The theory of probabilistic linguistic term sets (PLTSs) is very useful in objectively dealing with the multi‐criteria group decision making (MCGDM) problems in which there is hesitancy in providing linguistic assessments; and PLTSs allow experts to express their preferences on one linguistic term over another. In order to reflect the uncertainty and inconsistency of decision‐makers and handle incomplete linguistic information, we propose a new PLTS called interval‐valued probabilistic linguistic term set (IVPLTS). In addition, the existing approaches associated with PLTSs are limited or highly complex in real applications. Therefore, new operations, comparison laws, and aggregation operators are developed for IVPLTS. Furthermore, we establish an efficient framework for MCGDM problems based on the proposed comparison method and the fuzzy preference relation. Then we apply it to a real‐life case under linguistic environment. The extended TOPSIS methods combined with PLTSs by using different operational laws are also included for comparison. The final results demonstrate the efficiency and practicality of the new framework.
In this work, we propose a novel and facile route for the rational design of Si@SiO/C anode materials by using sustainable and environment-friendly cellulose as a carbon resource. To simultaneously obtain a SiO layer and a carbon scaffold, a specially designed homogeneous cellulose solution and commercial Si nanopowder are used as the starting materials, and the cellulose/Si composite is directly assembled by an in situ regenerating method. Subsequently, Si@SiO/C composite is obtained after carbonization. As expected, Si@SiO is homogeneously encapsulated in the cellulose-derived carbon network. The obtained Si@SiO/C composite shows a high reversible capacity of 1071 mA h g at a current density of 420 mA g and 70% capacity retention after 200 cycles. This novel, sustainable, and effective design is a promising approach to obtain high-performance and cost-effective composite anodes for practical applications.
Bimorph-type bending actuators have been widely used in many applications as converters of electric input to mechanical motion, or vice versa. In this paper a new piezoelectric model of a multilayer piezoelectric cantilever is obtained, and the analytic expressions for the curvature, displacement and tip-deflection of the multilayer structure are derived in the static state. With the use of this model and the solution, the tip-deflections of the piezoelectric bimorph cantilever in different working situations are compared and the effect of the metal electrodes on the tip-deflection of the cantilever is considered. The above-mentioned methods and conclusions can be used for optimized design of PZT cantilever structure.
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