Processing decision information is a vital part of Computer Science fields in which pattern recognition problems arise. Decision information can be generalized as alternative decisions (or classes), attributes and attribute values, which are the basis for classification. Different classification approaches exist, such as decision trees, decision tables and Naïve Bayesian classifiers, which capture and manipulate decision information in order to construct a specific decision model (or classifier). These approaches are often tightly coupled to learning strategies, special data structures and the special characteristics of the decision information captured, etc. The approaches are also connected to the way of how certain problems are addressed, e.g., memory consumption, low accuracy, etc. This situation causes problems for a simple choice, comparison, combination and manipulation of different decision models learned over the same or different samples of decision information. The choice and comparison of decision models are not merely the choice of a model with a higher prediction accuracy and a comparison of prediction accuracies, respectively. We also need to take into account that a decision model, when used in a certain application, often has an impact on the application's performance. Often, the combination and manipulation of different decision models are implementation- or application-specific, thus, lacking the generality that leads to the construction of decision models with combined or modified decision information. They also become difficult to transfer from one application domain to another. In order to unify different approaches, we define Decision Algebra, a theoretical framework that presents decision models as higher order decision functions that abstract from their implementation details. Decision Algebra defines the operations necessary to decide, combine, approximate, and manipulate decision functions along with operation signatures and general algebraic laws. Due to its algebraic completeness (i.e., a complete algebraic semantics of operations and its implementation efficiency), defining and developing decision models is simple as such instances require implementing just one core operation based on which other operations can be derived. Another advantage of Decision Algebra is composability: it allows for combination of decision models constructed using different approaches. The accuracy and learning convergence properties of the combined model can be proven regardless of the actual approach. In addition, the applications that process decision information can be defined using Decision Algebra regardless of the different classification approaches. For example, we use Decision Algebra in a context-aware composition domain, where we showed that context-aware applications improve performance when using Decision Algebra. In addition, we suggest an approach to integrate this context-aware component into legacy applications.

Processing decision information is a constitutive part in a number of applicationsin Computer Science fields. In general, decision information can be used to deduce the relationship between a certain context and a certain decision. Decision information is represented by a decision model that captures this information. Frequently used examples of decision models are decision tables and decision trees. The choice of an appropriate decision model has an impact on application performance in terms of memory consumption and execution time. High memory expenses can possibly occur due to redundancy in a decision model; and high execution time is often a consequence of an unsuitable decision model. Applications in different domains try to overcome these problems by introducing new data structures or algorithms for implementing decision models. These solutions are usually domain-specificand hard to transfer from one domain to another. Different application domains of Computer Science often process decision information in a similar way and, hence, have similar problems. We should thus be able to present a unifying approach that can be applicable in all application domains for capturing and manipulating decision information. Therefore, the goal of this thesis is (i) to suggest a general structure(Decision Algebra) which provides a common theoretical framework that captures decision information and defines operations (signatures) for storing, accessing, merging, approximating, and manipulating such information along with some general algebraic laws regardless of the used implementation. Our Decision Algebra allows defining different construction strategiesfor decision models and data structures that capture decision information as implementation variants, and it simplifies experimental comparisons between them. Additionally, this thesis presents (ii) an implementation of Decision Algebra capturing the information in a non-redundant way and performing the operations efficiently. In fact, we show that existing decision models that originated in the field of Data Mining and Machine Learning and variants thereof as exploited in special algorithms can be understood as alternative implementation variants of the Decision Algebra by varying the implementations of the Decision Algebra operations. Hence, this work (iii) will contribute to a classification of existing technology for processing decision information in different application domains of Computer Science. / <p>A thesis for the Degree of Licentiate of Philosophy in Computer Science.</p>