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Petri nets and Fuzzy Petri nets as modeling formalism are not adaptable according to the changes of the arc weight. Weights are the parameters that represent the new incoming data of the system modeled by a (Fuzzy) Petri net. The weight changes meet the system changes in a variety of application domains (e.g. Intelligent E-learning, Computer Numerical Control, Weather Forecasting, and Expert Systems). In this paper, we introduce a new class of Fuzzy Petri nets that takes into account the weight changes of the arc in the Fuzzy reasoning process. We give the formal description of the model, an algorithm for learning the weights without the need to transfer into a neural network, an algorithm for the fuzzy reasoning, the algebraic forms of the new state equation, and the stability analysis. Finally, we introduce a weather forecasting application as a real example. [ABSTRACT FROM AUTHOR]

Abstract: The direct numerical simulation of two phase interfacial flows can be computationally challenging, as the strong resolution needed to follow the deformations of the interface leads to a lot of time spent solving the whole computation domain. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. In this paper a parallel adaptive algorithm to solve incompressible two-phase flows with surface tension is presented: the AMR is handled with the help of the PARAMESH package. The free interface between fluids is tracked via Level Set approach; the jump conditions at the interface for pressure and velocity are imposed by the Ghost Fluid method. A multigrid preconditioned BiCG-stab solver adapted to the AMR data structure has been developed to allow high density ratio computations (up to 1:1000). Special treatment has been done at the refinement jumps to maintain the fine mesh accuracy. Computational results are compared in different test cases with analytical solutions or literature, and show very good agreement with the references. The effectiveness of PARAMESH parallelization has been quite well maintained, as shown in the strong and weak scaling tests. Speed-up capabilities of the AMR are demonstrated. [Copyright &y& Elsevier]

Abstract: Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi–Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings. [Copyright &y& Elsevier]