The Use of Relation Valued Attributes in Support of Fuzzy Data

• Main Author: Williams, Larry Ritchie, Jr.
• Format: Others
• Published: VCU Scholars Compass 2013
• Subjects: Fuzzy Data; Relational Database; Relation Valued Attribute; Computer Sciences; Physical Sciences and Mathematics
• Online Access: http://scholarscompass.vcu.edu/etd/3240; http://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=4239&context=etd

In his paper introducing fuzzy sets, L.A. Zadeh describes the difficulty of assigning some real-world objects to a particular class when the notion of class membership is ambiguous. If exact classification is not obvious, most people approximate using intuition and may reach agreement by placing an object in more than one class. Numbers or ‘degrees of membership’ within these classes are used to provide an approximation that supports this intuitive process. This results in a ‘fuzzy set’. This fuzzy set consists any number of ordered pairs to represent both the class and the class’s degree of membership to provide a formal representation that can be used to model this process. Although the fuzzy approach to reasoning and classification makes sense, it does not comply with two of the basic principles of classical logic. These principles are the laws of contradiction and excluded middle. While they play a significant role in logic, it is the violation of these principles that gives fuzzy logic its useful characteristics. The problem of this representation within a database system, however, is that the class and its degree of membership are represented by two separate, but indivisible attributes. Further, this representation may contain any number of such pairs of attributes. While the data for class and membership are maintained in individual attributes, neither of these attributes may exist without the other without sacrificing meaning. And, to maintain a variable number of such pairs within the representation is problematic. C. J. Date suggested a relation valued attribute (RVA) which can not only encapsulate the attributes associated with the fuzzy set and impose constraints on their use, but also provide a relation which may contain any number of such pairs. The goal of this dissertation is to establish a context in which the relational database model can be extended through the implementation of an RVA to support of fuzzy data on an actual system. This goal represents an opportunity to study through application and observation, the use of fuzzy sets to support imprecise and uncertain data using database queries which appropriately adhere to the relational model. The intent is to create a pathway that may extend the support of database applications that need fuzzy logic and/or fuzzy data.