Linear partial information

Linear partial information ( LPI ) is a linear modeling method for the practical decisions that are based on earlier fuzzy information. The theory was developed in 1970 by Edward Kofler in Zurich.

Concept formation, properties, ideas or models of our reality we will always make only with incomplete information. This also applies to our everyday language and logical considerations. Considered temporally changed this blurring (English fuzziness ) of our reality without interruption. But, even though we live in the area of incomplete information, rational decisions need to be made in our decision-making situations that carry this same blur account and avoid wrong decisions on the basis of only seemingly stable findings. This leads to the so-called soft modeling.

In many practical decisions are no complete information. Nevertheless, it is often possible forecasts to determine prudent strategies, fuzzy equilibrium points and stability conditions. For example, in investment models in portfolio decisions, in economic planning, but also in strategic conflict situations. The following applies: The more complex the decision situation presents itself, the softer, so with greater blur, the appropriate model is to be designed; only with progressive certainty, the blur of the model may be gradually reduced.

In decision-making situations is the uncertainty of the distribution of possible scenarios, as well as the final results (English outputs) considered.

Each activity is based on decisions that must be made in a world of fuzziness and uncertainty of the data, concepts and laws. The " fuzziness " of the world is a rule and not the exception. The optimality of our decisions that we want to achieve by classical methods under these conditions must be questioned. All this forces us to so-called soft ( fuzzy ) modeling. The more complex a considered system, the higher the uncertainty level of the data and the softer needs to be modeled is already said Lotfi Zadeh. The soft model has three important features:

• The likelihood of the model is larger compared with the sharp model in general.
• It is stable over time.
• It allows an adaptive method for new information with a corresponding adjustment to new conditions.

The soft modeling from the perspective of the great thinkers

Bertrand Russell claims that " ... the traditional logic talks about precise terms. Unfortunately, these are not applicable in our environment, most in an imaginary heavenly reality. In our conditions so there is nothing left than to the circumstances of focus to determine the model data. The probability of models and customization options should be considered for further information. "

Albert Einstein proclaimed, " Sharp claims about our reality are wrong, or vice versa, correct ideas about our reality do not lead to sharp assertions. " This really represents the Russell formulation in a form other words.

In another allegation, the fact of the reality of the decision elements is expressed analogously as regards the concepts of quiescence and motion in mechanics.

LPI fuzzy equilibrium and stability strategies

Although present in many practical decisions without complete information, yet it is possible to determine fuzzy equilibrium points and stability conditions. For example, in blurred investment models, portfolio decisions in economic planning models but also fuzzy in strategic situations of conflict and cooperative negotiations. In everyday decisions is often after a " modus vivendi " sought in mutual tolerance - which must also lead to blurred equilibrium strategies and stability conditions. The concepts of fuzzy equilibrium points (single- stability) and multilevel stability are interpreted due to the optimization principles in fuzzy data. In the decision aspect, the MaxEmin principle for the average value and the Prognostic decision principle ( PEP) is used for one-off decisions taking into account the individual risk tolerance of the decision maker in this way. In multistage fuzzy decision strategies the search for stabilizing with learning and control aspects of the adaptive process is connected.

Equilibrium points and stability under severe data

Each optimal strategy has the property of an equilibrium point. A deviation from this strategy generally leads to disappointment. This applies to a scenario - as well as multi - scenario in decisions sharp distribution (risk situations, normal distribution ). For example, the determination of a maximum expected value in investment models, portfolio decisions, even in multi-stage decisions. Also in strategic games have the equilibrium points that " deviation property ". Under condition of membership of the decision results to the stability range of the decision maker, the equilibrium strategies are considered as stabilization strategies. It follows from our considerations that the credibility of the sharp models and thus also of their associated decision aspects are questionable.

Blurred equilibrium and stability conditions for fuzzy data

The large credibility " LPI -based " uncertainty be considered as a perturbation quantity. The optimal strategies are determined by the MaxEmin principle for the average value and the Prognostic decision principle ( PEP) with one-off decisions in the field of LPI amount of interference taking into account the individual risk tolerance of the decision maker.