An extended database design methodology for uncertain data management
Introduction
Many real world systems and applications must deal with imprecise or vague data. This need arises because of a variety of factors, e.g., sources which provide the information may be unreliable, estimation or judgement may be involved in gathering the information, etc. For such systems, information management components are needed that provide support for managing this imprecise data. Fuzzy theory [31] has been identified as a successful technique for modeling such imprecise and vague data. Significant work has been done in developing extensions to the relational data model for representing and querying fuzzy data [2], [15], [16], [17], [20], [29], [30], [32] and to enhance object-oriented models to incorporate fuzzy data [7]. However, little research has been carried out towards modeling fuzziness in conceptual data models or for developing methodologies for mapping such enhanced data models to relational database management systems (DBMSs).
To fill this gap, we propose fuzzy entity-relationship methodology (FERM), which is a comprehensive methodology for design and development of fuzzy relational databases. A preliminary version of FERM has been reported on in a working conference [4]. In this paper we provide a complete and in-depth treatment of our approach. We utilize the popular entity-relationship (ER) data model for representing the conceptual data model and extend it to a fuzzy ER model. The fuzzy ER model allows modeling of imprecision in entities, relationships and attributes. We also propose additional constructs to facilitate integration across fuzzy and crisp (i.e., non-fuzzy) entities in the model. Further, we propose generic techniques for mapping this conceptual model to relational databases (RDBs) and prescribe a sequence of steps to implement a fuzzy RDB from the extended fuzzy ER model. FERM is thus the first comprehensive methodology for representing imprecision in the data model and for mapping the data model to RDBs.
We demonstrate the utility of our methodology by describing a detailed case study of applying these techniques to develop a fuzzy control system for application to VLSI manufacturing processes. The control system uses a database to store the results of the semiconductor process. Control decisions are undertaken based on this data. Difficulty in accurately measuring some of the parameters associated with the fabrication process means that the data is imprecise in many cases, whereas incomplete understanding of the semiconductor manufacturing process means that there is additional uncertainty in making the control decisions. The ability to store fuzzy data would allow the control system to handle imprecision in data and would facilitate decision making under uncertainty on this data. We have, therefore, utilized FERM to develop extensions to the control system to make it capable of handling fuzzy data and to augment the control system with a fuzzy rule-based decision making process to carry out control actions.
The rest of this paper is structured as follows. Section 2 of the paper contains background material on fuzzy theory. In Section 3, we review the ER design methodology for crisp databases. We then present the proposed extensions to the ER data model and the techniques for mapping this fuzzy ER data model to RDBs that together constitute FERM. Section 4 contains a description of the application of FERM to develop a fuzzy database for a control application. Section 5 contains a description of related work, while in Section 6 conclusions and a summary of future work are presented.
Section snippets
Background
A brief introduction to concepts of fuzzy sets is given in [31], followed by an introduction to fuzzy relational databases [2], [16], [17], [20], [29], [30], [32].
FERM: extending the data model and design methodology for fuzzy RDBs
In this section we first present extensions to enhance the ER data model to represent imprecision and vagueness. We then describe FERM, a design methodology for implementing fuzzy relational databases from fuzzy conceptual data descriptions.
Application: data and rule modeling for semiconductor manufacturing and control
As a case study we describe the application of FERM to a semiconductor control application [5]. The overall control system consists of multiple control levels, however our research is directed towards developing a fuzzy controller at the run-to-run (R2R) level (Fig. 5). At the R2R control level, control is carried out by utilizing data from the results of the last process run or a series of previous runs to derive a better model for the inputs to be set for the next run of the process. The R2R
Related work
Most previous research on fuzzy databases has focused on extending the relational data model. The fuzzy relational data model enhances the relational model by modeling imprecision in data and/or query [2], [16], [29], [32]. This is achieved by using the concepts of fuzzy sets and possibility distribution. To express imprecision of a data value, the set of possible attribute values allowed in the relational representation is extended from simple scalars or numbers to sets of scalars or numbers,
Conclusions and future work
Fuzzy theory allows us to model imprecise data. Significant work has been done in incorporating fuzziness in the relational data model, but little research has been carried out towards modeling fuzziness in conceptual data models or for developing a comprehensive methodology for implementing fuzzy RDBs. To fill this gap, we have proposed FERM – a design methodology for developing fuzzy RDBs. The fuzzy ER model of FERM allows modeling fuzziness of entities, relationships and attributes at the
Acknowledgements
This research was sponsored by the Semiconductor Research Council and the Center for Display Technology & Manufacturing, University of Michigan. The authors would like to thank Roland Telfeyan, Hossein Etemad, John Taylor and Arnon Hurwitz for their support.
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