Passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains: Fusion of R-DEMATEL and FNN

Abstract

At present, high-speed trains have become popular modern transportation. As a significant part of the high-speed train riding activity, the stowing and unloading luggage task has its characteristics. To comprehensively and reasonably evaluate passenger comfort of the stowing and unloading luggage task in high-speed trains. In this paper, passenger behavior characteristics are firstly analyzed by the author, the theoretical architecture of passenger comfort evaluation is constructed with the perspective of product aesthetics and ergonomics, and then the process of the passenger comfort evaluation is put forward. Secondly, a combination of Rough Number (RN) and Decision Making Trial and Evaluation Laboratory (DEMATEL) (i.e. R-DEMATEL) is utilized to solve the centrality degree of comfort influencing factors and determine comfort evaluation indexes. Furthermore, the passenger comfort evaluation model with Fuzzy Neural Network (FNN) is constructed and trained. After that, the sample data of the evaluation are collected through the simulated experiment of the stowing and unloading luggage task, and they are trained with FNN comparing to Back Propagation Neural Network (BPNN). Eventually, the result of examples testing is verified that the effectiveness of the proposed method.

Keywords

Comfort evaluation stowing and unloading luggage Rough-DEMATEL (R-DEMATEL)FNN high-speed trains

1 Introduction

The continuous development of science, technology and social economy, which leads that China is stepping into the era of high-speed railways. Higher requirements with passenger comfort in high-speed trains have emerged. Studies on passenger comfort [1, 2] showed that improving the sense of comfort associated with a trap could increase the proportion of passengers. Comfort is the pleasant state of physiological, psychological, and physical harmony between human beings and their environment [3]. How to provide passengers with a more comfortable, pleasant and safe riding environment is one of the problems that the high-speed railways’ ergonomic design industry requires to challenge. Passenger comfort of the stowing and unloading luggage task is a basic demand for passengers to take a high-speed train, as one of the most matter principles for luggage rack design and evaluation, it plays a momentous role in the field of high-speed trains.

The luggage rack is a part of cabin equipment in high-speed trains, the research on passenger comfort evaluation of the stowing and unloading luggage task is of great significance to optimize luggage rack design, and it will be conducive to improve the riding comfort of high-speed trains [4]. Whereas passenger comfort influencing factors of the stowing and unloading luggage task in high-speed trains are numerous and the hierarchy levels are complex. At the same time, current comfort evaluations are lacking the comprehensive evaluation with quantitative and qualitative methods for referred users, products and environment of the task. Especially, when it comes to the user perception for comfort during subjective evaluation, it often seems that the results are vague and different. How to effectively evaluate passenger comfort of the stowing and unloading luggage task is a key issue for the comfort research in high-speed trains.

The determination of evaluation indexes can be regarded as the decision-making problem in this paper. There are quite a few proven methods to solve the criteria weights. For example, West-Worst Method (BWM) has fewer pairwise comparisons and agile ability to handle inconsistencies while it requires consistency examination, and BWM is often used to calculate subjective weights [5]. Level Based Weight Assessment (LBWA) is a subjective weighting method based on pairwise comparisons of criteria which eliminating the need to redefine ordinal scale [6]. Full Consistency Method (FUCOM) is a model to determine the weight coefficient of respective criteria objectives in multi-objective problems, and it can yield more consistent results with mathematical calculation [7]. Besides, DEMATEL is developed to solve complex problem groups, and it assumes that all criteria determined are in interaction with each other, evaluates the effect levels among criteria [8]. Especially, it is an objective method to eliminate less significant criteria and attributes [9]. At present, it also has been widely used in criteria determination due to its practicability and convenience. Thus, DEMATEL is more proper to eliminate less significant criteria and objectively determine criteria weights compared with the above methods. Meanwhile, to more accurately describe the relationship between various factors, we have researched RN, fuzzy number, grey number and neutrosophic number. In the imprecise and vague evaluating information of criteria, we have found the benefits of RN that it not only could maintain the objectivity of the original data but also could better reflect the subjective and fuzzy perceptions of experts or decision-makers, as well it could more completely express the information compared with other methods [10]. Therefore, we propose that RN and DEMATEL are combined to describe the express information and determine weights when analyzing passenger comfort influencing factors for the stowing and unloading luggage task.

Comfort evaluations generally have objective and subjective criteria. In multicriteria evaluation methods, there are Multi-Attributive Border Approximation Area Comparison (MABAC), Compromise Solution (MARCOS), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) and so on. For example, MABAC can calculate the distance between each alternative and the best alternative [11]. In MARCOS, the alternatives are ranked for the final utility function, then to determine the best one [12]. TOPSIS is an effective and reliable tool to obtain the optimal alternative, its conception is to find a positive ideal solution (PIS) and a negative ideal solution (NIS) as comparison standards for each alternative, and measure the separation of each alternative from the PIS and NIS [13]. VIKOR method can evaluate the ranking of the alternatives, and it is better to TOPSIS in computational complexity [7]. While, passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains has objective and subjective contents, among the subjective evaluation has the characteristics of uncertainty and vagueness, the objective evaluation has abundant data to handle. Thus, it is necessary to explore an approach to deal with this situation. Relative to the general neural network, FNN not only has the advantage of the fuzzy logic system, which is good at utilizing expert language information but also the strong self-learning ability and self-adaptability, it can deal with quantitative and qualitative knowledge.

