Software architecture provides a blueprint for a software-intensive system. The IEEE 1471-2000 standard defines software architecture as the fundamental organization of a system embodied in its components, their relationships to each other and to the environment and the principles guiding its design and evolution. However, most architectural design only depicts components and connectors, but omits the design decisions and design rationale. This may lead to 1) costly support efforts for system evolution, 2) lack of stakeholder communication and 3) limited reusability of software system. To address these problems, new approaches are developed in recent years that focus on providing decision support and documenting design decisions as core entities of software architecture. These approaches have some common features: 1) treat architecture design as a design decision process; 2) manage architectural knowledge, emphasizing the organisation and documentation of design decisions explicitly; 3) integrate techniques/methodologies in the design reasoning process; 4) capture and document design rationale. Some of these approaches include Archium, Akerman's Ontology, AREL, ArchDesigner, Bayesian Network based Alternatives Selection Method, AQUA, and Automated Solution Synthesis Method. We consider them to be decision-centric architecture design approach. In addition, we also study PAKME and ADDSS for they provide tool support for knowledge management and decision making by maintaining an architecture knowledge repository (i.e. architectural styles and design patterns) even though they do not provide specific design techniques. All these software architecture decision-centric approaches share some common characteristics. They either capture design rationale and/or provide methods to support design reasoning, they use requirements as a basis to support reasoning and they employ different techniques to justify a design. However, they also differ in many ways. The design reasoning process they employ differs greatly, and as a result the reasoning process and the resulting design rationale varies. Some approaches address high-level architectural design whilst others also encompass the design at the programming level. The main objectives of this study are two folds. Firstly, to provide a bird's eyes view of this developing field, and to differentiate the differences and the similarities of these approaches. Secondly, through the analysis, we aim to identify the strengths and weaknesses of theses approaches to uncover new research alignments and questions. In this report, we use three key perspectives to analyse nine decision-centric methods. These perspectives are based on the referential models on software architecture knowledge management and design rationale. We apply these methods to an industry case study to compare the decisions and the design outcomes that each one of them produces.