Analyzing Fuzzy Flip-Flops Based on Various Fuzzy Operations

Abstract

This paper concerns the role that fuzzy operations play in the study of behavior of fuzzy J-K and D flip-flops (F3). We define various types of F3-s based on well known operators, presenting their characteristic equations, illustrating their behavior by their respective graphs belonging to various typical values of parameters. Connecting the inputs of the fuzzy J-K flip-flop in a particular way, namely, by applying an additional inverter in the connection of the input J to K (K=1-J), a fuzzy D flip-flop is obtained. When input K is connected to the complemented output (K =J-Q), or in the case of K = 1-J, the J-Q(t+ 1 )characteristics of the F3s derived from the Yager, Dombi, Hamacher, Frank, Dubois-Prade and Fodor t-norms present more or less sigmoidal behavior. Two different interpretations of fuzzy D flip-flops are also presented. We pointed out the strong influence of the idempotence axiom in D F3• s behavior. A method for constructing Multilayer Perceptron Neural Networks (MLP NN) with the aid of fuzzy systems, particularly by deploying fuzzy flip-flops as neuron is proposed.