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Classical Decision Theory

The Classical Decision Theory deals with situations when a decision-maker can choose between different actions - which may depend on the situation he is in - leading to different results.

It is distinguished between Descriptive and Normative (prescripitiv) Decision Theory. Descriptige Decision Theory analyses empirically how decision-maker actually behave. Normative Decision Theory helps the decision-maker to analyse the decision situation in which he is and enables him to come to a best possible decision. This paper gives the Normative Decision Theory special emphasis.

Generally you can distinguish between the following decision situations:

Multi-dimensional decision situation

Hier verfolgt der Entscheider verschiedene, teilweise zueinander im Gegensatz stehende Ziele. Gesucht ist diejenige Alternative, die möglichst optimal bezüglich aller Ziele ist. Dies geschieht, indem die einzelnen Ziele vom Entscheider geordnet oder mittels einer Gewichtung zusammengefasst werden. Mit verschiedenen Rechenverfahren kann dann häufig eine optimale Lösung gefunden werden (im linearen Fall zum Beispiel mit dem Simplex-Verfahren).

Decision by uncertainty

In many cases the result doesn't only depend on the chosen alternative, but also depends on the environmental situation of the decision-maker. Often the decision-maker doesn't know exactly all of this situation. If the decision-maker can't even give approximate information about the particular probability of the environmental situation, there's talk of decisions by uncertainty. In this case there generally can't be optimal decisions found out, since an essential information is missing, the distribution of probability. The different models, however, help the decision-maker to anlyse his situation.
(Example picking fungus with the alternatives tasty – dangerous – fatal)

Decision by risk

In contrast to uncertainty the decision-maker can the environmental situations assign to probabilities in decisions by risk. With a benefit function the liking of or dislike of risk of a decision-maker can be modelled.
Axiomatic the benefit function was set up by von Neumann / Morgenstern. An alternative formulation comes from Luce / Raiffa. By use of the axioms the benefit function of a decision-maker can be found out.
Often the application of a benefit function is also called Bernoulli-Principle.

Classical Decision Theory and fuzzy mathematics

Formulations for using methods of fuzzy mathematics consist where subjective assessments of the decision-maker are considered:

• In multi-dimensional decisions: Findings of the weight function of the aims
• In decisions by risk: Findings of the benefit function

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