A Hopfield neural network applied to the fuzzy maximum cut problem under credibility measure

This paper deals with maximum cut problem on a graph with fuzzy edges. This problem is studied to cluster data under imprecise dependency. Applying the credibility measure, this fuzzy problem is transformed into a nonlinear mixed-integer programming problem. To solve the problem, an adaptive Hopfield neural network is proposed, with modern simulated annealing cooling schedule, which converges into an equilibrium status within few iterations. To illustrate the efficiency of this network, it is simulated on some benchmark examples. Also, webpage clustering problem is solved to illustrate the application of the studied fuzzy problem and neural network solutions.