Decisions: Algebra and Implementation

Abstract

Processing decision information is a constitutive part in a number of applications in 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-specific and 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 strategies for 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.