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Aguilera, Ana Universidad de Carabobo, Valencia, Venezuela.
Mata-Toledo, Ramon A. Department of Computer Science, James Madison University, Harrisonburg, Virginia.
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Traditional relational databases (DBs) are not designed, implemented, and populated to store and retrieve information using data that can be considered uncertain or imprecise. Imprecise data frequently occurs when we refer to extant documents where the best we can do is to approximately date them. For example, the Dead Sea scrolls are generally dated between the years 150 BC and AD70. In this case, it is clear that some uncertainty exists when we consider the exact date when these documents were written. In other cases, the degree of uncertainty may not be clear. Consider, for example, a group of people whose height is being measured. By current universal standard, we can safely assume that a person who is 6 ft (183 cm) tall can be considered a tall individual. However, if somebody is only 5 ft 11 in. (180 cm), can we say that this person is not tall? Here the distinction between being tall and not being tall is not that clear. To address issues concerning data that is uncertain or imprecise, it is necessary to consider a new type of databases called fuzzy databases (FDBs). Fuzzy databases are called “fuzzy” because their theoretical formalization is based on fuzzy logic (FL) and fuzzy set theory (FST). The former deal primarily with reasoning that is approximate rather than fixed. That is, in fuzzy logic, there is a gradation of values between something being absolutely false (generally indicated with a value of 0) and something being absolutely true (generally indicated with a value of 1). For this reason, fuzzy logic is said to be a many-valued logic as opposed to traditional logic for which there are only two possible values: true or false. Fuzzy logic, in turn, is based on the concept of fuzzy set theory in which the notion of membership may range between the values 0 (not belonging to the set) and 1 (belonging to the set). For example, considering the previous examples of individuals and their heights we can say that a person who is 6 ft 4 in. (193 cm) belongs to the set of tall people. This person has a membership value of 1 because he or she clearly belongs to the set of tall people. A person who is 5 ft 11 in. (180 cm) may have a 0.7 membership value in the set of tall people. Therefore, whenever we consider the concept of fuzzy database (FDBs) it is necessary to view it as including and being based on FL and FST. These two concepts are present at different levels during the operation of a fuzzy database, particularly at the representation and storage of imprecise or vague data and during the access of the data stored in an FDB through queries (questions posed to the database) that may contain imprecise data. FL and FST also are present during the entire life cycle of the FDB. Since their inception, the concepts of FL and FST have been widely applied in science and technology fields. In computer science, the concept has been gaining relevance because of the growing and more demanding needs for applications that require that data be manipulated in a more human-like rather than machine-like manner. Applications of this type are common in medical and business environments.
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