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Fuzzy databases: Principles and applications
EngngApplic. Artif. lntell. Vol. 10, No. 4, pp. 413-415, 1997
Pergamon
© 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0952-1976/97 $17.00 + 0.00
Book Reviews Fuzzy Databases: Principles and Applications by Frederick E. Petry. Kluwer Academic Publishers, Boston, MA (1995). 240 pp., £66.75, ISBN: 0792396677. Databases have traditionally handled only precise and certain data. A lot of real-life data is, however, vague, imprecise or uncertain in nature, and there are a number of applications where it is desirable to handle imprecision and uncertainty in data. Fuzzy-set theory was developed to handle this kind of data. This book, according to the authors, "presents the results of approximately 15 years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases". The book consists of six chapters, which divide themselves into three logical parts, which can best be summarized as "Foundations", "Principles" and "Applications" of fuzzy database systems. The first part consists of Chapters 1 and 2, and covers introductory and background material. Chapter 1 reviews general database fundamentals, while Chapter 2 introduces relational database theory and fuzzy-set theory, with an emphasis on the fuzzy-set aspects used in fuzzy database models. The main approaches used in fuzzy databases are covered in Chapters 3, 4 and 5, which form the second logical part of the book. Chapters 3 and 4 discuss extensions to the major database paradigm--the relational model--to handle fuzziness. There are two major approaches for this. The first, covered in Chapter 3, essentially replaces ordinary equivalence among domain values by measures of nearness such as "similarity relationships", "proximity relationships" and "distinguishability functions". In simple terms, they allow a mechanism for saying that two values in a domain are neither completely equal, nor completely unequal, but "similar" to a greater or lesser degree. The traditional equality then becomes a special case of complete similarity or zero distinguishability. For example, in a pollution database, we can set up a domain called "effect" to signify the effect of pollutants on a region, to take values such as "minimal", "limited", "tolerable", "moderate", "severe", "major", "extreme" and "irreversible", and then set up a similarity function between any two of these values. This would allow us, say, to make fuzzy queries such as, "How many experts more or less agree with each other about the effect of pollutant X on region Y?" Essentially, this first approach involves specifying a similarity function external to the attribute values (i.e., at the domain level). The second approach involves directly using possibility distributions for attribute values. For example, we can use a
possibility function to represent the value "salary" of an employee. This gives us a uniform way to represent all the following different kinds of salary values--non-applicable, known and precise, existing but of unknown value, and even cases where it could be any of the preceding types, i.e., completely unknown. Chapter 5 of the book surveys alternative fuzzy data models, including fuzzy extensions to the network and object-oriented data models. The use of fuzzy modeling in Geographical Information Systems (GIS) is also described. The final chapter examines issues related to the commercialization of fuzzy databases. Several specific industrial and commercial products and applications are described, in the context of issues relevant to the practical use of fuzzy databases. They include approaches to developing fuzzy front-end systems, and special-purpose systems incorporating fuzziness. The authors make the pertinent point that though the feasibility of the fuzzy database models has been established, actual implementations in the conventional database arena have not been many, mainly from considerations of efficiency. The biggest short-term potential is for fuzzy front-ends to conventional crisp databases, and for specialized fuzzy applications. Success in these is likely to trigger the demand for fuzzy models to be built into core database models, particularly for the rapidly developing object-oriented domain. Fuzzy-set theory is a fairly mathematical subject. The authors have done a good job of introducing a potentially opaque subject in an understandable way, with a fair number of examples thrown in. The book can be usefully read by anyone who has a basic grasp of set theory and rudimentary discrete mathematics (concepts such as functions). The book has the following minor flaws: • There are quite a few typographical errors (such as missing articles and prepositions) of the kind that cannot be caught by a spell-checker, but could be rectified by a meticulous proof-reader. • A few of the theoretical sections of the book still remain somewhat inaccessible to the lay reader. No attempt has been made to mark such passages explicitly as advanced material, for skimming by readers who are more interested in the applications rather than the theory. Doing so would greatly enhance the readability and usability of the book. All in all, this is an interesting book and one that should be of use to anyone who has an interest in the theory or applications of databases, knowledge representation or AI.
