- Email: [email protected]
Cognitive sciences, decision technology, and fuzzy sets
INFORMATION
SCIENCES
57-58,
287-295 (1991)
Cognitive Sciences, Decision Technology,
287
and Fuzzy Sets
H.-J. ZIMMERMANN RWTH Auchen,
5100 Auchen.
Germuny
ABSTRACT Cognitive sciences, decision theory, artificial intelligence, operations research, and fuzzy set theory are areas which are inter related; they either share their origins, their main subject, or they use quite similar approaches. This contribution investigates the relationships between these disciplines and tries to explore inheritage, common features and basic differences.
1. INTRODUCTION Cognitive Science focuses on one of the oldest subject areas of scientific reflection, human thinking itself. What does it mean that somebody thinks, imagines, or perceives? How does a human brain perform these functions, and can this behavior be imitated by artificial constructions? For a long time, the location of scientific reflection on thinking was philosophy. This branch of scientific endeavor included psychology. In the 19th century, sciences split up into more focused disciplines, psychology parted from philosophy and added an “empirical leg” to its so-far-existing “philosophical leg.” In addition, new scientific areas developed in the 20th century, such as decision theory, operations research, management science, and artificial intelligence, which all to a higher or lower degree were concerned with either cognition, decision, thinking, or information processing. Nowadays the meaning of cognitive science may be quite different from its definition in the 19th century, and so may be its semantic interpretation and scope. In the following, we will try to trace connections and differences between some of these similar but also different areas with “cognitive concern.” It is hoped that this may avoid misinterpretations of results in one of these areas by researchers of another of these disciplines. 2.
COGNITIVE SCIENCES VS. DECISION TECHNOLOGY
Let us first review the origin and the development of cognitive science in somewhat more detail: as mentioned above, the origin of psychology can be 0 Elsevier Science Publishing Co., Inc. 1991 655 Avenue of the Americas, New York, NY 10010
0020-0255/91/$03.50
288
H.-J. ZIMMERMANN
found in philosophy. Behaviorism certainly opened psychology for approaches that before were used in natural sciences. It opened the door to the use of experiments and computer simulation to explore mental processes. On the other hand, it reduced the perspective to only observing stimulus-reaction schemes, regarding the human brain as a black box. This prevented us from looking for and finding adequate models for human mental processes. In this sense, the new cognitive science did not start before the ’60s of this century. In cognitive psychology, the computer and the emergence of programs like the logic thinker (LT) had a profound effect, even though cognitive psychology does not share the enthusiasm of information-processing psychology for computer models: “The activities of the computer itself seemed in some ways akin to cognitive processes. Computers accept information, manipulate symbols, store items in “memory” and retrieve them again, classify inputs, recognize patterns, and so on. Whether they do these things just like people was less important than that they do them at all. The coming of the computer provided a much-needed reassurance that cognitive processes were real. . . . Some theorists even maintained that all psychological theories should be explicitly written in the form of computer programs.“[4]
These theorists were Newell, Simon, and J. C. Shaw. Their position that computer programs can be psychological theories is the point at which cognitive psychology and information-processing psychology part company. For most cognitive psychologists, information processing is a metaphor for human thought, a means of focusing attention on new and interesting questions about the mind. Very few cognitive psychologists have implemented informationprocessing models-programs-of their theories. At the present time, two major paradigms in cognitive sciences can be recognized, both of which claim to supply adequate models for cognitive phenomena: 1. The more orthodox cognitive science has the basic paradigm which is characterized by the “computational theory of mind.” Intelligent systems are regarded as “physical symbol systems” and a necessary condition for their intelligent behavior is the rule-inducted manipulation of internal symbolical structures. This is an approach which is still very common in operations research, in cognitive decision theory, and in “classical” expert system technology. 2. A newer paradigm, on which the connectionism is based, is the idea that cognitive systems consist of a very large number of primitive subsystems. Two levels of consideration can be distinguished: on the one hand, global cognitive aspects of the systems behavior are described, and on the other hand, on a more microscopic level, the local interactions of elementary units
COGNITIVE SCIENCES
289
