More attention has been drawn to the selection of contractors in recent years,but little research has been conducted on distinguishing representation of performance values for qualitative and quantitative criteria in one decision-making(DM) problem yet.Thus a novel method based on fuzzy number is proposed to solve the representation issue,in which linguistic terms and fuzzy memberships are used to separately describe qualitative and quantitative criteria,and then the linguistic terms are translated into fuzzy numbers which will be defuzzified and unified with fuzzy memberships.The novel method is used to develop a synthetic decision model for selection of contractors.The model is developed to verify the feasibility of the novel method,which(1) builds a twolevel criteria system based on survey and literature summary;(2)utilizes the analytic network process(ANP) to determine criteria weights;(3) uses the novel method to make different representations of performance values for qualitative and quantitative criteria in one DM problem and then unifies different representations for decision matrices;(4) utilizes three multi-criteria decision-making(MCDM) methods containing simple additive weighting(SAW),technique for order preference by similarity to ideal solution(TOPSIS) and complex proportional assessment(COPRAS) to deal with decision matrices.Besides,a case of contractor selection is given to check the novel method by applying developed model,and the case results show that the novel method can suitably solve the representation issue of the performance values for two types of criteria as well as simplify the processes of TOPSIS and COPRAS.
Granular materials are ubiquitous in nature and important in various applications such as road and railway engineering. Granular materials exhibit complicated mechanical behaviors, which are affected significantly by the irregular shape of particles. Currently, the discrete element method (DEM) has been accepted as an effective approach to investigate the mechanical behaviors of granular materials. However, there are scarce simulations based on DEM in literatures considering the irregularity of particle shape. A new method is proposed to simulate individual real particle with irregular shape using clump constituted by overlapping spheres. First, the geometric model of real particle with surface nodes and inner nodes is established through digitally processing the computerized tomography (CT) scanning data. Second, a clump consisting of spheres is generated to simulate the real particle using a minimum distance criterion. The criterion is implemented by tree optimization algorithm. Influential factors are also introduced to balance the model accuracy and computing cost. Effects of the influential factors, including the density of geometric grid and the minimum distance, on simulations are discussed. Results show that this new method is simpler and more efficient than the previous methods in terms of the model accuracy and computing cost.
