Of decisions under security one speaks in the context of the decision theory if the decision maker knows the occurring environmental condition with security (w_j=1) and it thus all consequences from an action to forecast can. Decisions with several objectives (multikriterielle decision problems) play thereby the most important role.

General information

The acceptance that in advance admits all consequences of an action are, appears intuitively completely unrealistically. The importance of decision rules under security is nevertheless very great. So for example certain linear decision problems can be transferred with decisions under uncertainty into a decision situation under security with several objectives.

Examples: (Laux, 2003, S. 65ff.):

• The goal actually aimed at cannot be measured directly, besides the influence of certain parameters of action on this goal is not with security well-known.
• The complexity with a decision on the basis a global goal (maximization of profit) is not controllable any longer, so that individual Unterziele is defined, whose influence on the global goal admits at least tendentious is.

Thus for example an enterprise will make a decision over a new location as a rule under the goal of the long-term maximization of profit, the respective influence of the possible locations on the profit is however not not directly assignable. However the location characteristics are well-known like for example infrastructure, labour costs, taxes, granted subsidies, construction costses etc. with security, equally knowledge of the connection between these factors and the global goal exists. From the linear decision under uncertainty so a multidimensional (multikriterielle) decision becomes with security.

Linear decision problems

A little relevant problem is present, if only one goal is pursued and goal development with the choice of different alternatives admits is. Two cases can be differentiated:

• Unlimited objective: A maximization or a minimization of goal development is aimed at. Example: Maximization of profit, minimizing the risk.
• Limited objective: At least/at the most here a goal is to be achieved either exactly (adjustment) or (Satisfizierung). Example: In order to reach a flight, one must be at the latest 1 hour before at the airport, it is however no matter whether one is in former times there (Satisfizierung). Starting from a certain quantity of sweets one with one more becomes rather bad at sweets, it gives an optimal quantity, with which deviations are bad upward and down (adjustment).

Multikriterielle of decision problems

A decision (the selection of an alternative course of action from several alternatives the available is called) has usually consequences for several goals, so that a multikriterielles decision problem is present. Since for each alternative course of action the available all consequences admits are (goal sizes) and admits is, which development of the individual goals is desired (preference relation) is present a target system. The goals of this target system can stand in different relations to each other

Target system

The goal sizes in a target system represent, which consequences of its action alternatives a Entscheider meaning measures out and form the yardstick for the evaluation of the alternative by the evaluation of the action alternatives regarding in each case a consequence. The target system depends on individual Entscheider.

Example:

For the way to the work are available the travel with the car or the The target system of the Entscheiders looks then for example in such a way:

{| border= " 0 "

! width= " 5% " |! width= " 10% " align= " right " |z_1! width= " 10% " align= " right " |z_2! width= " 10% " align= " right " |z_3 | -! a_1 | align= " right " | 40 | align= " right " | 5 | align= " right " | 8 | -! a_2 | align= " right " | 45 | align= " right " | 4 | align= " right " | 4 |} 

With z_1 to z_3 the different goals (here: z_1 = travel duration in minutes, z_2 = costs for each travel into euro, z_3 = comfort on a scale of 1 to 10) and a_1 = travel with the car and a_2 = travel with the

Another Entscheider at another place of the city can have another target system, for example:

{| border= " 0 "

! width= " 5% " |! width= " 10% " align= " right " |z_1! width= " 10% " align= " right " |z_2! width= " 10% " align= " right " |z_3 | -! a_1 | align= " right " | 30 | align= " right " | 4 | align= " right " | -5 | -! a_2 | align= " right " | 60 | align= " right " | 6 | align= " right " | -2 |} 

This Entscheider could thereby the comfort be completely all the same, so that for it z_3 is an expression for the ecological consequences of the respective means of transport.

Regarding desired goal developments said the above applies: Are possible maximization, minimization, adjustment or Satisfizierung.

Goal relations

Goals can stand in different relations to each other (Laux, 2003, S. 67ff.):

• Zielindifferenz and/or goal neutrality: Will not affected the reaching of the goal by the other goal, the decision problem can into linear in each case sub-problems be divided.
• : The reaching of the goal facilitates the reaching of the other goal. Example: English knowledge and vacation in England. If a goal is 1, as well as possible English to be able and a goal 2 is to spend as much as possible vacation in England then a high reaching of the goal 2 (much vacation in England) improves automatically the Zielerreichung with a goal 1.
• Conflicting aims

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