are considered. This paradigm is pretty young and develops in the direction of neural nets. At the present time, this paradigm just starts to enter disciplines, such as artificial intelligence, primarily via neural net theory. Even though these two paradigms can be found in both subdisciplines, artificial intelligence still seems to be the more engineering-type discipline supplying the methods for the construction of intelligent systems and their realization, while cognition psychology is part of psychology, which is concerned with empirical research of cognitive phenomena under controlled conditions. The term “intelligence” as used in AI is certainly not the term as it is used in psychology but follows more the intuitive and very ill-defined term as it is used in the day-to-day language. Advantages and disadvantages of the two paradigms shall not be discussed here in detail. It should, however, be mentioned that the classical paradigm seems to be more appropriate intuitively but sometimes excludes, particularly when thinking of expert systems, exactly the potential of the experts: very often, for instance, certain inferences of human experts derived on the basis of highly sophisticated performance of the human cognitive system are used, which are only modelable in a very incomplete fashion in a natural language and quite less in a formal language. In this respect available results of empirical research in fuzzy-set theory dealing with semantic interpretations of linguistic variables and formal operators (and, or, etc.) are of particular interest. Using the second paradigm, the ability of a system to learn is already given on a cognitively independent level, a neural level; therefore, the designer of a cognitive system does not have to introduce explicitly knowledge which is already included in the structure of the system. The real goal of cognitive sciences is to investigate function, structure, and performance of cognitive systems. It is assumed that a detailed understanding can only be achieved by and through the construction of a model for which two strategies are basically possible: 1. One designs as detailed as possible the functional architecture of a natural cognitive system in order to reconstruct the desired cognitive behavior. 2. One abstracts entirely from natural systems and tries to realize cognitive processes by the construction of artificial systems which are realized, i.e., we experiment with these systems and investigate their “cognitive” behavior. Essentially, three major subgoals can be recognized: a. investigation of natural cognitive systems b. validation of cognitive models c. design of artificial cognitive systems. Looking at handbooks or journals of artificial intelligence, it becomes ob-
290
H.-J. ZIMMERMANN
vious that this area during the last three decades has been concentrating on a number of theoretical and also applied topics, each of which has grown into an almost separate discipline; just to mention some of them: search, knowledge representation, natural language understanding, programming languages for A.I., automatic programming, automatic deduction, vision, learning, and inductive inference and problem-solving. One of the last and youngest of the children is certainly the area of expert systems, the origin of which might be found in the research of the general problem solver (GPS) in the ’50s and ’60s in Pittsburgh. This type of research had disappeared from the public view for quite a while, probably due to a lack of processing power of the then available computers. It has reappeared almost explosively during the ’80s. Expert system technology can certainly be considered a child of artificial intelligence; still I would like to distinguish three very different types of views on expert systems: 1. Expert system technology as a specific type of programming computer systems 2. Expert systems as a child of the general problem solver which are directed at rather ill-structured problems which so far could only be solved by a human expert 3. Expert systems as a quite easily sellable product in the market of computer programs Re 1. This is a concept of an expert system which is certainly very computer science-oriented and represents very strongly the computer science fatherhood of artificial intelligence. This is probably still the most common approach and can be considered an extension of higher programming languages and programming concepts which are more or less independent of the application areas and the intended hardware. Programming languages such as LISP, PROLOG, tools such as OPSS, KEE, etc., and a large number of so-called shells belong into this area. Re 2. This second type bases on the distinction between facts and programs (knowledge base and inference engine) which was already used in the general problem solver. It can also be considered as an extension of decision support systems and other computer supported systems which always assume that the problem situation can be structured well in a mathematical sense. This becomes particularly obvious when considering so called “second or third generation expert systems” which distinguish between “shallow knowledge” (which is the real expert knowledge) and “deep knowledge” (which corresponds to the traditional algorithmic knowledge used in decision-support sys-
COGNITIVE
SCIENCES
291
terns). For this type of expert system inheritage can certainly be asserted from the general problem solver as a father. Expert systems of this type are normally considered to have the following features: a) they are aimed at ill-structured and uncertain problem situations b) they have some inference capabilities c) they apply only to very narrow domains d) they contain “expert knowledge” in an appropriate representation to either substitute or support experts e) they are particularly user-friendly as interactive systems f) because they do not offer the “correctness-guaranty,” they should offer an explanatory module. This type of expert system makes a lot of sense to me as somebody coming and being in the area of operations research as an extension of the traditional and well-developed OR systems. Unfortunately, not too many of these systems are yet available. I will come back to this type of system a little bit later. Re 3. A third type of system is what one finds generally in practice apart from the numerous shells and tools: the driving force for this third type of expert system seems to be the selling power of the term “expert system.” For some reasons unknown to me, expert systems in large parts of our economies and public administrations have become synonymous