical supervisory controller performing mode selection with that a fuzzy supervisorv controller performing mode melding. ·

4 Interpolative, Qualitative, and Plausible Reasoning Modes with Fuzzy Sets Didier Dubois and Henri Prade

On the one hand, fuzzy sets are a. simple but powerful tool for modeling flexibility and gra.dualit.y in knowledge representation, when specifying soft constraints, criteria., queries, or expert rules. Then satisfaction, compatibility become a matter of degree . On the other hand. the concept of a possibility distribution for modeling impre­ cise or uncertain information. introduced by Zadeh in the seventies and the basic principles of approximate reasoning based on the combination and projection of possibilit.y distributions . offer a unified view of soft con­ straint propagation and automated reasoning under un­ certainty. U ncertaint.y is then captured in terms of two modalities graded by possibility and necessity measures. The underlying model of uncert.aint.y is more qualita­ tive than the probabilistic model since based on order­ ing rather than additivity. Especially the grades in the scale [OJ] are mainly used in a purely ordinal manner . An advantage is that it is less demanding in terms of in­ put data than probability theory and that it better gets along with usual symbolic deduction techniques.

Introducing flexibility in the satisfaction of constraints or queries enables the system to avoid situations where there is no solution, or too-many solutions, because the specifications are too demanding. or too permissive. So­ lutions can then be ordered according to the level of satisfaction of the specifications. Graduality in the sat­ isfaction of the condit.ion parts of rules enables the sys­ tem to modulate its conclusion according to the extent. to which the rules apply to a given situation. IVIoreover pos­ sibility theory, a companion framework based on fuzzy sets. offers an original and effective approach for dealing with uncertain and imprecise facts or conclusion parts of rules.

Inference methods ba.<;ed on fuzzy sets can be applied with success to a great variety of reasoning modes. Inter­ polative rea.<;oning enables a control syst.em to determine the value of the command to apply in situations which are intermediary between prototypical ones (where the actions to perform are known). This is encoded by rules of the form "the more the condition is satisfied, the closer we should be to what is prescribed in the conclusion''. By attaching levels of certainty to logical formula.c;, pos­ sibilistic logic offers a simple tool for propagating un­ certainty in deductive reasoning and for dealing with in­ consistency in agreement with non-monotonic reasoning. This corresponds more generally to rules of the form ,. the more the condit.ion is satisfied. the more certain the con­ clusion". Possibilistic ATMS based on possibilistic logic offer a tool for implementing hypothetical reasoning in presence of uncertainty. Analogical reasoning is captured using rules of the form ''the more similar two situations according to some features , the more possible the simi­ larity of the situations with respect. to other features". In abductive reasoning, fuzzy causal relations have been used for a long time. A fuzzy causal relation can be in­ terpreted in different ways. It. may express the intensity of presence of non-binary effects for a given cause, or qualify the possibility or certainty of presence of binary effects. Besides the handling of qualitative or imprecise orders of magnitude in possibility theory is of interest for qualitative rea.c;oning. and for numericalsymbolic in­ terface.

Thus, applications concerned by fuzzy set-ba.c;ed rea­ soning methods are of various types : control systems, decision support. systems, advanced information systems and knowlPdge-based systems .

5 Beyond Fuzzy Sets Christian Freksa

Although Fuzzy Set Theory was mot.ivatl."d largely by properties of natural* human C011Ctpts. thf theory has been most sucNssful in artificial* engineering domaius . so far . vVe will look at 'fuzzy knowledge. from a cognitiw point of view and identify several kinds of representa­ tion relations in each of which fuzziness plays a different roll.". We discuss differences between ahst.ract domains. artificial real domains , and natural real domains and we argue that. dealing with cognitively available knowledge suggests a different. approach for dealing with fuzziness than dealing with formal knowledge.

We propose a fuzzy set - based approach to overcome certain problems of dealing with natural concepts. Like na.t.ural cognitive systems, this approach does not require numbers for representing fuzzy relations. however; in­ stead. the notion of ··conceptual neighborhood'' that we have used in qua.lit.a.t.ive temporal and spatial rea.c;oning is used for representing the mutual arrangement and or­ dering of concepts. Concept. ordering is shown to be important. along two distinct dimensions : 1) the order­ ing of competing concepts (horizontal dimension) and 2) the ordering of concepts according to different granular­ it.y levels (vertical dimension) .

In our view, concepts cognitively typically refer to dear cut ca.c;es rather than to marginal cases. It is good practice to select concepts which fully apply to a given sit.uat.ion (if possible) rather than marginal con­ cepts which apply to a low degree. Fuzziness mainly becomes an issue when we simultaneously deal with two distinct domains, for example with the physical domain and the conceptual domain or with the conceptual do­ mains of two individuals; it. is much less an issue within the conceptual domain of a single individuum. This is true particularly when this individuum deals with con­ cepts abstractly. In other words, not the concepts are fuzzy but. their compatibility with other entities.

