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This paper aims to apply an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach to a multi-hierarchy grey relational analysis (GRA) model. Consistent with the most real-life applications, the authors focus on a two-level hierarchy in which the attributes of similar characteristics can be grouped into categories. Nevertheless, the proposed approach can be easily extended to a three-level hierarchy in which attributes might also belong to different sub-categories and further be linked to categories.

The procedure of incorporating the DEA and AHP methods in a two-level GRA may be broken down into a series of steps. The first three steps are under the heading of attributes and the latter three steps are under the heading of categories as follows: computing the grey relational coefficients of attributes for each alternative using the basic GRA model which further provides the required (output) data for an additive DEA model; computing the priority weights of attributes and categories using the AHP method which provides a priori information on the adjustments of attributes and categories in additive DEA models; computing the grey relational grades of attributes in each category for alternatives using an additive DEA model; converting the grey relational grades of attributes to the grey relational coefficients of categories; computing the grey relational grades of categories for alternatives using an additive DEA model; computing the dissimilarity grades of categories for the tied alternatives using an additive DEA exclusion model.

The proposed approach provides a more reasonable and encompassing measure of performance in a hierarchy GRA, based on which the overall ranking position of alternatives is obtained. A case study of a wastewater treatment technology selection verifies the effectiveness of this approach.

This research is a step forward to overcome the current shortcomings in a hierarchy GRA by extracting the benefits from both the objective and subjective weighting methods.

Ride comfort is one of the important factors affecting passenger health. Therefore, the elevator industry usually uses the International Organization for Standardization (ISO) 18738-1 standard to evaluate elevator ride quality and optimize elevator design. However, this method has certain limitations in its evaluation of comfort due to the problem of boundary division. The ISO 2631-4 standard is used as a general method of comfort evaluation in the current rail transit system, but it has not been applied in the elevator industry. In order to explore the difference and connection between the two standards, the author aims to conduct a detailed analysis on this.

Based on the elevator internet, a large amount of measured data of normal and abnormal vibration of elevator car were collected and analyzed and preprocessed; based on ISO 18738-1:2012 standard and ISO 2631-4:2001 standard, the differences of ride comfort assessment methods in the two standards were analyzed, and the ride comfort assessment study of elevator under normal and abnormal vibration conditions was carried out.

The experimental results show that the comfort assessment results of ISO 2631-4:2001 standard and ISO18738-1:2012 standard are consistent under two vibration conditions. At the same time, ISO 2631-4:2001 can not only provide a more accurate quantitative description of comfort, but also roughly determine the comfort interval of each vibration, which can provide theoretical reference for elevator vibration classification and car comfort design.

The authors designed an Internet of Things (IOT)-based elevator vibration signal acquisition method to address the shortcomings of the previous elevator ride comfort assessment methods, which can realize the dynamic assessment of elevator ride comfort; by comparing the assessment results of elevator ride comfort under normal vibration and abnormal vibration, the feasibility of ISO 2631-4:2001 for elevator ride comfort assessment was fully verified. In addition, the experimental results also give the influence of abnormal vibration on elevator riding comfort under the stages of start-stop, uniform speed, acceleration and deceleration, which can provide theoretical support for elevator vibration suppression and comfort transformation.