with modern problem-solving. The situation is somewhat similar to that at the beginning of the ’60s when the availabillity of a computer was equated to modern management. If one looks more closely at these systems, they match most the first type of expert system in which they are programmed differently from the traditional software. They have some inference capability, are normally rule-based, apply to only narrow domains, are relatively user-friendly but they hardly ever aim at ill-structured problems, disregard uncertainty almost altogether, supply hardly any facility for learning or knowledge acquisition, and their explanatory module is extremely elementary if it exists at all. Still these systems seem to serve a certain purpose in practice, particularly since practitioners, in my experience, are not yet very sensitive and aware of uncertainty in their diagnostic or planning processes. Let us now turn to “decision technology”: Decision theory as a formal theory, nowadays often called “statistical decision theory,” “prescriptive decision theory,” has its origins already in decision theory,” or “normative the 18th century and before, when scientists started to think about probability (Bernoulli 1654-1705, Laplace 1749-1827, etc.). Another source is certainly the theory of games predominantly developed by von Neumann and Mor-
292
H.-J. ZIMMERMANN
genstern in the first half of this century. This type of decision theory, even though probably still used most often as a reservoir to model decisions in business administration, management science, etc., is not concerned with cognition at all. In it, “decision” is defined as quadruple or quintuple or as a timeless abstract act of choice. Having hardly anything in common with this theory-apart from the name-is the much younger “descriptive decision theory” or, better, “empirical cognitive decision theory” which, in contrast to the normative decision theory, is a factual science [lo]. Its roots are very similar to those of artificial intelligence and names such as Newell and Simon [5], Miller 133,Pribram 161 and others are very often cited as scientists who have at least strongly influenced the initial stages of this theory. Here a decision is seen as a special mental or cognitive process. This process of information processing is very similar to processes which are assumed for cognitive activities such as planning, problem solving, etc. This type of research seems to belong quite clearly to cognitive science. By decision technology, decision aid, etc., one normally means either computer-supported or even other supporting systems which help either to improve human decisions or even delegate them to, for instance, electronic data processing systems. The main motive of these areas is not search for (scientific) truth but improvement of existing systems or processes. 3. OPERATIONS RESEARCH, DECISION TECHNOLOGY, FUZZY SET THEORY
AND
Operations research, decision technoloogy and fuzzy-set theory are often mentioned in one breath and they really have a lot in common. Decision technology has already been characterized briefly. It would certainly exceed the scope of this contribution to describe OR and fuzzy-set theory in detail. Therefore, just a few of their characteristics shall be mentioned. Operations research, born in 1937, is probably the oldest of the areas and is reaching the age of grandfathers. Whether the best parts of its life are still ahead of it will largely depend on the directions it develops in the future. Operations research (OR), similar to AI and, as we will see, fuzzy-set theory, has very strong relationships to information processes and to decision making. It also has the following two features: 1, It has many facets, i.e., not a unique generally accepted definition. Some people look at it as a part of mathematics; others, including me, regard it as a technology which does not search for truth, as a science does, but which wants to improve sociotechnological processes and systems, mainly by using mathematical models and methods. Besides these approaches, heuristics is probably the most typical tool of OR of the second kind. It is exactly this
COGNITIVE SCIENCES
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area which offers the most links to the other two areas and probably also the largest future potential for OR. 2. It has gone through ups and downs, similar to AI. In the ’50s and ’60s it was restricted to mathematically well-structured, mainly operational, problems, and consequently to the development of powerful mathematical tools. Ill-structured and strategic problems were left to other, more qualitative, disciplines. This, in the ‘7Os, led to the situation of disillusion when companies closed down their OR departments and famous colleagues claimed that “OR is dead and just not yet buried.” Since the middle of the ‘8Os, chances for the development of OR have appeared which have hardly ever existed before. Three of the main barriers to successful applications of OR in the ’60s and ’70s have disappeared: missing data, missing efficient software and missing high-powered and cheap hardware. Let’s now turn to our third area. Fuzzy-sets theory is obviously different from cognitive science in at least two aspects: It was begun by one man, Lotfi Zadeh [9], and it started as a formal concept and not as research on a real object such as cognitive processes. This notion should not be misunderstood: Zadeh’s ideas may have been inspired by looking at reality, but they first resulted in formal concepts and theories. In the meantime, fuzzy-set theory has developed in a very diverse fashion which certainly speaks well for the high potential of the original concept. The development concerns the theory itself as a formal theory, it concerns the development of a number of specialized subtheories (possibility theory, rough