Z. Zhu

X. Wu, Z. Zhu, G. Çaylı et al.

The picture fuzzy set, characterized by three membership degrees, is a helpful tool for multi-criteria decision making (MCDM). This paper investigates the structure of the closed operational laws in the picture fuzzy numbers (PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an admissible order for PFNs and prove that all PFNs form a complete lattice under this order. Then, we give some specific examples to show the non-closeness of some existing picture fuzzy aggregation operators. To ensure the closeness of the operational laws in PFNs, we construct a new class of picture fuzzy operators based on strict triangular norms, which consider the interaction between the positive degrees (negative degrees) and the neutral degrees. Based on these new operators, we obtain the picture fuzzy interactional weighted average (PFIWA) operator and the picture fuzzy interactional weighted geometric (PFIWG) operator. They are proved to be monotonous, idempotent, bounded, shift-invariant, and homogeneous. We also establish a novel MCDM method under the picture fuzzy environment applying PFIWA and PFIWG operators. Furthermore, we present an illustrative example for a clear understanding of our method. We also give the comparative analysis among the operators induced by six classes of famous triangular norms.

Q. Jiang, S. Li, Z. Zhu et al.

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing matrix is designed by minimizing a weighted function such that the Gram of the equivalent dictionary is as close to the Gram of dictionary as possible. An analytical solution for the corresponding sensing matrix is derived which leads to low computational complexity. We also exploit this prior information through the sparse recovery stage and propose a probability-driven orthogonal matching pursuit algorithm that improves the accuracy of the recovery. Simulations for synthetic data and application scenarios of surveillance video are carried out to compare the performance of the proposed methods with some existing algorithms. The results reveal that the proposed CS system outperforms existing CS systems.