According to the above analyses, DEMATEL is effective to explore the relationship between factors and obtain the criteria, while it lacks the mechanism of manipulating subjective and ambiguous judgments. It is necessary to use a mathematical method to analyze the judgments. And the rough DEMATEL method is more appropriate to solve the problem. Then to achieve a comprehensive evaluation, the passenger comfort evaluation model is built with the advantages of FNN. Through the evaluation model, the non-linear relationship between objective and subjective evaluations is constructed to retain the expert experience and knowledge, further to come true rapid and accurate comfort evaluations. The scientific and reasonable approach to passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains will have an important significance in improving the quality of luggage rack product design.

2 Literature review

Comfort evaluation methods are classified into subjective, objective and comprehensive evaluation methods, which are mainly including mathematical model-based evaluation, fuzzy evaluation, grey correlation evaluation, artificial neural network evaluation, etc. At present, the research on comfort evaluations has passenger comfort, manipulating comfort, visual comfort and others, which referring aviation, aerospace, navigation, automobile, railway train and other fields. Among them the comfort of standing posture, sitting posture and using facilities are common. Moraes et al. [14] studied the comfort evaluation of airplane business class passengers with standing and sitting. The airplane cabin comfort model proposed by Ahmadpour et al. [15] had proved the importance of the physical interaction between passengers and the luggage compartment. Kumar et al. [16] built a mathematical model for the evaluation of car passenger comfort. In research of manipulating comfort evaluations, upper limb manipulation comfort has been widely concerned. Li et al. [17] proposed to use a real-time optical motion capture system to obtain the experimental data of the human upper limb, then the human upper limb motion comfort was evaluated by calculating the real-time load rate of human upper limb muscles. Zahedi et al. [18] developed a VR simulator to measure and analyzed the movements of upper limb joints to evaluate user performance. From that, it can be seen that comfort studies have been obtained some achievements.

At the same time, the applications of DEMATEL, ANP, AHP and MULTIMOORA methods are familiar in the decision-making and evaluation problem. Liu et al. [19] considered the mutual relationship of aircraft cabin comfort evaluation standards, the model of DEMATEL was applied to study the evaluation of cabin environment, facilities and layout, seats, etc. Petrović [6] proposed that criteria and attributes determination were carried out by DEMATEL with eliminating less significant criteria and attributes, criteria weights were determined with AHP. And Chen et al. [20] integrating the advantages of DEMATEL and ANP proposed DEMATEL-ANP to decompose the complex evaluation problem into an understandable structural model and reduce the calculation work in evaluation issues. In some selection problems, the MULTIMOORA approach is applied to rank alternatives after determining the criteria [21]. They have largely applied to the study of evaluations. It is seen that DEMATEL, ANP, AHP are generally combined to determine weights according to relevant experts’ emphasis on each criterion. Besides, Rough Set Theory (RST) is proposed by Z. Pawlak, which is an effective mathematical tool for analyzing and processing uncertain, inconsistent and incomplete information, and it also applied to evaluation problems [22]. Kong et al. [23] put forward a quality evaluation method with RST. Song et al. [24] used the merit of RST in manipulating subjective judgments and combined the DEMATEL method to evaluate the interaction between requirements of the product-service system. Therefore, the combination of RST and DEMATEL is more effective to explore the relationship of factors under an uncertain environment.

With the rapid development of the neural network, more and more scholars have researched comfort evaluation methods with intelligent neural networks on account of the strong learning capability of networks. FNN is an artificial neural network combined with fuzzy theory, hence it has the advantage of the fuzzy logic system that is good at utilizing expert language information. At present, FNN has largely applied to the evaluation problem [25]. In the evaluation problem, Gao et al. [26] applied FNN to evaluate the visual comfort of light sources. Zhao et al. [27] aiming at the uncertainty and fuzziness in the evaluation of standing posture handling comfort, built an evaluation model of the handling comfort with T-S fuzzy neural network. Xu et al. [25] put forward a method for reliability evaluation of wireless sensor networks with FNN. To ensure more accurate evaluations, the researchers have taken a variety of methods that are frequently used recently.

At present, there are still limited researches on comfort evaluations of the stowing and unloading luggage task. Physiology and psychology elements are mainly studied from the perspective of users. How to comprehensively integrate objective and subjective criteria into the evaluation will become a more concerning issue for researchers. Multiple dimensions of physical, behavior and cognition are comprehensively considered in this paper and the passenger comfort evaluation system is proposed. To scientifically and accurately evaluate passenger comfort of the stowing and unloading luggage task in high-speed trains, the R-DEMATEL method is put forward to determine the evaluation indexes, and the evaluation model is established based on FNN.

3 Passenger comfort evaluation system of the stowing and unloading luggage task in high-speed trains

In this chapter, the physical performance of products, the behavior and the psychological cognition of users are considered into passenger comfort evaluation with characteristics of the stowing and unloading luggage task in high-speed trains, then the responding passenger comfort evaluation system is put forward.