sets, named sets, etc.), and it concerns the application and use of concepts of a fuzzy theory to other areas such as mathematical areas (topology, etc.), optimization, mathematical programming, cluster theory, fuzzy control, approximate reasoning, economic theory, muticriteria analysis, and uncertainty modeling. The last area is certainly shared with other theories such as probability theory, belief theory, and evidence theory. But I believe that fuzzy-set theory has, to a very large degree, made many people aware of different types of uncertainty (lexical uncertainty, etc.) which were before either not recognized at all or modeled by probability theory. The character of the presently existing models and theories varies considerably. There are parts which can certainly be considered as a formal science, there are other parts which understand themselves as factual science (and then sometimes come pretty close to cognitive science), and there are numerous models and techniques which can be regarded as a technology. The possibly unexpected fast development of fuzzy-set theory worldwide and in many directions has also led to a few weaknesses in the sense that a variety of areas which already exist do not yet represent a homogeneous theoretical body in terms of terminology or methodology. We do not yet have any unique semantic interpretation of fuzziness except that it
H.-J. ZIMMERMANN means a gradual transition from one extreme to the other. This can, however, be from certainty to impossibility, from full membership to non-membership, from feasibility to nonfeasibility, or from optimality to far from optimum. Rather than investigating the present status of fuzzy-set theory, I shall now turn to the inter-relationships between OR, expert systems as part of AI, and fuzzy-set theory (FSTH): It seems to be obvious that fuzzy-set theory as a whole cannot be part of cognitive science because considerable parts of fuzzy-set theory do not focus on cognitive processes at all. This is particularly true for mathematical developments in fuzzy-set theory and for the applications of fuzzy sets to mathematical theories. On the other hand, fuzzy-set applications in psychology seem to me clearly part of cognitive psychology. Similar statements can be made about the relationship of FSTH to OR. FSTH is certainly not part of OR, but fuzzy linear programming would, for instance, be considered as belonging to OR. The same holds for fuzzy pert, fuzzy multi criteria analysis and approximate reasoning methods in production control. Maybe the question is ill-posed: Rather than asking “Does FSTH belong to cognitive sciences, to OR, or to AI?,” which certainly cannot be answered affirmatively, one should ask “What are the potential synergetic effects of these three areas?” For an outsider it sometimes seems difftcult to understand how some areas of artificial intelligence, such as knowledge representation, vision, understanding natural and spoken language, can do without efficient and appropriate tools to model context dependently gradual relationships and generic phenomena, This would not have to be fuzzy-set theory. But fuzzy-set theory would certainly be well suited for it. I think the reason why AI overwhelmingly still neglects tools such as fuzzy-set theory is that the subtasks of transforming a non-dichotomous structure into a dichotomous structure are mostly left to the heads of the human beings. 4.
DECISION SCIENCES AS AN UMBRELLA?
So far, we can conclude that the intersection of (new) cognitive science, operations research, and fuzzy-set theory is not empty but that none of these three areas can be considered to contain the other two. One phenomenon which, to my mind, plays a central part in all three disciplines is that of a decision. Admittedly, the inte~retation of “decision” is not the same in these three areas and the term does not even have a unique semantic definition in two of the three: In OR a decision as an act of choice
COGNITIVE
SCIENCES
29.5
is the model one looks at when calling optimization models special-decision models. On the other hand, when designing adequate interfaces between EDP systems and human users, OR people base their considerations more on the views of descriptive-decision theory than on those of decision logic. It is similar in fuzzy-set theory: When Bellman and Zadeh [1970] defined “a dethey had the model of normative decision cision in a fuzzy environment,” theory in mind. On the other hand, information processing is the core issue when talking about fuzzy sets, linguistic variables, or approximate reasoning in the context of, for instance, expert systems which might be used for decision support. The question of whether the concern with cognitive processes, their paradigms, or their consideration of decision is the strongest link between the areas considered is probably difficult to answer. Maybe their strongest common feature is the fact that in all three aspects they have similar views? REFERENCES 1. K. M. Colby, Arti’cial Paranoia: Computer Simulation of Paranoid Processes. Pergamon Press. Elmsford, N.Y.. 1975. 2. C. Lischka, and J. Diederich, Gegenstand und Methode der Kognitionswissenschaft. Der-GMD-Spiegel 213121-31 (1987) 3. G. A. Miller, Thinking. cognition, and learning. in The Behavioral Sciences
4. 5. 6. 7. 8.
To-day, B.
Berelson, (Ed.) Evanston, New York 1964. U. Neisser, Cognition and Reality. Freeman, San Francisco, 1976. A. Newell, and H. Simon, The logic theory machine. IRE Transactions on Information Theory 3:61-79 (1956). K. H. Pribram, On the neurology of thinking, Beh. SC.. pp. 265 (1959). Z. W. Pylyshyn, Computation and Cognition. Toward a Foundation of Cognitive Science, MIT Press, Cambridge, 1984. P. Smolensky, Connectionist AI, symbolic AI, and the brain. Art. fnt. Review 1:95-
109 (1987). 9. L. A. Zadeh, Fuzzy sets, lnf. Control 8:338-353
(1965).
