Sustainable product designs always draw much attention. However, sustainable or green products are usually costly. This contradiction can be solved via blue design. The concept of blue design originates from the blue economy which is a popular strategy for providing sustainable, healthy, but cheap socioeconomic activities. This study innovatively implements the ideas of sustainability and economy from the blue economy, and the affection (or Kansei in Japanese) from the Kansei engineering into a product design process to become a novel affective-blue design methodology of a product form. The proposed methodology mainly contains three aspects. The first aspect is the merge of a novel Kansei blue model with the traditional Kansei engineering to deal with the semantic space and form decomposition issues encountered in the product form designing process. The second aspect is the adoption of proper data mining schemes to optimally trim and obtain the kernel information from the Kansei evaluation data of products. The third aspect is the usage of appropriate machine learning schemes to establish a precise relationship between product images and design elements from the kernel information. A case study was conducted for the form design of a computer-numerical-control lathe to evaluate the effectiveness of our proposed methodology. The verification results, that all predictive errors are within 4.5% for test samples, show that our blue-affective design methodology is quite satisfying. Through applying this proposed methodology, designers may correctly evaluate and easily catch the essential blue and affective design factors for designing a good industrial product, such as a computer-numerical-control machine tool.

The uncertainty of information plays an important role in practical applications. Uncertainty measurement (UM) can help us in disclosing the substantive characteristics of information. Probabilistic set-valued data is an important class of data in machine learning. UM for probabilistic set-valued data is worth studying. This paper measures the uncertainty of a probability set-valued information system (PSVIS) by means of its information structures based on Gaussian kernel method. According to Bhattacharyya distance, the distance between objects in each subsystem of a PSVIS is first built. Then, the fuzzy Tcos-equivalence relations in a PSVIS by using Gaussian kernel method are obtained. Next, information structures in a PSVIS are defined. Moreover, dependence between information structures is investigated by using the inclusion degree. As an application for the information structures, UM in a PSVIS is investigated. Finally, to evaluate the performance of the investigated measures, effectiveness analysis is performed from dispersion analysis, correlation analysis, and analysis of variance and post-hoc test.

Thermal errors have the largest contribution, as much as about 70%, to the machining inaccuracy of computer-numerical-controlled (CNC) machining centers. The error compensation method so far plays the most popular and effective way to minimize the thermal error. How to accurately and quickly build an applicable thermal error model (TEM) is the kernel work of thermal error compensation. On the basis of some comprehensive machine-learning schemes, past proposed TEMs had impressive merits for dealing with the thermal error modeling of single-function (milling or turning cutting) machine tools with only considering one set of thermal key points. These proposed modelling methodologies become worse when applied to CNC compound milling-turning machining centers in actual cutting applications. This paper proposes a two-mode integral TEM based on the Lasso and the random forest regression schemes to quickly and accurately predict the thermal deformations of such a machine. The first mode is the thermal error modeling for milling cutting conditions, and the second mode is that for turning cutting conditions. For data reduction, two different sets of temperature key points, one for milling and the other for turning, are obtained. Then, on the basis of the random forest regression scheme, we separately establish two TEMs but concurrently use them to predict the tool-center-point deformations of both milling as well as turning spindles. Further, we compare our proposed TEM with several frequently-used machine-learning-based TEMs and the results show that our proposed TEM are the best among all, no matter in the modelling experiment or in the test experiment. The proposed TEM has a maximum prediction error of 6.08 m  for milling cutting and that of 1.455 m  for turning cutting in the modeling experiment. By our proposed twomode integral TEM, the thermal error of a multi-function milling-turning machining center can be accurately predicted and quickly compensated.INDEX TERMS Thermal error model, thermal error compensation, CNC milling-turning machine tools, Lasso regression, machining learning.