3.1 Passenger behavior characteristics of the stowing and unloading luggage task

The process of stowing and unloading luggage in high-speed trains involves multiple disciplines, such as anthropometrics, anthropotomy, physiology, biomechanics, psychology, etc. According to the classification of moving actions with upper limbs, the stowing and unloading luggage actions can be divided into lifting, pushing, pulling and unloading [28]. The most common actions are lifting and unloading in this process and the rest are micro-adjustments for luggage, in which they involve the position of head, neck, trunk, upper limbs, lower limbs, waist and others. Under the joint action of physiological and psychological activities, the physical and psychological loads of passengers are generated. Among them, physical loads are produced from local muscle loads, i.e. trunk muscle, hand muscle, back muscle, neck muscle and other muscle loads. All local muscle loads will affect passenger comfort, the involved local muscles and theirs parameters are shown in Table 1. The influencing factors of psychological loads are including passenger experience, psychological cognition level, cabin internal environment, etc. SWAT scale can be utilized to analyze passenger psychological loads for the stowing and unloading luggage task.

Table 1
The passenger comfort influencing factors of the stowing and unloading luggage task and the parameter of local muscle load

Comfort influencing factors The description

Muscle name Muscle load v

The weight of luggage Trunk muscle L4, L5 peak torque

The volume of luggage Hand lifting position Lifting frequency

The height of luggage rack Back load L5, S1 peak torque

Lifting speed Low back pain Recovery time

Environment factor Neck fatigue Muscle pain

Personal factor Angle of trunk L4, L5 pressure

Comfort influencing factors	The description
The weight of luggage	Trunk muscle	L4, L5 peak torque
The volume of luggage	Hand lifting position	Lifting frequency
The height of luggage rack	Back load	L5, S1 peak torque
Lifting speed	Low back pain	Recovery time
Environment factor	Neck fatigue	Muscle pain
Personal factor	Angle of trunk	L4, L5 pressure

Surface Electromyography (sEMG) is a technique to measure muscle electrical activity through electrodes covering the muscle skin, and it usually requires electrodes to record the voltage difference between independent electrodes to obtain the data of subjects. At present, sEMG has become the main measurement method for quantifying human muscle activity [29]. Where Maximum Voluntary Contraction (MVC) of muscles can perfectly reflect muscle fatigues [30]. Therefore, this paper will collect the MVC value of muscles in the process of stowing and unloading luggage with sEMG, and analyze the status of local muscle fatigues through the muscle data for key positions.

3.2 The architecture of passenger comfort evaluation

(1) Physical layer analysis

The aesthetic and usable characteristics of product design involving appearance, material, structure, etc. will have a certain impact on user psychology, visual comfort, task load and operation mode when using a product and determine the overall quality of product design. The luggage rack function of high-speed trains mainly displays different user reactions in the process of user interaction with a product. Thus, the performance elements of physical layer that influencing comfort should be considered in passenger comfort evaluation. Passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains can analyze aesthetic features of luggage rack product, like modeling, color, material, structure, etc.

(2) Behavior layer analysis

The main purpose of ergonomic evaluation method research is to convert the human comfort, fatigue values and other indexes into the intuitively expressed data through qualitative and quantitative methods, to analyze and evaluate the most demanded data in design under the constraints of limited time and cost. With the ergonomics theory, this paper proposes to analyze comfort influencing factors of the stowing and unloading luggage task in high-speed trains from the perspective of behavior layer.

In the human-machine-environment system of stowing and unloading luggage, human elements are including physical and behavioral characteristics of passengers, machine elements are composed of the parameter of luggage rack design and luggage, and environment elements are involving compartment environment of high-speed trains (seen in Fig. 1). With the above analysis, the passenger characteristic, the task load, the parameter of luggage rack and luggage are taken into consideration on evaluation factors that influencing passenger comfort of the stowing and unloading task in high-speed trains.

Fig. 1

The interaction of the human-machine-environment system in user behavior layer.

(3) Cognition layer analysis

Psychological cognition differences of passengers in the stowing and unloading luggage task, which will affect the comfort evaluation results.

In the user cognitive layer, psychological load factors influencing passenger comfort are determined that it consisting of time load, effort load and psychological stress load with the cognitive psychological analysis for the stowing and unloading luggage task.

Considering the influence of different aspects during passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains, the evaluation architecture is constructed as shown in Fig. 2.

Fig. 2

The architecture of passenger comfort evaluation in the stowing and unloading luggage task.

3.3 The process of passenger comfort evaluation

Aiming at the problem of how to accurately determine comfort evaluation indexes, with the advantages of RST in dealing with fuzziness and uncertainty and the DEMATEL method in determining the mutual influence relationship among various factors, the R-DEMATEL method is discussed to confirm comprehensive comfort evaluation indexes. Moreover, to solve the problem of uncertainty and fuzziness during passenger comfort evaluation, the passenger comfort evaluation model is proposed with FNN to train the relationship between the parameter of objective evaluations and the result of subjective evaluations. As well, the evaluation process is shown in Fig. 3.

Fig. 3

The process of passenger comfort evaluation in the stowing and unloading luggage task.

4 An approach to determining comfort evaluation indexes with R-DEMATEL

4.1 Solve the centrality degree of comfort influencing factors with R-DEMATEL

Rough Number (RN) is developed from RST, which is composed of a set of closed intervals including the lower and upper limit with flexible boundaries. RN can handle out data sets that do not require prior knowledge [30], thus it is widely used for knowledge discovery, data mining, decision analysis, pattern recognition, etc. Through an approximate representation of the membership function, RN can describe the fuzziness and the uncertainty over the boundary region of sets.

