Objectives and Multi-objective Decision Making Under Uncertainty

1. The Concept of Objectives.- 1.1. The Decision Situation under Consideration.- 1.2. The Concept of Objectives under Certainty.- 1.2.1. "Aspects" and "Points of View".- 1.2.2. The Category of Ordered Topological Spaces. The Ordinal and the Cardinal Category.- 1.2.3. The Definition of an Objective Under Certainty.- 1.2.4. An Illustration of the Introduced Concepts.- 1.2.5. Side Conditions under Certainty.- 1.3. The Concept of Objectives under Uncertainty.- 1.3.1. Excursus: Axiomatical Treatment of the Bernoulli-Principle. Some Results on Continuity and Integrability of Utility Functions.- 1.3.1.1. The Natural ?-Algebra and the Interval Topology.- 1.3.1.1.1. Measurable Structures.- 1.3.1.1.2. Topological Structures.- 1.3.1.1.3. Connections between the Measurable and the Topological Structures of Preference Ordered Sets.- 1.3.1.2. The Expected-Utility-Theorem.- 1.3.1.3. A Special Case: The Utility Function as an Algebraic Homomorphism.- 1.3.2. Substantiation of the Information Requirements of the Objective-Concept4l.- 1.3.3. An Example46 1.4. Partial Objectives and Managerial Decisions.- 2. Formal Statement of the Problem.- 2.1. Complete Systems of Objectives.- 2.2. Criteria Vectors.- 2.3. The Treatment of the Problem on Principle.- 2.4. Excursus: The Vector Maximum Problem.- 2.4.1. The Concept of a Solution.- 2.4.2. The Treatment of the Vector Maximum Problem in the Literature.- 2.4.3. The 2-dimensional Vector Maximum Problem.- 2.4.3.1. Abstract Treatment of the Problem.- 2.4.3.2. The Algorithm for the Case of Two Dimensions.- 2.4.4. Linear Preference Structures and the Determination of Weights.- 2.4.5. Hyperbolic Preferences and. the Determination of the Exponential Weights.- 2.4.6. Generalization.- 2.4.7. Sketch of an Algorithm to the n-dimensional Vector Maximum Problem.- 3. Solution Approaches to the Problem of Multi-Objective Decision Making under Uncertainty.- 3.1. The Linear Model.- 3.2. The Quadratic Model.- 3.3. The Hyperbolic Model.- 3.3.1. An Axiomatical Treatment of Hyperbolic Preferences.- 3.3.2. On the Uniqueness of the Utility Function.- 3.4. A Collection of Models.- 4. Application.- References.