Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

In this paper, a new chaotic system is proposed based on mixing three-dimensional Chen chaotic system with a chaotic tactics. This new system is proved to be chaotic under Wiggins' chaos definition and can generate chaotic sequences with high complexity. Furthermore, we propose a new pseudorandom bit generator (PRBG) based on this new system. A coding algorithm is used to make the sequences uniform. Both statistical and security tests are provided to show the generated sequences are with good randomness and high complexity to withstand attacks.

Single-valued neutrosophic cubic set is a good tool to solve the vague and uncertain problems because it contains more information. The article first gives the correlation coefficient of single-valued neutrosophic cubic sets. Then, a decision method is proposed, and an application in pattern recognition is considered. Finally, examples are given to explain the feasibility of this method. At the same time, the comparative analysis shows the superiority of this method.

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