Flexible Databases Supporting Imprecision and Uncertainty

Managers rely more and more on the use of databases to obtain insights and updated information on activities of their institutions and companies. More and more people, from experts to non-experts, are depending on information from databases, to fulfill everyday tasks, notably those related to decision making. Basically, the content of a database describes selected aspects of the real world relevant for a given company, institution, etc. Often, our knowledge about the entities represented in a database as well as our preferences as to what should be retrieved from a database are imperfect or imprecise. This raises a question of a proper modeling of imperfect information in the context of database management systems (DBMSs).

In this chapter, extended relational databases are considered where some attribute values are imprecisely known. The need for imperfect data is more and more recognized and imprecise information can appear in diverse situations such as data warehouses, forecasts, incomplete archives, structured data extracted from texts, or systems where information issued from automated recognition procedures is stored. Different formalisms can be used to represent imprecise information (see [7] for instance), and the possibilistic setting is assumed in the rest of the chapter. A key question is to define a sound semantics for queries addressed to imprecise databases. Since imprecise data are represented as (possibly infinite) sets of acceptable candidates, an imprecise database can be seen as a set of regular databases, called worlds, associated with a choice for each attribute value. This approach provides a rational starting point for the definition of a query in the sense that its result is the set of the results obtained for each world (or interpretation). Unfortunately, such an approach is intractable, obviously in the case of an infinite number of worlds, but also due to the possibly huge number of worlds when it is finite. This observation leads to consider only specific queries which can be processed directly against the possibilistic database (the processing is then called “compact”), while delivering a result equivalent to the one defined in terms of worlds. The principle of the approach advocated is summarized in figure 1.

The mathematical logic, supporting a database model, largely determines the behavior and interaction of the model on constraint satisfaction and on database querying. For traditional database models that only handle perfectly described data and do not explicitly deal with missing information, the classical two-valued Boolean logic is well suited: both integrity constraints and querying criteria can be described by Boolean expressions, which should evaluate to true in order to be satisfied.

As long as there have been database search engines there has been the problem of what to present to the user when there is no perfect match and how to present that query result to the user. Respecting the user’s search preferences is the suitable way to search for best matching alternatives. Modelling such preferences as strict partial orders in “A is better than B” semantics has been proven to be user intuitive in various internet applications. The better the search result, the better is the psychological advantage of the presenter. Thus, there is the necessity to know the quality of the search result with respect to the search preferences. This chapter introduces a novel personalized and situated quality assessment for query results. Based on a human comprehensible linguistic model of five quality categories a very intuitive framework for valuations is defined for numerical as well as for categorical search preferences. These quality valuations provide human comprehensible presentation arguments. Moreover, they are used to compute the situated overall quality of a search result. For delivery of the results a flexible and situated fillter decides which results to present, e.g. by respecting quality requirements of the user. A so called presentation preference determines which results are predestined to be especially pointed out to a user. Eventually, it will be evaluated how ecommerce applications will profit from the use of a preference based search in combination with the introduced human comprehensible quality assessment. Considering the procurement of goods via internet the idea is simple. A customer expects to have at least the service he or she has when directly contacting a human sales person. That means the customer wants to be treated individually according to his or her needs. But the misery already begins with the first step, the usage of the search engine.

A major goal for database research has been the incorporation of additional semantics into database models. It is recognized that the relational database model has semantic and structured drawbacks when it comes to modeling some emerging applications such as computer aided design (CAD), geographical information systems (GIS), and artificial intelligence. In response to this problem, some attempts to relax the first normal form (1NF) limitation, which is the most fundamental normalization constraint in the relational databases, are made and one kind of data model, called non-first normal (or nested) relational database model, has been introduced. In common sense, the nested relational database model means that attribute values in the relational instances are either atomic or set-valued and even relations themselves. In addition, the next generation of database models takes the form of rich data models such as the object-oriented database model and the semantic (conceptual) data models.

Databases integration, federated databases, multidatabases, databases merging ([3], [1], [2], [17], [5], [12], [14], [10], [4]) are close problems which aim to query several independent databases viewed as a single one.