For the passenger comfort evaluation problem of the stowing and unloading luggage task in high-speed trains, an approach to determining comfort evaluation indexes with a combination of RST and DEMATEL (i.e. R-DEMATEL) is utilized to solve the centrality degree of comfort influencing factors with the advantage of information, rather than the traditional single analysis of influencing factors. And the detailed process is as follows.

Firstly, the direct relationship matrix of different influencing factors in passenger comfort is established with the experts’ judgment. Suppose that s experts are invited to pairwise compare the influencing relationship among different factors, and the group direct relationship matrix R^* is represented in Equation (1). Among them, $r_{ij}^{k}$ denotes the influencing degree judgment value of the k^th expert between the i^th and the j^th influencing factor.

$R^{*} = [\begin{matrix} 0 & r_{12}^{*} & \dots & r_{1 m}^{*} \\ r_{21}^{*} & 0 & \dots & r_{2 m}^{*} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{m 1}^{*} & r_{m 2}^{*} & \dots & 0 \end{matrix}]$ (1)

Secondly, the rough group direct relationship matrix is determined. The rough sequence $RN (r_{ij}^{*})$ and the mean rough interval $\bar{RN ({\tilde{r}}_{ij}^{*})}$ are respectively shown in Equations (3).

$R N (r_{i j}^{*}) = {[r_{i j}^{1 L}, r_{i j}^{1 U}], [r_{i j}^{2 L}, r_{i j}^{2 U}], \dots, [r_{i j}^{k L}, r_{i j}^{k U}], \dots, [r_{i j}^{s L}, r_{i j}^{s U}]}$ (2) $\bar{RN ({\tilde{r}}_{ij}^{*})} = [r_{ij}^{* L}, r_{ij}^{* U}]$ (3)

Where $r_{ij}^{* L} = \frac{\sum_{k = 1}^{s} r_{ij}^{kL}}{s}$ , $r_{ij}^{* U} = \frac{\sum_{k = 1}^{s} r_{ij}^{kU}}{s}$ .

Therefore, the rough group direct relationship matrix D is expressed in Equations (6).

$\begin{matrix} D = {\bar{[RN (r_{ij}^{*})]}}_{m \times m} = \\ [\begin{matrix} [0, 0] & [r_{12}^{* L}, r_{12}^{* U}] & \dots & [r_{1 m}^{* L}, r_{1 m}^{* U}] \\ [r_{21}^{* L}, r_{21}^{* U}] & [0, 0] & \dots & [r_{2 m}^{* L}, r_{2 m}^{* U}] \\ ⋮ & ⋮ & [0, 0] & ⋮ \\ [r_{m 1}^{* L}, r_{m 1}^{* U}] & [r_{m 2}^{* L}, r_{m 2}^{* U}] & \dots & [0, 0] \end{matrix}] \end{matrix}$ (4) ${\bar{RN ({\tilde{r}}_{ij}^{*})}}^{'} = \frac{\bar{RN ({\tilde{r}}_{ij}^{*})}}{δ} = [\frac{r_{ij}^{* L}}{δ}, \frac{r_{ij}^{* U}}{δ}]$ (5) $δ = max_{1 ⩽ i ⩽ m} (\sum_{j = 1}^{m} r_{ij}^{* U})$ (6)

According to the rough group direct relationship matrix, the rough total relationship matrix T is determined. T is described as T = [t_ij] _m×m, at the same time, $T^{p} = [t_{ij}^{p}]_{m \times m} = D^{'^{p}} (I - D^{'^{p}})^{- 1}$ . Where p = L, U, well I is the unit matrix.

DEMATEL is used to acquire the influencing degree of each factor relative to another by the transformation of the direct influencing matrix. Then, the centrality degree (C_i) of passenger comfort influencing factors are represented with the calculation of the influencing degree in Equations (8). $C_{i} = r_{i} + c_{i}$ (7) $r_{i} = [\sum_{j = 1}^{m} t_{ij}]_{m \times 1}, c_{i} = [\sum_{i = 1}^{m} t_{ij}]_{1 \times m}$ (8)

4.2 Determine evaluation indexes for the stowing and unloading luggage task in high-speed trains

Evaluation hierarchy (H), evaluation index (I), evaluation weight (W), evaluation data (D) are involved in the evaluation system. The mathematical representation of the passenger comfort evaluation system is described as S = f (H, I, W, D). The evaluation objectives are divided into several subsystems based on constitutions, as well they are gradually subdivided into each part that can be described and implemented with specific indexes.

Physiological, psychological and aesthetic demands of passengers are analyzed according to the collected data and relevant experience summaries in the early stage, and passenger comfort influencing factors are extracted in this paper. The importance judgments between one factor and another factor are produced by experts and handled with RN. Then, the normalization for the upper and lower limit of rough centrality degree is carried out with R-DEMATEL, and the calculation formulas of C_i are shown in Equations (10). ${\tilde{C}}_{i}^{L} = \frac{C_{i}^{L} - min C_{i}^{L}}{max C_{i}^{U} - min C_{i}^{L}}, {\tilde{C}}_{i}^{U} = \frac{C_{i}^{U} - min C_{i}^{L}}{max C_{i}^{U} - min C_{i}^{L}}$ (9) $C_{i} = α {\tilde{C}}_{i}^{L} + β {\tilde{C}}_{i}^{U}, α + β = 1$ (10)

Next, these factors are ranked according to the magnitude of the centrality degree. Eventually, comfort evaluation indexes for the stowing and unloading luggage task in the high-speed trains are determined by the centrality degree threshold. Then, the evaluation model should be conducted.