IO. H.-J. Zimmermann, Testability and meaning of mathematical models in social sciences, Math. Mode/ 1:123-139 (1980). II. H.-J. Zimmermann, Fuzzy Set Theory- and its Applications. Kluwer-Nijhoff, Boston. 1985. 12. H.-J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems. Kluwer-Nijhoff, Boston, 1987. 13. H.-J. Zimmermann, Probabilistic and non-probabilistic representation of uncertainties in expert systems, in Mathematical Mode/s for Decision Support, G. Mitra (Ed.) Springer. Berlin, Heidelberg, N.Y., 1988. p. 613-630. Received
15 March 1990; revised 25 July 1990
SCIENCES
57-58,
287-295 (1991)
Cognitive Sciences, Decision Technology,
287
and Fuzzy Sets
H.-J. ZIMMERMANN RWTH Auchen,
5100 Auchen.
Germuny
ABSTRACT Cognitive sciences, decision theory, artificial intelligence, operations research, and fuzzy set theory are areas which are inter related; they either share their origins, their main subject, or they use quite similar approaches. This contribution investigates the relationships between these disciplines and tries to explore inheritage, common features and basic differences.
1. INTRODUCTION Cognitive Science focuses on one of the oldest subject areas of scientific reflection, human thinking itself. What does it mean that somebody thinks, imagines, or perceives? How does a human brain perform these functions, and can this behavior be imitated by artificial constructions? For a long time, the location of scientific reflection on thinking was philosophy. This branch of scientific endeavor included psychology. In the 19th century, sciences split up into more focused disciplines, psychology parted from philosophy and added an “empirical leg” to its so-far-existing “philosophical leg.” In addition, new scientific areas developed in the 20th century, such as decision theory, operations research, management science, and artificial intelligence, which all to a higher or lower degree were concerned with either cognition, decision, thinking, or information processing. Nowadays the meaning of cognitive science may be quite different from its definition in the 19th century, and so may be its semantic interpretation and scope. In the following, we will try to trace connections and differences between some of these similar but also different areas with “cognitive concern.” It is hoped that this may avoid misinterpretations of results in one of these areas by researchers of another of these disciplines. 2.
COGNITIVE SCIENCES VS. DECISION TECHNOLOGY
Let us first review the origin and the development of cognitive science in somewhat more detail: as mentioned above, the origin of psychology can be 0 Elsevier Science Publishing Co., Inc. 1991 655 Avenue of the Americas, New York, NY 10010
0020-0255/91/$03.50
288
H.-J. ZIMMERMANN
found in philosophy. Behaviorism certainly opened psychology for approaches that before were used in natural sciences. It opened the door to the use of experiments and computer simulation to explore mental processes. On the other hand, it reduced the perspective to only observing stimulus-reaction schemes, regarding the human brain as a black box. This prevented us from looking for and finding adequate models for human mental processes. In this sense, the new cognitive science did not start before the ’60s of this century. In cognitive psychology, the computer and the emergence of programs like the logic thinker (LT) had a profound effect, even though cognitive psychology does not share the enthusiasm of information-processing psychology for computer models: “The activities of the computer itself seemed in some ways akin to cognitive processes. Computers accept information, manipulate symbols, store items in “memory” and retrieve them again, classify inputs, recognize patterns, and so on. Whether they do these things just like people was less important than that they do them at all. The coming of the computer provided a much-needed reassurance that cognitive processes were real. . . . Some theorists even maintained that all psychological theories should be explicitly written in the form of computer programs.“[4]
These theorists were Newell, Simon, and J. C. Shaw. Their position that computer programs can be psychological theories is the point at which cognitive psychology and information-processing psychology part company. For most cognitive psychologists, information processing is a metaphor for human thought, a means of focusing attention on new and interesting questions about the mind. Very few cognitive psychologists have implemented informationprocessing models-programs-of their theories. At the present time, two major paradigms in cognitive sciences can be recognized, both of which claim to supply adequate models for cognitive phenomena: 1. The more orthodox cognitive science has the basic paradigm which is characterized by the “computational theory of mind.” Intelligent systems are regarded as “physical symbol systems” and a necessary condition for their intelligent behavior is the rule-inducted manipulation of internal symbolical structures. This is an approach which is still very common in operations research, in cognitive decision theory, and in “classical” expert system technology. 2. A newer paradigm, on which the connectionism is based, is the idea that cognitive systems consist of a very large number of primitive subsystems. Two levels of consideration can be distinguished: on the one hand, global cognitive aspects of the systems behavior are described, and on the other hand, on a more microscopic level, the local interactions of elementary units
COGNITIVE SCIENCES
289
