Analyzing Fuzzy Flip-Flops Based on Various Fuzzy Operations

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 F3s 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=1-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 neurons is proposed.