To increase product competitiveness, today’s manufacturing enterprises have to deliver their products at reduced cost and high quality in a short time. The change from sellers’ market to buyers’ market results in a steady decrease in the product life cycle time and the demands for tailor made and small-batch products. All these changes require that manufacturing enterprises quickly respond to market changes. Traditional production patterns and manufacturing technologies may find it difficult to satisfy the requirements of current product development. Many types of advanced manufacturing techniques, such as Computer Integrated Manufacturing, Agile Manufacturing, Concurrent Engineering, and Virtual Enterprise based on global manufacturing have been proposed to meet these requirements. One of the foundational supporting strategies is the computer-based information technology. Information systems have become the nerve center of current manufacturing systems. It should be noted that, for various organizational and technological reasons, multiple information systems used in information-based manufacturing enterprises are independently developed, locally administered, and different in logical or physical design [10, 24]. Therefore, a fundamental challenge in heterogeneous and distributed enterprise information management is the sharing of information for enterprise users across organizational boundaries [20].

Today, many important database applications have to deal with data that is both semistructured and either imprecise or uncertain. As an example, scientific databases are likely to contain data affected by some types of imperfection, with a schema that is not well-defined a priori [6, ch.10]. A different area with similar features is that of structured information retrieval, which has become very popular after the spread of XML documents [15].

An immediate problem in approaching GIS (Geographic Information Systems) consists in giving a sufficiently agreed definition of what GIS actually are. For present purposes it seems reasonable to consider GIS as being characterized by a twofold nature. On the one hand, GIS consist of a technology used for certain purposes. From this perspective, the crucial issues in GIS research amount to computing problems, both on the hardware and software level. On the other hand, however, GIS research is increasingly more focussed on theoretical issues concerning the representation of geographic information. According to the latter point of view GIS problems include, at the very least, issues of knowledge representation and reasoning. In this chapter we investigate some of the consequences deriving from approaching GIS from the latter point of view. In particular, we will be insisting on the fact that its s‘conceptual side’, so to speak, commits GIS research to achieving scientific goals which happen to be closely related to some of those pursued in Artificial Intelligence (AI) research.³ In doing so, we adopt a perspective according to which GIS are essentially construed as artificial intelligent agents reasoning about a certain classes of natural environments.

We collect and store data to derive information and make judgments about a world of our interest. Ideally, they should indicate in a unique and certain way which possible world corresponds to the actual world [17]. Imperfection arises when this is not possible. Imprecision is a type of imperfection that is often encountered. Data are imprecise if we cannot precisely define the actual world, i.e. several worlds satisfy the data. A specific type of imprecision is vagueness [17; 22], which is the focus of this study. A concept is vague if objects exist that cannot be classified either to the concept or to its complement. Vagueness arises in the presence of borderline cases [18]. It is often present in collected spatial information, such as forest inventories, or geological, soil, and vegetation maps. Soil or vegetation classes are such that they cannot be defined sharply. The change from one class to another is gradual. This is in confliict with current geographical information systems (GIS) which assume that spatial objects are precisely defined, sharp objects, using points, lines, and polygons as representations.

Spatial database systems have become a popular research area since they find applications in diverse fields where there is the need to manage geometric, geographic or spatial data, which means data related to space such as the physical world (geography, urban planning, astronomy), parts of living organisms (body anatomy), engineering design (VLSI circuits, molecular structures) etc. When the earth surface and subsurface are the space of interest, the systems are called the Geographic Information Systems (GIS). A distinguished feature of spatial database systems is the management of sets of entities with a spatial reference, which means that spatial database systems provide operations to deal with the extent, location, and relationships of the spatial elements. However, it is generally recognized that current spatial database systems are inadequate to support typical applications of GIS and CAD, and also for potential applications such as data warehousing. This is the reason that motivates current research aimed at improving the functionalities and the performance of the available spatial database management systems, including the modelling of continuous fields, the management of large data sets and the design of user interfaces for simplifying the user-system interaction [1; 7; 26; 27]. Specifically, current spatial query languages are inadequate to perform spatial analysis for many reasons [3; 7; 14; 20; 25; 27]: one reason is that they force users to formulate their often vague requests by means of crisp selection conditions on spatial data. For many categories of users, such as planners and resource managers, the possibility to express tolerant conditions on conventional and spatial data, and to retrieve discriminated spatial information in decreasing order of relevance, can greatly simplify their spatial