The linguistic Multi-Criteria Group Decision-Making (MCGDM) problem involves various types of uncertainties. To deal with this problem, a new linguistic MCGDM method combining cloud model and evidence theory is thus proposed. Cloud model is firstly used to handle the fuzziness and randomness of the linguistic concept, by taking both the average level and fluctuation degree of the linguistic concept into consideration. Hence, a method is presented to transform linguistic variables into clouds, and then an asymmetrical weighted synthetic cloud is proposed to aggregate the clouds of decision makers on each criterion. Moreover, evidence theory is used to handle the imprecision and incompleteness of the group assessment, with the belief degree and the ignorance degree. Hence, the conversion from the cloud to the belief degree is investigated, and then the evidential reasoning algorithm is adopted to aggregate the criteria values. Finally, the average utility is applied to rank the alternatives. A numerical example, which is given to confirm the validity and feasibility, also shows that the proposed method can take advantage of cloud model and evidence theory to efficiently deal with the uncertainties caused by both the linguistic concept and group assessment.

Due to the inevitable data missing problem during visual data acquisition, the recovery of color images and videos from limited useful information has become an important topic, for which tensor completion has been proved to be a promising solution in previous studies. In this paper, we propose a novel completion scheme, which can effectively recover missing entries in color images and videos represented by tensors. We first employ a modified tensor train (TT) decomposition as tensor approximation scheme in the concept of TT rank to generate better-constructed and more balanced tensors which preserve only relatively significant informative data in tensors of visual data. Afterwards, we further introduce a TT rank-based weight scheme which can define the value of weights adaptively in tensor completion problem. Finally, we combine the two schemes with Simple Low Rank Tensor Completion via Tensor Train (SiLRTC-TT) to construct our completion algorithm, Low Rank Approximated Tensor Completion via Adaptive Tensor Train (LRATC-ATT). Experimental results validate that the proposed approach outperforms typical tensor completion algorithms in recovering tensors of visual data even with high missing ratios.