Fuzzy Database Modeling

The evolution of database systems was initially driven by the requirements of traditional data processing. The drawbacks of the network and hierarchical data model coupled with the need for a formally based database model, which clearly separate the physical and logical model led to the definition of the relational database model by Codd [7]. The initial reaction of IS community to the relational model was lukewarm, however the maturing of this technology led to general acceptance by the mid-80’s and almost universal usage in the 90’s. Indeed it is hard to conceive of any organization utilizing the older network and hierarchical data models today. This acceptance came about due to the phenomenal improvements in relational technology since its original definition by Codd. Software improvements took place in storage structures, retrieval algorithms, optimization techniques, parallel processing and user interface technologies. Simultaneously, hardware improvements in chip and data storage technology were taking place. This made it possible to efficiently store and retrieve terabytes of information using the relational data model.

Considerable research effort has been spent on methods for representing imprecise information in various database models by using the fuzzy set theory. However, the research directed toward access structures to handle fuzzy querying effectively is still at an immature stage. Fuzzy querying involves more complex processing than the ordinary querying does. A larger number of tuples are possibly selected by fuzzy queries as compared to the crisp queries. It is obvious that the need for fast response time is very important when the database systems deal with imprecise (fuzzy) data. The current crisp index structures are inappropriate for representing and efficiently accessing fuzzy data. It is necessary to allow both the non-fuzzy and fuzzy attributes to be indexed together; therefore, a multidimensional access structure is required. In this chapter we describe a multi-dimensional data structure, namely Multi Level Grid File (MLGF), which can efficiently access both crisp and fuzzy data from fuzzy databases. Besides suitable access structures, an effective partitioning, representation, and storage of fuzzy data are necessary for efficient retrieval. The implementation of the access structure is described and compared with extant fuzzy access methods.

Trends in databases leading to complex objects present opportunities for representing imprecision and uncertainty that were difficult to model in simpler database models. At the conceptual level uncertainty assumptions may be represented and transformed into a logical database model having the requisite semantic foundations on which to base a meaningful query language. In this chapter we describe a constructive approach starting with IFO Data Model, and extending this model for complex and uncertain information — the ExIFO data model. We further extend ExIFO to handle object-oriented constructs and uncertainty — the ExIFO₂ data model. The conceptual schema is verified with respect to the constraints imposed on the schema definition. For the purpose of verification of a conceptual schema represented by the ExIFO or ExIFO₂ data models, invariants are introduced. The steps of mapping from a conceptual schema into logical one are straightforward, unambiguous, computationally efficient, and preserves the relevant information, including information concerning uncertainty.

In recent years, a primary objective of the database community has been the incorporation of structured and complex data types. This has led to new database models based on both the established relational paradigm as well as the object-oriented paradigm. These new database models are the non-1NF relational data model (also called NF² data model), object-oriented data model, and deductive object-oriented data model. These models are considered appropriate for modeling many non-traditional applications, such as CAD/CAM, imagery, multimedia, meteorology, geographic information systems, oceanography, etc. The NF² data model is better suited for office automation systems. On the other hand, object-oriented databases are more appropriate for CAD/CAM, multimedia database and geographical, meteorological, and oceanographic applications. Object-oriented databases coupled with logic and as the more integrated approach, deductive object-oriented databases are more appropriate for knowledge intensive applications such as expert database systems. In this chapter, we introduce the logical database models such as the extended NF² data model, the fuzzy object-oriented data model, and the fuzzy deductive object-oriented data model to deal with complex information and uncertainty that arise in non-conventional applications.

This chapter introduces a new definition for the conformance of tuples existing in similarity-based fuzzy database relations. Then the formal definitions of fuzzy functional and multi-valued dependencies are given on the basis of the conformance values presented here. These dependencies are defined to represent relationships between domains of the same relation that exist. The definitions of the fuzzy dependencies presented in this chapter allow a sound and complete set of inference rules. In this chapter, we include examples to demonstrate how the integrity constraints imposed by these dependencies are enforced whenever a tuple is to be inserted or to be modified in a fuzzy database relation.