are considered. This paradigm is pretty young and develops in the direction of neural nets. At the present time, this paradigm just starts to enter disciplines, such as artificial intelligence, primarily via neural net theory. Even though these two paradigms can be found in both subdisciplines, artificial intelligence still seems to be the more engineering-type discipline supplying the methods for the construction of intelligent systems and their realization, while cognition psychology is part of psychology, which is concerned with empirical research of cognitive phenomena under controlled conditions. The term “intelligence” as used in AI is certainly not the term as it is used in psychology but follows more the intuitive and very ill-defined term as it is used in the day-to-day language. Advantages and disadvantages of the two paradigms shall not be discussed here in detail. It should, however, be mentioned that the classical paradigm seems to be more appropriate intuitively but sometimes excludes, particularly when thinking of expert systems, exactly the potential of the experts: very often, for instance, certain inferences of human experts derived on the basis of highly sophisticated performance of the human cognitive system are used, which are only modelable in a very incomplete fashion in a natural language and quite less in a formal language. In this respect available results of empirical research in fuzzy-set theory dealing with semantic interpretations of linguistic variables and formal operators (and, or, etc.) are of particular interest. Using the second paradigm, the ability of a system to learn is already given on a cognitively independent level, a neural level; therefore, the designer of a cognitive system does not have to introduce explicitly knowledge which is already included in the structure of the system. The real goal of cognitive sciences is to investigate function, structure, and performance of cognitive systems. It is assumed that a detailed understanding can only be achieved by and through the construction of a model for which two strategies are basically possible: 1. One designs as detailed as possible the functional architecture of a natural cognitive system in order to reconstruct the desired cognitive behavior. 2. One abstracts entirely from natural systems and tries to realize cognitive processes by the construction of artificial systems which are realized, i.e., we experiment with these systems and investigate their “cognitive” behavior. Essentially, three major subgoals can be recognized: a. investigation of natural cognitive systems b. validation of cognitive models c. design of artificial cognitive systems. Looking at handbooks or journals of artificial intelligence, it becomes ob-
290
H.-J. ZIMMERMANN
vious that this area during the last three decades has been concentrating on a number of theoretical and also applied topics, each of which has grown into an almost separate discipline; just to mention some of them: search, knowledge representation, natural language understanding, programming languages for A.I., automatic programming, automatic deduction, vision, learning, and inductive inference and problem-solving. One of the last and youngest of the children is certainly the area of expert systems, the origin of which might be found in the research of the general problem solver (GPS) in the ’50s and ’60s in Pittsburgh. This type of research had disappeared from the public view for quite a while, probably due to a lack of processing power of the then available computers. It has reappeared almost explosively during the ’80s. Expert system technology can certainly be considered a child of artificial intelligence; still I would like to distinguish three very different types of views on expert systems: 1. Expert system technology as a specific type of programming computer systems 2. Expert systems as a child of the general problem solver which are directed at rather ill-structured problems which so far could only be solved by a human expert 3. Expert systems as a quite easily sellable product in the market of computer programs Re 1. This is a concept of an expert system which is certainly very computer science-oriented and represents very strongly the computer science fatherhood of artificial intelligence. This is probably still the most common approach and can be considered an extension of higher programming languages and programming concepts which are more or less independent of the application areas and the intended hardware. Programming languages such as LISP, PROLOG, tools such as OPSS, KEE, etc., and a large number of so-called shells belong into this area. Re 2. This second type bases on the distinction between facts and programs (knowledge base and inference engine) which was already used in the general problem solver. It can also be considered as an extension of decision support systems and other computer supported systems which always assume that the problem situation can be structured well in a mathematical sense. This becomes particularly obvious when considering so called “second or third generation expert systems” which distinguish between “shallow knowledge” (which is the real expert knowledge) and “deep knowledge” (which corresponds to the traditional algorithmic knowledge used in decision-support sys-
COGNITIVE
SCIENCES
291
terns). For this type of expert system inheritage can certainly be asserted from the general problem solver as a father. Expert systems of this type are normally considered to have the following features: a) they are aimed at ill-structured and uncertain problem situations b) they have some inference capabilities c) they apply only to very narrow domains d) they contain “expert knowledge” in an appropriate representation to either substitute or support experts e) they are particularly user-friendly as interactive systems f) because they do not offer the “correctness-guaranty,” they should offer an explanatory module. This type of expert system makes a lot of sense to me as somebody coming and being in the area of operations research as an extension of the traditional and well-developed OR systems. Unfortunately, not too many of these systems are yet available. I will come back to this type of system a little bit later. Re 3. A third type of system is what one finds generally in practice apart from the numerous shells and tools: the driving force for this third type of expert system seems to be the selling power of the term “expert system.” For some reasons unknown to me, expert systems in large parts of our economies and public administrations have become synonymous with modern problem-solving. The situation is