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Based on extension models of a new science called Extenics, this paper presents formalized study on similarity and similarity reasoning. The concepts of δ-similarity and δ-similar extension elements are introduced firstly, and then the substitution principles of similarity for solving incompatible problems are set up, showing that similarity substitution is an effective way to solve incompatible problems in the practical world. In addition, the quantitative calculation of similarity is discussed. Finally, three basic rules for similarity reasoning are developed as well.

The processes of generating innovative solutions mostly rely on skilled experts who are usually unavailable and their outcomes have uncertainty. Computer science and information technology are changing the innovation environment and accumulating Big Data from which a lot of knowledge is to be discovered. However, it is a rather nebulous area and there still remain several challenging problems to integrate the multi-information and rough knowledge effectively to support the process of innovation. Based on the new cross discipline Extenics, the authors have presented a collaborative innovation model in the context of Big Data. The model has two mutual paths, one to transform collected data into an information tree in a uniform basic-element format and another to discover knowledge by data mining, save the rules in a knowledge base, and then explore the innovation paths and solutions by a formularized model based on Extenics. Finally, all possible solutions are scored and selected by 3D-dependent function. The model which integrates different departments to put forward the innovation solutions is proved valuable for a user of the Big Data by a practical innovation case in management.

Intelligent behavior that appears in a decision process can be treated as a point y, the dynamic state observed and controlled by the agent, moving in a factor space impelled by the goal factor and blocked by the constraint factors. Suppose that the feasible region is cut by a group of hyperplanes, when point y reaches the region’s wall, a hyperplane will block the moving, and the agent needs to adjust the moving direction such that the target is pursued as faithfully as possible. Since the wall is not able to be represented by a differentiable function, the gradient method cannot be applied to describe the adjusting process. We, therefore, suggest a new model, named linear step-adjusting programming (LSP) in this paper. LSP is similar to a kind of relaxed linear programming (LP). The difference between LP and LSP is that the former aims to find the ultimate optimal point, while the latter just does a direct action in a short period. Where will a blocker encounter? How do you adjust the moving direction? Where further blockers may be encountered next, and how should the direction be adjusted again?$\dots$ If the ultimate best is found, that’s a blessing; if not, that’s fine. We request at least an adjustment should be got at the first time. However, the former is idealism, and the latter is realism. In place of a gradient vector, the projection of goal direction g in a subspace plays a core role in LSP. If a hyperplane block y goes ahead along with the direction d, then we must adjust the new direction $d^{\prime }$ as the projection of g in the blocking plane. Suppose there is only one blocker at a time. In that case, it is straightforward to calculate the projection, but how to calculate the projection when more than one blocker is encountered simultaneously? It is still an open problem for LP researchers. We suggest a projection calculation using the Hat matrix in the paper. LSP will attract interest in economic restructuring, financial prediction, and reinforcement learning.

Due to the independence and out-sync of different monitoring items for deep foundation pit, the existing research have not made good use of monitoring information. To assess the overall safety status of deep foundation pit reasonably, an assessment system was established according to monitoring programs in construction site, furthermore, safety grade of deep foundation pit and index classification were determined. Besides, the matter-element model was set up based on Extenics theory and safety level of deep foundation pit was decided according to maximum correlation principle. Finally, this method was applied to Wuhan Greenland Center, result showed that the safety status was class1, which meant the deep foundation pit was safe.