| 词条 | Linear partial information |
| 释义 |
Linear partial information (LPI) is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish–Swiss mathematician Edward Kofler (1911–2007) to simplify decision processes. Compared to other methods the LPI-fuzziness is algorithmically simple and particularly in decision making, more practically oriented. Instead of an indicator function the decision maker linearizes any fuzziness by establishing of linear restrictions for fuzzy probability distributions or normalized weights. In the LPI-procedure the decision maker linearizes any fuzziness instead of applying a membership function. This can be done by establishing stochastic and non-stochastic LPI-relations. A mixed stochastic and non-stochastic fuzzification is often a basis for the LPI-procedure. By using the LPI-methods any fuzziness in any decision situation can be considered on the base of the linear fuzzy logic. DefinitionAny Stochastic Partial Information SPI(p), which can be considered as a solution of a linear inequality system, is called Linear Partial Information LPI(p) about probability p. It can be considered as an LPI-fuzzification of the probability p corresponding to the concepts of linear fuzzy logic. Applications
To obtain the maximally warranted expected value, the decision maker has to choose the strategy which maximizes the minimal expected value. This procedure leads to the MaxEmin – Principle and is an extension of the Bernoulli's principle.
This principle leads to the maximal guaranteed weight function, regarding the extreme weights.
This principle is based on the prognosis interpretation of strategies under fuzziness. Fuzzy equilibrium and stabilityDespite the fuzziness of information, it is often necessary to choose the optimal, most cautious strategy, for example in economic planning, in conflict situations or in daily decisions. This is impossible without the concept of fuzzy equilibrium. The concept of fuzzy stability is considered as an extension into a time interval, taking into account the corresponding stability area of the decision maker. The more complex is the model, the softer a choice has to be considered. The idea of fuzzy equilibrium is based on the optimization principles. Therefore, the MaxEmin-, MaxGmin- and PDP-stability have to be analyzed. The violation of these principles leads often to wrong predictions and decisions. LPI equilibrium pointConsidering a given LPI-decision model, as a convolution of the corresponding fuzzy states or a disturbance set, the fuzzy equilibrium strategy remains the most cautious one, despite of the presence of the fuzziness. Any deviation from this strategy can cause a loss for the decision maker. See also{{div col|colwidth=25em}}
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External links
6 : Information theory|Fuzzy logic|Randomized algorithms|Algorithmic information theory|Decision theory|Mathematical modeling |
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