somewhat similar to that at the beginning of the ’60s when the availabillity of a computer was equated to modern management. If one looks more closely at these systems, they match most the first type of expert system in which they are programmed differently from the traditional software. They have some inference capability, are normally rule-based, apply to only narrow domains, are relatively user-friendly but they hardly ever aim at ill-structured problems, disregard uncertainty almost altogether, supply hardly any facility for learning or knowledge acquisition, and their explanatory module is extremely elementary if it exists at all. Still these systems seem to serve a certain purpose in practice, particularly since practitioners, in my experience, are not yet very sensitive and aware of uncertainty in their diagnostic or planning processes. Let us now turn to “decision technology”: Decision theory as a formal theory, nowadays often called “statistical decision theory,” “prescriptive decision theory,” has its origins already in decision theory,” or “normative the 18th century and before, when scientists started to think about probability (Bernoulli 1654-1705, Laplace 1749-1827, etc.). Another source is certainly the theory of games predominantly developed by von Neumann and Mor-
292
H.-J. ZIMMERMANN
genstern in the first half of this century. This type of decision theory, even though probably still used most often as a reservoir to model decisions in business administration, management science, etc., is not concerned with cognition at all. In it, “decision” is defined as quadruple or quintuple or as a timeless abstract act of choice. Having hardly anything in common with this theory-apart from the name-is the much younger “descriptive decision theory” or, better, “empirical cognitive decision theory” which, in contrast to the normative decision theory, is a factual science [lo]. Its roots are very similar to those of artificial intelligence and names such as Newell and Simon [5], Miller 133,Pribram 161 and others are very often cited as scientists who have at least strongly influenced the initial stages of this theory. Here a decision is seen as a special mental or cognitive process. This process of information processing is very similar to processes which are assumed for cognitive activities such as planning, problem solving, etc. This type of research seems to belong quite clearly to cognitive science. By decision technology, decision aid, etc., one normally means either computer-supported or even other supporting systems which help either to improve human decisions or even delegate them to, for instance, electronic data processing systems. The main motive of these areas is not search for (scientific) truth but improvement of existing systems or processes. 3. OPERATIONS RESEARCH, DECISION TECHNOLOGY, FUZZY SET THEORY
AND
Operations research, decision technoloogy and fuzzy-set theory are often mentioned in one breath and they really have a lot in common. Decision technology has already been characterized briefly. It would certainly exceed the scope of this contribution to describe OR and fuzzy-set theory in detail. Therefore, just a few of their characteristics shall be mentioned. Operations research, born in 1937, is probably the oldest of the areas and is reaching the age of grandfathers. Whether the best parts of its life are still ahead of it will largely depend on the directions it develops in the future. Operations research (OR), similar to AI and, as we will see, fuzzy-set theory, has very strong relationships to information processes and to decision making. It also has the following two features: 1, It has many facets, i.e., not a unique generally accepted definition. Some people look at it as a part of mathematics; others, including me, regard it as a technology which does not search for truth, as a science does, but which wants to improve sociotechnological processes and systems, mainly by using mathematical models and methods. Besides these approaches, heuristics is probably the most typical tool of OR of the second kind. It is exactly this
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area which offers the most links to the other two areas and probably also the largest future potential for OR. 2. It has gone through ups and downs, similar to AI. In the ’50s and ’60s it was restricted to mathematically well-structured, mainly operational, problems, and consequently to the development of powerful mathematical tools. Ill-structured and strategic problems were left to other, more qualitative, disciplines. This, in the ‘7Os, led to the situation of disillusion when companies closed down their OR departments and famous colleagues claimed that “OR is dead and just not yet buried.” Since the middle of the ‘8Os, chances for the development of OR have appeared which have hardly ever existed before. Three of the main barriers to successful applications of OR in the ’60s and ’70s have disappeared: missing data, missing efficient software and missing high-powered and cheap hardware. Let’s now turn to our third area. Fuzzy-sets theory is obviously different from cognitive science in at least two aspects: It was begun by one man, Lotfi Zadeh [9], and it started as a formal concept and not as research on a real object such as cognitive processes. This notion should not be misunderstood: Zadeh’s ideas may have been inspired by looking at reality, but they first resulted in formal concepts and theories. In the meantime, fuzzy-set theory has developed in a very diverse fashion which certainly speaks well for the high potential of the original concept. The development concerns the theory itself as a formal theory, it concerns the development of a number of specialized subtheories (possibility theory, rough sets, named sets, etc.), and it concerns the application and use of concepts of a fuzzy theory to other areas such as mathematical areas (topology, etc.), optimization, mathematical programming, cluster theory, fuzzy control, approximate reasoning, economic theory, muticriteria analysis, and uncertainty modeling. The last area is certainly