We like to suggest that a significant fraction of a rea­ soning process can and should be carried out qualita­ tively within the conceptual domain without the need of going through fuzzy relations. Fuzzy relations, on the other hand, should be represented without numeri­ cal functions when we want. to have a cognitively more adequate model. This requires the development of more elaborate models of the different domains involved in rea­ soning and their int.eraction. Specifically, we must rep­ resent. situation contexts and concept contexts and their interaction in order to go beyond the comparatively well defined domain of engineering applications.

6 Fuzzy Logic: What and Why Enrique H. Ruspini

We will discuss the ba.c;ic concepts that underly fuzzy logic and explain the rea.c;ons for the success of this basic technology. In particular, we will focus on important conceptual connections between the notion of possibility and the concepts of similarity and utility.

\<\'e will also compare fuzzy logic with other approaches to approximate reasoning focusing on the import.ant con­ ceptual differences bet.ween probability and possibility theory.

Our discussion of fundamental concepts and their mo­ tivation will be illustrated by examples drawn from the application of fuzzy logi c to the control of SR.I's Au­ tonomous Mobile Vehicle. which recently participated in the Robot Competition of the 1 9D:) AAAI N a tiona! Con­ ference . We will also describe results from our research on intelligent control and analogical reasoning to clarify our conceptual points.

7 Local Fuzzy Logics m Large Modular Expert Systems

Ramon Lopez de Mantaras

Two of the main characteristics of human problem solv­ ing when faced to complex tasks are : the adequation of general knowledge to particular problems and the de­ pendence of the kind of uncertainty management t.o dif­ ferent subtasks of the problem. Specific subtasks gener­ ally make use of only a subset of the KB. l'v1odulariza­ tion techniques are genera.lly used to build such st.ruc­ t.ured KBS's. From the managementofuncertainty point. of view. modularization allows to associate different lo­ cal uncert.ainty calculi to the different modules if nec­ essary. This rises a communication problem between the modules because facts deduced in a module (with their associated certainty value according to the local uncertainty calculus within this module) will be used by another module using a different uncertainty calculus and in general a different set of certainty values. One way to address this problem is using the capabilities of fuzzy logic as local logics and defining inference preserv­ ing mappings between these local logics. \Ve hav defined and implemented a modular language that, among other characteristics. allows to use fuzzy local logic with a fi­ nite number of linguistic certainty values in the differ­ ent modules used to represent the deductive and control knowledge associated to the different. subtasks of a given problem. This approach has been (and is being) used in the development of several large medical expert sys­ tems where the possibility t.o define fuzzy local logics greatly facilitated the solution to the problems encoun­ tered. Two large expert systems (one over 1000 rules and 400 facts and another with over 1500 rules and almost. 500 fact.s ar;; well as close to 100 meta-rules) have been developed and fully validated by means of a multi-centre validation involving six hospitals whose physicians had not been involved with the development of thr systems.

For one of the applications we could compare the per­ formance of the expert system with the physicians while it was being used in a field test in the urgency service of one hospital. The validation results show a superior per­ formance since only tow of the specialists where dearly better than the system.

8 Summary

We briefly summanze the statements of the panelists below:

1. In ·what applications areas in AI has fuzzy logic of­ fered important. contributions?
2. Intelligent control systems ( Bonissone. Zadeh . Dubois and Prade)
3. Expert systems (!Vlantaras. Zadeh. Dubois and Prade)
4. Data compression techniques (Zadeh)
5. Image processing (Zadeh)
6. Decision support syst.ems (Zadeh. Dubois and Prade)
7. Advanced information systems (Dubois and Prade)
8. Autonomous mobile robot (Ruspini)
9. \Vhat techniques in AI have been successfully inte­ grated with fuzzy logic'?
10. Possibility theory (Dubois and Prade)
11. Aut.omated reasoning under uncertainty ( R.us­ pini. Dubois and Prade)
12. Case-based reasoning ( Bonissone)
13. What techniques in AI can be synergistically inte­ grated with fuzzy logic'?
14. Soft constraint. satisfaction (Dubois and Prade)
15. Qualitative reasoning ( Freksa)
16. What idea<>/techniques in AI can contribute to the further advancement of fuzzy logic technology?
17. Nonmonotonic rear;;oning and ATMS (Dubois and Prade)
18. Multimodal matching and multicriteria deci­ sion making ( Freksa)
19. What role will fuzzy logic play in the next. genera­ tion intelligent syst.ems'?
20. Integrating symbolic reasoning with learning capabilities of neural networks and genetic al­ gorithms (Zadeh, Dubois and Prade)
21. Soft computing (Zadeh)