5 The passenger comfort evaluation model building with FNN and data processing

After determining the evaluation system and evaluation indexes, the evaluation model is necessary to be constructed. FNN can extract fuzzy rules through adaptive neural network learning, effectively calculate the optimal parameter of the membership function. Thus, the mapping relationships between the input and the output of the evaluation model are established through fuzzy reasoning [31], which has better evaluation effectiveness. The passenger comfort evaluation model of the stowing and unloading luggage task in high-speed trains is constructed with FNN, and the evaluation process is shown in Fig. 4.

Fig. 4

Flow chart of passenger comfort evaluation of the stowing and unloading luggage task.

The evaluation model based on FNN has a four-layer feedforward neural network. Among them, the first layer to the fourth layer, respectively, is the input layer, the membership function layer, the fuzzy reasoning layer and the output layer [32], and the network structure is shown in Fig. 5. Among them, the input variables of the evaluation model are the objective evaluation indexes over passenger comfort of stowing and unloading task, and the output variable is the subjective overall comfort evaluation scoring. Then, the threshold values are set with the training data.

Fig. 5

The four-layer feedforward neural network structure of the evaluation model.

The input and output of each node in the input layer of the evaluation model are as follows. ${Out}_{1} (i) = {In}_{1} (i) = x_{i}, i = 1, 2, \dots, n .$ (11)

Where In₁(i) and Out₁(i) are respectively described as the input and the output of ith node in the input layer. In the membership function, the Gauss function is adopted to the membership function, among μ and σ are respectively the center and base length. The membership function is as follows. ${Out}_{2 i}^{k} = μ_{i}^{k} = exp (- {(x_{i} - μ_{ik})}^{2} / σ_{ik}^{2})$ (12)

Where i = 1, 2,..., n; k = 1, 2,..., m; Out_2i^k, μ_i^k and σ_ik are respectively the neuron output value, μ and σ of the m_i^k neuron.

In the fuzzy reasoning layer, the output of the node is calculated by fuzzy AND, and the product operators are adopted to obtain the excitation intensity of each rule, thus the input and the output are as follows. ${Out}_{3 k} = {In}_{3 k} = \prod {Out}_{2 i}^{k}$ (13)

Where In_3k and Out_3k are respectively the input and the output values of the kth neuron in the third layer.

The output layer of the evaluation model represents the result of the subjective fuzzy evaluation, and its output value is as follows. ${Out}_{4} = {In}_{4} = \sum k = 1 m (w_{k} {Out}_{3 k})$ (14)

Where In₄ is described as the input of the fourth layer. w^k is the connecting weight of the kth node in the hidden layer to the output layer in the fuzzy reasoning layer.

The evaluation model utilizes the principle of FNN that retaining the expert experience and knowledge, to obtain the membership degree relationship between the sample data through the training. Eventually, it realizes the rapid and accurate comfort evaluation of the stowing and unloading luggage task.

The passenger comfort evaluation includes subjective and objective data. In terms of the objective data, it can be obtained from the experimental measurement. About the sEMG data of local muscle loads, Delysis Analysis software will be used to analyze and process the data with the second-order IIR Butterworth filter. As well, regarding the subjective evaluation data, it is necessary to conduct data analysis for the mental load and the overall comfort evaluation data with quantitation in order to train the evaluation model.

There is a close relationship between SWAT scale and mental load, thus the authors will be set out the SWAT scale of passenger mental load in the stowing and unloading task based on the normal SWAT scale assessment criterion and the mental load variational characteristics during this specific environment (as shown in Table 2). It is used to collect the information of the SWAT scale with the questionnaire survey, the reliability and the validity of the SWAT scale are certified with the statistical method. The scores in mental loads are acquired with SWAT scale scoring criteria (shown in Table 3), where T, E and S respectively representing time load, mental effort load and mental stress load [33], and then the subjective assessments for mental loads in the stowing and unloading luggage task in high-speed trains have been acquired.

Table 2

The SWAT scale of mental load in the stowing and unloading luggage task

Item	Description of the stowing and unloading luggage task	Rating level
Time load	How much time is needed in the process of stowing and unloading luggage?	Light	Middle	High
Mental effort load	How much effort is required in the process of stowing and unloading luggage?	Light	Middle	High
Mental stress load	How much the mood is changed when encountering difficulties in the process of stowing and unloading luggage?	Light	Middle	High

Table 3

The group and scoring of the mental load SWAT scale in the stowing and unloading luggage task

Scoring	The group						Scoring	The group
	TES	TSE	ETS	EST	STE	SET		TES	TSE	ETS	EST	STE	SET
1	111	111	111	111	111	111	15	223	232	223	322	232	322
2	112	121	112	211	121	211	16	231	213	321	123	312	132
3	113	131	113	311	131	311	17	232	223	322	223	322	232
4	121	112	211	112	211	121	18	233	233	323	323	332	332
5	122	122	212	212	221	221	19	311	311	131	131	113	113
6	123	132	213	312	231	321	20	312	321	132	231	123	213
7	131	113	311	113	311	131	21	313	331	133	331	133	313
8	132	123	312	213	321	231	22	321	312	231	132	123	123
9	133	133	313	313	331	331	23	322	322	232	232	223	223
10	211	211	121	121	112	112	24	323	332	233	332	233	323
11	212	221	122	221	122	212	25	331	313	331	133	313	133
12	213	231	123	321	321	312	26	332	323	332	233	323	233
13	221	212	221	122	212	122	27	333	333	333	333	333	333
14	222	222	222	222	222	222

