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Frequent practical problems from decision-making as well as automatic control lead to intuitively monotone fuzzy rule bases. let us assume an appropriate ordering of fuzzy sets is defined. Then by the monotone fuzzy rule base we mean a rule base consisting of such fuzzy rules expressing the monotone dependence of consequent fuzzy sets on antecedent fuzzy sets. In other words the “bigger” antecedent...
At first sight, it seems that ordered linguistic values for all input variables and the output variable and a set of rules describing a monotone system are all that is needed for a monotone model. However, this is not the case. In this study, we show that the choice of the mathematical operators used when calculating the model output and the properties of the membership functions in the output domain...
We investigate the Cauchy problem for ordinary differential equation (ODE) with fuzzy initial condition. We define a solution to this problem and propose a new method of how an approximate solution can be constructed. The proposed method is based on the technique of fuzzy transforms and ends up with a solution of a system of fuzzy relation equations. The approximate solution is expressed symbolically...
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