413
DURGESH RAO
Pergamon
© 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0952-1976/97 $17.00 + 0.00
Book Reviews Fuzzy Databases: Principles and Applications by Frederick E. Petry. Kluwer Academic Publishers, Boston, MA (1995). 240 pp., £66.75, ISBN: 0792396677. Databases have traditionally handled only precise and certain data. A lot of real-life data is, however, vague, imprecise or uncertain in nature, and there are a number of applications where it is desirable to handle imprecision and uncertainty in data. Fuzzy-set theory was developed to handle this kind of data. This book, according to the authors, "presents the results of approximately 15 years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases". The book consists of six chapters, which divide themselves into three logical parts, which can best be summarized as "Foundations", "Principles" and "Applications" of fuzzy database systems. The first part consists of Chapters 1 and 2, and covers introductory and background material. Chapter 1 reviews general database fundamentals, while Chapter 2 introduces relational database theory and fuzzy-set theory, with an emphasis on the fuzzy-set aspects used in fuzzy database models. The main approaches used in fuzzy databases are covered in Chapters 3, 4 and 5, which form the second logical part of the book. Chapters 3 and 4 discuss extensions to the major database paradigm--the relational model--to handle fuzziness. There are two major approaches for this. The first, covered in Chapter 3, essentially replaces ordinary equivalence among domain values by measures of nearness such as "similarity relationships", "proximity relationships" and "distinguishability functions". In simple terms, they allow a mechanism for saying that two values in a domain are neither completely equal, nor completely unequal, but "similar" to a greater or lesser degree. The traditional equality then becomes a special case of complete similarity or zero distinguishability. For example, in a pollution database, we can set up a domain called "effect" to signify the effect of pollutants on a region, to take values such as "minimal", "limited", "tolerable", "moderate", "severe", "major", "extreme" and "irreversible", and then set up a similarity function between any two of these values. This would allow us, say, to make fuzzy queries such as, "How many experts more or less agree with each other about the effect of pollutant X on region Y?" Essentially, this first approach involves specifying a similarity function external to the attribute values (i.e., at the domain level). The second approach involves directly using possibility distributions for attribute values. For example, we can use a
possibility function to represent the value "salary" of an employee. This gives us a uniform way to represent all the following different kinds of salary values--non-applicable, known and precise, existing but of unknown value, and even cases where it could be any of the preceding types, i.e., completely unknown. Chapter 5 of the book surveys alternative fuzzy data models, including fuzzy extensions to the network and object-oriented data models. The use of fuzzy modeling in Geographical Information Systems (GIS) is also described. The final chapter examines issues related to the commercialization of fuzzy databases. Several specific industrial and commercial products and applications are described, in the context of issues relevant to the practical use of fuzzy databases. They include approaches to developing fuzzy front-end systems, and special-purpose systems incorporating fuzziness. The authors make the pertinent point that though the feasibility of the fuzzy database models has been established, actual implementations in the conventional database arena have not been many, mainly from considerations of efficiency. The biggest short-term potential is for fuzzy front-ends to conventional crisp databases, and for specialized fuzzy applications. Success in these is likely to trigger the demand for fuzzy models to be built into core database models, particularly for the rapidly developing object-oriented domain. Fuzzy-set theory is a fairly mathematical subject. The authors have done a good job of introducing a potentially opaque subject in an understandable way, with a fair number of examples thrown in. The book can be usefully read by anyone who has a basic grasp of set theory and rudimentary discrete mathematics (concepts such as functions). The book has the following minor flaws: • There are quite a few typographical errors (such as missing articles and prepositions) of the kind that cannot be caught by a spell-checker, but could be rectified by a meticulous proof-reader. • A few of the theoretical sections of the book still remain somewhat inaccessible to the lay reader. No attempt has been made to mark such passages explicitly as advanced material, for skimming by readers who are more interested in the applications rather than the theory. Doing so would greatly enhance the readability and usability of the book. All in all, this is an interesting book and one that should be of use to anyone who has an interest in the theory or applications of databases, knowledge representation or AI.
413
DURGESH RAO