As for the vagueness and uncertainty of subjective judgments in the overall comfort evaluation of stowing and unloading luggage, we propose that the intuitionistic fuzzy method is applied to handle out the subjective evaluation. The evaluation results are divided into different levels described with language terminology set, where it including {extremely comfortable, highly comfortable, comfortable, little comfortable, generally comfortable, little uncomfortable, uncomfortable, highly uncomfortable, extremely uncomfortable}. To obtain the accurate result of subjective evaluations, the intuitionistic fuzzy function is utilized to map vague language descriptions into corresponding intuitionistic fuzzy numbers.

The language descriptions of the subjective comfort evaluation are eventually quantified into the attribution values, while the language variables and the values are shown in Table 4. And the evaluation attribution value q_A = μ_A - v_A · π_A, where μ_A, v_A and π_A respectively represent the membership degree, the non-membership degree and the uncertainty degree.

Table 4

Language variables of the subjective passenger comfort evaluation and the attribute value

Language variable	The intuitionistic fuzzy numbers [μ _A, v_A, π_A]	The attribution value
Extremely comfortable	[0.95, 0.05, 0.00]	0.950
Highly comfortable	[0.85, 0.10, 0.05]	0.845
Comfortable	[0.75, 0.15, 0.10]	0.735
Little comfortable	[0.65, 0.25, 0.10]	0.625
Generally comfortable	[0.50, 0.40, 0.10]	0.460
Little uncomfortable	[0.35, 0.55, 0.10]	0.295
Uncomfortable	[0.25, 0.65, 0.10]	0.185
Highly uncomfortable	[0.15, 0.80, 0.05]	0.100
Extremely uncomfortable	[0.05, 0.95, 0.00]	0.050

6 A case study

6.1 The determination of evaluation indexes

In this paper, passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains is taken as an example for verification of the proposed evaluation method. The first thing is passenger comfort influencing factors of the stowing and unloading luggage task need to preliminarily be proposed with the typical parameters (referring to Table 1), the analysis of passenger behavior characteristics and the hierarchical architecture of the evaluation system (proposed in subsection 3.2), and Table 5 provides the twelve passenger comfort influencing factors.

Table 5
Passenger comfort influencing factors of the stowing and unloading luggage task

Influencing factor

e ₁ The BMI of passenger e ₇ The volume of luggage

e ₂ The age of passenger e ₈ The weight of luggage

e ₃ The height of luggage rack e ₉ The muscle fatigue

e ₄ The status of passenger e ₁₀ Psychological factors

e ₅ The form design of luggage rack e ₁₁ The environment of compartment

e ₆ The color of luggage rack e ₁₂ Seat parameter

Influencing factor
e ₁	The BMI of passenger	e ₇	The volume of luggage
e ₂	The age of passenger	e ₈	The weight of luggage
e ₃	The height of luggage rack	e ₉	The muscle fatigue
e ₄	The status of passenger	e ₁₀	Psychological factors
e ₅	The form design of luggage rack	e ₁₁	The environment of compartment
e ₆	The color of luggage rack	e ₁₂	Seat parameter

The following is that the comfort evaluation system of the stowing and unloading luggage task is constructed and five experts are invited to judge the influencing degree of one factor (e_i) relative to another factor (e_j) by paired comparison with stary nine levels scale (1-9), the factors are described as e₁, e₂,..., e_i,..., e_j,..., e_n. Then, R-DEMATEL is utilized to solve the rough total-relation matrix with the e₂,..., e_i,..., e_j,..., e_n. Then, R-DEMATEL is utilized to solve the rough total-relation matrix with Equations (6) and the results are shown in Table 6.

Table 6

Passenger comfort influencing factors and theirs the rough centrality degree

	e ₁	e ₂	e ₃	. . .	e ₁₀	e ₁₁	e ₁₂
e ₁	[0.0018, 0.0045]	[0.0045, 0.0085]	[0.0019, 0.0025]	. . .	[0.0022, 0.0030]	[0.0064, 0.0095]	[0.0090, 0.0280]
e ₂	[0.0382, 0.0602]	[0.0016, 0.0058]	[0.0022, 0.0032]	. . .	[0.0027, 0.0053]	[0.0310, 0.0597]	[0.0289, 0.0580]
e ₃	[0.1094, 0.1421]	[0.0908, 0.1214]	[0.0017, 0.0061]	. . .	[0.0109, 0.0361]	[0.0893, 0.1276]	[0.0733, 0.1294]
e ₄	[0.0462, 0.0698]	[0.0357, 0.0722]	[0.0031, 0.0051]	. . .	[0.0028, 0.0060]	[0.0438, 0.0616]	[0.0377, 0.0588]
e ₅	[0.0713, 0.0791]	[0.0506, 0.0750]	[0.0033, 0.0045]	. . .	[0.0029, 0.0043]	[0.0461, 0.0639]	[0.0440, 0.0565]
e ₆	[0.0092, 0.0244]	[0.0082, 0.0282]	[0.0019, 0.0026]	. . .	[0.0021, 0.0026]	[0.0111, 0.0164]	[0.0066,0.01790]
e ₇	[0.0844, 0.1124]	[0.0630, 0.0906]	[0.0069, 0.0283]	. . .	[0.0055, 0.0226]	[0.0557, 0.0959]	[0.0500, 0.0779]
e ₈	[0.1337, 0.1789]	[0.1100, 0.1591]	[0.0391, 0.0825]	. . .	[0.0584, 0.0754]	[0.1147, 0.1659]	[0.0951, 0.1575]
e ₉	[0.1273, 0.1673]	[0.0967, 0.1415]	[0.0505, 0.0696]	. . .	[0.0689, 0.0815]	[0.1047, 0.1534]	[0.0894, 0.1360]
e ₁₀	[0.0934, 0.1260]	[0.0623, 0.1145]	[0.0131, 0.0327]	. . .	[0.0018, 0.0052]	[0.0676, 0.1039]	[0.0596, 0.0909]
e ₁₁	[0.0297, 0.0390]	[0.0053, 0.0165]	[0.0021, 0.0031]	. . .	[0.0027, 0.0041]	[0.0017, 0.0045]	[0.0148, 0.0364]
e ₁₂	[0.0211, 0.0391]	[0.0057, 0.0175]	[0.0022, 0.0040]	. . .	[0.0032, 0.0046]	[0.0097, 0.0294]	[0.0017, 0.0055]

