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11. Fuzzy Systems and their Game Theoretical Solutions

Application in Political-Economic Decisions

Prof. Dr. Eduard Kofler and Lorentz Götte

Institute for Empirical Economic Research , University of Zurich, Switzerland

Official Paper at the International Conference on Operations Research 2000, ETH Zurich
Section 10, Fuzzy Systems and Neural Networks

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Abstract


Situations of our reality in decision aspect have to be considered as fuzzy systems only. Any crisp model leads often to erratic decisions. It particularly applies to political-economic systems. Inputs, outputs, possible scenarios with incomplete information have to be analyzed as fuzzy only. For this reason for the optimal strategies, regarding the equilibrium points, the fuzziness of the data have to be considered.


A simple way of finding the optimal strategies is a linearization of any fuzzines (Linear Partial Information, LPI). It is however necessary to consider linear restrictions for the state, normalized weight distribution and situation outputs.


In the decision aspects, fuzzy systems are analyzed as fuzzy games. For that reason the classical principles of expected utility maximization, the Minimax theorem have to be extended for the case of uncertainty. The optimal decisions in fuzzy games will be determined by maximization of the minimal preferences or the minimal weighted sums. This way fuzzy equilibrium points and stability conditions can be calculated in political-economic systems. That way possibility of making an erratic decisions can be decreased.


Credibility of the degree of fuzziness can be tested using statistical methods. In the domain of multistage decisions, optimal strategies can be determined, using fuzzy decision trees or supergames. Aspects of adaptivity learning and control can be taken into account.


As regards applications, some examples of political-economic decisions are considered. For instance, in the tax compliance policy a transition from the classic to the fuzzy model is analyzed.

 

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