Projection measure is one of important tools for handling decision-making problems. First, the paper proposes projection and bidirectional projection measures between single-valued neutrosophic sets, and then the comparison of numerical examples shows that the bidirectional projection measure is superior to the general projection measure in measuring closeness degree between two vectors. Next, we develop their decision-making method for selecting mechanical design schemes under a single-valued neutrosophic environment. Through the projection measure or bidirectional projection measure between each alternative and the ideal alternative with single-valued neutrosophic information, all the alternatives can be ranked and the best one can be selected as well. Finally, the proposed decision-making method is applied to the selection of design schemes of punching machine and its effectiveness and advantages are demonstrated by comparison with relative methods.

The purpose of this paper is to propose a compound sine function neural network (NN) with continuous learning algorithm for the velocity and orientation angle tracking control of a mobile robot. Herein, two NN controllers embedded in the closed-loop control system are capable of on-line continuous learning and do not require any knowledge of the dynamics model. The neuron function of the hidden layer in the three-layer feed-forward network structure is on the basis of combining a sine function with a unipolar sigmoid function. In the NN algorithm, the weight values are only adjusted between the nodes in hidden layer and the output nodes, while the weight values between the input layer and the hidden layer are one, that is, constant, without the weight adjustment. The developed NN controllers have simple algorithm and fast learning convergence. Therefore, the proposed NN controllers can be suitable for the real-time tracking control of the mobile robots. The simulation results show that the proposed NN controller has better control performance in the tracking control of the mobile robot. The compound sine function NN provides a new way to solve tracking control problems for a mobile robot.