In Table 6, the rough centrality degree of one factor (e_i) relative to another factor (e_j) is consisting of the upper limit value and the lower limit value, and the larger value represents the greater influencing degree. Eventually, the centrality degree of each influencing factor can be acquired with Equations (10), and the calculated results are shown in Table 7.

Table 7

The centrality degree of each influencing factor

Factor	The centrality degree	Factor	The centrality degree
e ₁	0.289	e ₇	0.411
e ₂	0.212	e ₈	0.721
e ₃	0.438	e ₉	0.635
e ₄	0.332	e ₁₀	0.378
e ₅	0.418	e ₁₁	0.235
e ₆	0.235	e ₁₂	0.283

From the Table 7, we can see that the centrality degree ranking of each influencing factors is e₈ > e₉ > e₃ > e₅ > e₇ > e₁₀ > e₄ > e₁ > e₁₂ > e₆ > e₁₁ > e₂, and we set the centrality threshold (0.250) in this paper. Thus, the age of passenger, the color of luggage rack and the environment of compartment are not considered in the objective indexes of passenger comfort. According to the centrality degree ranking and the local muscle loads analysis, objective passenger comfort evaluation indexes of the stowing and unloading luggage task in high-speed trains are ultimately determined as shown in Table 8.

Table 8

Passenger comfort evaluation indexes of the stowing and unloading luggage task

Factor	Evaluation index
Physical	The form design	Luggage rack groove
	Passenger characteristics	Passenger behavior
	Luggage parameters	Weight
		Volume
	Luggage rack parameter	Height
Ergonomics	Physical index (EMG signals of Muscle fatigue)	Trapezius middle fibers (Tmf)
		Biceps brachii (Br)
		Thoracic erector spinae (Tes)
		Lumbar erector spinae (Les)
		Rectus abdominis (Ra)
Cognitive psychology	Psychological index	Time load
		Metal effort load
		Mental stress load

6.2 The evaluation model training and the result analysis

After determining passenger comfort evaluation indexes, the experiment of stowing and unloading luggage with upper limbs is designed. The experiment simulates the airtight environment of the high-speed train compartment to set up luggage racks with different parameters (a height of 165, 172.5 and 180 cm), select luggage of which have different weights and volumes (3, 6, 10KG and 16, 18, 20 inches).

In this experiment, twenty right-handed subjects are required to stow and upload luggage under different conditions, and the valid data of 54 groups tasks are acquired, as well some pictures of the experimental process are shown in Fig. 6. The sEMG data of subjects in local muscle load is collected by physiological polyconductors and processed with Delysis Analysis software (seen in Table 9).

Fig. 6

Pictures of the experiment process: (a) preparation; (b) the stowing luggage task; (c) the unloading luggage task.

Table 9

The sEMG data of subjects in muscle load

No.	Tmf	Br	Tes	Les	Ra
1	14.0658	6.8925	9.2553	14.4168	2.2574
2	10.9105	4.7945	7.7873	16.4287	1.9575
3	10.8808	4.4438	8.0198	14.7575	2.3460
4	10.1102	6.0700	8.0343	17.5110	2.3729
5	14.6657	5.1061	8.6546	14.0871	1.5616
6	15.6505	7.0587	9.6566	16.2675	1.4505
7	16.1897	17.3399	13.1706	17.7351	1.4516
8	14.7760	6.8236	10.7210	18.7721	1.4937
9	18.1665	43.8802	12.8691	16.7827	1.4190
10	12.9205	6.0290	11.9124	16.5654	1.8797
. . .
108	44.1638	14.2644	23.7895	31.8394	7.9331

Then the subjective overall comfort evaluation results of the stowing and unloading luggage task and mental loads of the subjects with the SWAT scale are collected after the experiment. Among them the reliability and the validity of the SWAT scale are analyzed by SPSS software [34], the analysis results are shown in Table 10. Among them, the result of Cronbach’s α coefficient is 0.717 (Cronbach’s α>0.6), it is shown that the test contents of each entry have good homogeneity in this scale; the check result of KMO is 0.669 (KMO > 0.5) as well Bartlett’s spherical check result has statistical significance, thus this scale is appropriate to the factorial analysis. The subjective comfort evaluation results are processed with the intuitionistic fuzzy function.