shared with other theories such as probability theory, belief theory, and evidence theory. But I believe that fuzzy-set theory has, to a very large degree, made many people aware of different types of uncertainty (lexical uncertainty, etc.) which were before either not recognized at all or modeled by probability theory. The character of the presently existing models and theories varies considerably. There are parts which can certainly be considered as a formal science, there are other parts which understand themselves as factual science (and then sometimes come pretty close to cognitive science), and there are numerous models and techniques which can be regarded as a technology. The possibly unexpected fast development of fuzzy-set theory worldwide and in many directions has also led to a few weaknesses in the sense that a variety of areas which already exist do not yet represent a homogeneous theoretical body in terms of terminology or methodology. We do not yet have any unique semantic interpretation of fuzziness except that it
H.-J. ZIMMERMANN means a gradual transition from one extreme to the other. This can, however, be from certainty to impossibility, from full membership to non-membership, from feasibility to nonfeasibility, or from optimality to far from optimum. Rather than investigating the present status of fuzzy-set theory, I shall now turn to the inter-relationships between OR, expert systems as part of AI, and fuzzy-set theory (FSTH): It seems to be obvious that fuzzy-set theory as a whole cannot be part of cognitive science because considerable parts of fuzzy-set theory do not focus on cognitive processes at all. This is particularly true for mathematical developments in fuzzy-set theory and for the applications of fuzzy sets to mathematical theories. On the other hand, fuzzy-set applications in psychology seem to me clearly part of cognitive psychology. Similar statements can be made about the relationship of FSTH to OR. FSTH is certainly not part of OR, but fuzzy linear programming would, for instance, be considered as belonging to OR. The same holds for fuzzy pert, fuzzy multi criteria analysis and approximate reasoning methods in production control. Maybe the question is ill-posed: Rather than asking “Does FSTH belong to cognitive sciences, to OR, or to AI?,” which certainly cannot be answered affirmatively, one should ask “What are the potential synergetic effects of these three areas?” For an outsider it sometimes seems difftcult to understand how some areas of artificial intelligence, such as knowledge representation, vision, understanding natural and spoken language, can do without efficient and appropriate tools to model context dependently gradual relationships and generic phenomena, This would not have to be fuzzy-set theory. But fuzzy-set theory would certainly be well suited for it. I think the reason why AI overwhelmingly still neglects tools such as fuzzy-set theory is that the subtasks of transforming a non-dichotomous structure into a dichotomous structure are mostly left to the heads of the human beings. 4.
DECISION SCIENCES AS AN UMBRELLA?
So far, we can conclude that the intersection of (new) cognitive science, operations research, and fuzzy-set theory is not empty but that none of these three areas can be considered to contain the other two. One phenomenon which, to my mind, plays a central part in all three disciplines is that of a decision. Admittedly, the inte~retation of “decision” is not the same in these three areas and the term does not even have a unique semantic definition in two of the three: In OR a decision as an act of choice
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is the model one looks at when calling optimization models special-decision models. On the other hand, when designing adequate interfaces between EDP systems and human users, OR people base their considerations more on the views of descriptive-decision theory than on those of decision logic. It is similar in fuzzy-set theory: When Bellman and Zadeh [1970] defined “a dethey had the model of normative decision cision in a fuzzy environment,” theory in mind. On the other hand, information processing is the core issue when talking about fuzzy sets, linguistic variables, or approximate reasoning in the context of, for instance, expert systems which might be used for decision support. The question of whether the concern with cognitive processes, their paradigms, or their consideration of decision is the strongest link between the areas considered is probably difficult to answer. Maybe their strongest common feature is the fact that in all three aspects they have similar views? REFERENCES 1. K. M. Colby, Arti’cial Paranoia: Computer Simulation of Paranoid Processes. Pergamon Press. Elmsford, N.Y.. 1975. 2. C. Lischka, and J. Diederich, Gegenstand und Methode der Kognitionswissenschaft. Der-GMD-Spiegel 213121-31 (1987) 3. G. A. Miller, Thinking. cognition, and learning. in The Behavioral Sciences
4. 5. 6. 7. 8.
To-day, B.
Berelson, (Ed.) Evanston, New York 1964. U. Neisser, Cognition and Reality. Freeman, San Francisco, 1976. A. Newell, and H. Simon, The logic theory machine. IRE Transactions on Information Theory 3:61-79 (1956). K. H. Pribram, On the neurology of thinking, Beh. SC.. pp. 265 (1959). Z. W. Pylyshyn, Computation and Cognition. Toward a Foundation of Cognitive Science, MIT Press, Cambridge, 1984. P. Smolensky, Connectionist AI, symbolic AI, and the brain. Art. fnt. Review 1:95-
109 (1987). 9. L. A. Zadeh, Fuzzy sets, lnf. Control 8:338-353
(1965).
IO. H.-J. Zimmermann, Testability and meaning of mathematical models in social sciences, Math. Mode/ 1:123-139 (1980). II. H.-J. Zimmermann, Fuzzy Set Theory- and its Applications. Kluwer-Nijhoff, Boston. 1985. 12. H.-J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems. Kluwer-Nijhoff, Boston, 1987. 13. H.-J. Zimmermann, Probabilistic and non-probabilistic representation of uncertainties in expert systems, in Mathematical Mode/s for Decision Support, G. Mitra (Ed.) Springer. Berlin, Heidelberg, N.Y., 1988. p. 613-630. Received
15 March 1990; revised 25 July 1990