Table 10

The results of the reliability and the validity analysis in the SWAT scale

The reliability analysis		The validity analysis
Coefficient	Value	Coefficient	Value
Cronbach’s α coefficient	0.717	KMO	0.669
Spilt-half reliability coefficient	0.584	Factor load	Time load	Mental effort load	Mental stress load
Spearman-Brown	0.737	Common factor variance	0.767	0.798	0.834
Sig (P)	0.000 (P < 0.05)		0.589	0.638	0.695

According to the above objective and subjective evaluation experiments, we have found that different manipulation conditions influenced the comfort experience with subjects. And the characteristics of luggage, luggage rack and subjects parameter have an effect on muscle fatigue, which could provide certain references for the comfort evaluation.

The passenger comfort evaluation model with FNN is built, the objective subjective comfort evaluation data are respectively taken as the input and output variables to explore their interrelationships. The input and output of the model are respectively 13 dimensions and 1 dimension, thus, the structure of the model is 13-26-1, and 14 groups of the fuzzy system parameter (P0 to P13) are selected, randomly obtaining the center (c) and width (b) of the fuzzy membership function and using the Gauss Function as the fuzzy membership function. In the training model of FNN, 90%of the experiment data (the valid data of 54 groups tasks) are used as the training set and 10%are used as the test set.

After normalizing the data, the evaluation model based on FNN is repeatedly trained 100 times to adjust the initial weight of the model. Then the central membership degree of each input and output is calculated with the fuzzy membership function. As such, the BPNN-based model is trained to compare with the FNN-based model. It is verified the effectiveness of the proposed method by comparing the performance of the model (seen in Table 11).

Table 11

Comparisons of the performance of the FNN-based and BPNN-based training model

Networks	Iterations	Maximum relative error	Mean relative error	Training goal
FNN-based	100	0.0296	0.0250	10^-3
BPNN-based		0.2401	0.1398	10^-6

It can be seen from the comparison results that the maximum relative error and the mean relative error of the training model based on FNN have a relatively small value compared with BPNN. Thus, the output value of the proposed method is closer to the real expected value and the evaluation results would have good consistency with the expected value than the BPNN-based training model. It is shown that the FNN-based model also has smaller errors than BPNN with a bigger training goal. Moreover, the lower error of the training model is indicating the merit of FNN with the comparations.

In the case of passenger comfort evaluation of the stowing and unloading luggage task in high-speed trains, the evaluation index is determined by experts’ decisions and RST considering the vagueness in the decision-making process can provide the rough intervals to accurately deal with subjective judgments. In addition, the evaluation process not only involves the objective experiment but also has subjective judgments, thus FNN is suitable to handle the vagueness and overcome the randomness in subjective evaluation with defuzzification.

7 Conclusions

In this paper, the passenger comfort evaluation system of the stowing and unloading luggage task in high-speed trains is established with the perspective of physical, behavioral and cognitive layers. Then the passenger comfort evaluation is proposed fusion of R-DEMATEL and FNN. Passenger comfort evaluation indexes of the stowing and unloading luggage task are determined with R-DEMATEL, and the relationship between the output layer and the output layer of the passenger comfort evaluation model is trained with FNN to accurately complete the passenger comfort evaluation. The main innovations are as follows. According to the characteristics of stowing and unloading luggage and passengers’ load, the comfort influencing factors are clarified, and the evaluation method system with subjective and objective analysis is proposed to provide technical and theoretical support for the evaluation. Besides, the judgment process of the comfort influencing factors is the subjectivity and vagueness, thus R-DEMATEL is more appropriate to quantify factor weights, which can be helpful to improve the scientificity of the evaluation. Eventually, subjective evaluation and FNN are combined to evaluate passenger comfort, which overcomes the randomness of subjective evaluation.

The advantages of this paper mainly are as follows. (1) Passenger comfort of the stowing and unloading luggage task is considered from different dimensions that providing the theoretical basis for the evaluation system building. (2) The objective and subjective ways are incorporated to effectively achieve passenger comfort evaluation. (3) R-DEMATEL is utilized to more accurately acquire passenger comfort evaluation indexes, and fuzzy logic and the strong self-learning ability of FNN is utilized to train the relationship of the input and the output in the evaluation model to improve the evaluation efficiency. However, there are some shortcomings, the evaluation criteria are not fully comprehensive. And the learning algorithm of FNN in the evaluation model has not high ideal, it needs to be improved.

Since then, the hierarchical evaluation system of passenger comfort of the stowing and unloading luggage task in high-speed trains will be consummated in our future research. Meanwhile, in the passenger comfort evaluation model with FNN, the training efficiency will be improved through the modified algorithm.

Footnotes

Acknowledgment

This work is supported by the National Key Research and Development Project of China (grant number: 2019YFB1405701).

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Comfort influencing factors	The description
	Muscle name	Muscle load v
The weight of luggage	Trunk muscle	L4, L5 peak torque
The volume of luggage	Hand lifting position	Lifting frequency
The height of luggage rack	Back load	L5, S1 peak torque
Lifting speed	Low back pain	Recovery time
Environment factor	Neck fatigue	Muscle pain
Personal factor	Angle of trunk	L4, L5 pressure