A. Study on passenger satisfaction

The concept of customer satisfaction was first proposed by Richard (1965) [3], and subsequent studies have elaborated on the concept of customer satisfaction from different research perspectives. Many experts and scholars comprehensively used various methods to establish an evaluation model for measuring customer satisfaction. Early studies mainly included Oliver (1980) who established an expected inconsistency model [4], Fornell C., Larcker D. F. (1981) studied the structural equation model with latent variables and measurement errors [5], Churchillg. A. J r and Carol Surprenant’s (1982) cognitive performance model [6], Sasser’ s (1987) customer service level model [7], Engel and Blackwell’s (1993) weighted evaluation model [8]. The method of determining the weight is varied, it is particularly important to choose the right weight determination method; in general, the structural equation method (SEM) and driver measurement method have been widely applied [9].

The SERVQUAL (Service Quality) model was established in 1988 by three scholars, A. Prasuraman, Valarie A. Zeithaml and Leonard L.berry (PZB for short). The SERVQUAL model introduces regression analysis into the research and uses this method to assign the weight of customer satisfaction factors in data processing, which is of great significance to the study of customer satisfaction [10]. Sweden established the Sweden Customer Satisfaction Barometer in 1989, and the United States established the ACSI (American Customer Satisfaction Index) based on the Swedish Customer Satisfaction Barometer in 1994. After Sweden and the United States, the European Customer Satisfaction Index (ECSI) model has been established in Europe, and its internal structure has been innovated based on the research in the first two countries to make it develop continuously. New Zealand, Canada, South Korea and other countries have followed suit by creating their customer satisfaction measurement systems. In 2018, a new methodology for improving the measurement of the quality of the service consisting of three phases has been developed [11], the new methodology considers the assessment of the quality dimensions of a large number of participants (customers), on the one hand, and experts’ assessments on the other hand. The methodology was verified through the research carried out in an express post company. In 2019, optimal route criteria for Transport of hazardous material (THM) are selected using a new approach in the field of multi-criteria decision-making [12]. Weight coefficients of these criteria were determined by applying the Full Consistency Method (FUCOM). Evaluation and selection of suppliers is determined by applying the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and the MABAC (Multi-attributive Border Approximation Area Comparison) methods. The proposed route model was tested on the real example of the transport Eurodiesel in Serbia. When defining criteria that have an influence on traffic accessibility, Stanković, M [13] compare the significance of particular criteria using the Fuzzy AHP method and the Rough AHP method, which would show differences in the values of weight significance criteria and their ranking.

Ruisong Yu and Junxiang Cai (2012) proposed a "last kilometer" bus satisfaction evaluation model for Shanghai city by analyzing the operation characteristics of shuttle-bus lines in suburban areas and aiming at the difficulty of traveling in the "last kilometer" of public transport [14]. Jie Yu (2013) [15] focused on the study of conventional bus transit service in small and medium-sized cities, starting from the characteristics of conventional bus transit in small cities, he established a satisfaction evaluation index system for conventional bus transit service in small and medium-sized cities and studied it with the matter-element model. Yucheng Dong (2015) [16] took conventional bus transit of Lianyungang city as an example and constructed a service satisfaction evaluation index system by using WLS method to analyze factors such as bus running speed, ticket price, the attitude of personnel, in-car facilities and station density. Yakun Liu (2015) took 6 districts and counties in Urumqi city as research objects through a questionnaire survey, and conducted the satisfaction evaluation of conventional bus transit with the method of fuzzy evaluation [17]. Huanming Wang and Dajian Zhu (2010), combined with the performance evaluation of public transport services in Shanghai, proposed measures to improve the satisfaction of public transport services, including institutional and financial aspects [18]. Hongmei Wang and lingyu Jia (2011) used the matter-element model to analyze and evaluate the passenger satisfaction of public transport, specifically considering the core needs of passengers for public transport services [19].

B. Empirical study of evaluation on public transport service

Friman et al. (2001) established an evaluation model to evaluate the customer satisfaction of public transport and concluded that the overall satisfaction was positively correlated with the cumulative satisfaction [20]. Kennedy et al. (2005) believed that the public should participate in public transport management and analyzed the influence of the public on the satisfaction of public transport [21]. Tyrinopoulos and Antoniou (2008) respectively used the factor analysis model and logit model to analyze passenger satisfaction with public transport performance [22]. Based on the survey data of South Africa, Mokonyama and Venter (2013) used the joint analysis model to identify the satisfaction levels of different service levels of the public [23]. Fiorio et al. (2013) used the survey data of 33 European cities in 2009 to analyze the correlation between public satisfaction and LPT (Local Public Transport), and found that the highest level of public satisfaction was associated with a single LPT provider [24]. Also, the researchers also studied and analyzed the passenger satisfaction of public transport services in Stockholm, Sweden [25], Bilbao, Spain [26], and Istanbul, Turkey [27]. In 2019, a new model that implies the integration of Full Consistency Method and a Rough Power Heronian aggregator for the selection of criteria for the quality of passenger service in rail transport, from the perspective of persons with disabilities as the main category of passengers, has been created [28]. The survey has covered 168 criteria classified in several groups and the entire territory of Serbia. Blagojević, A [29] In order to solve the criteria selection problem, the Fuzzy Analytical Hierarchical Processes (FAHP) method was experimented with, which showed the priority of the assessment of the efficiency of railway undertakings, on the basis of the five groups of criteria.

Fanghui Zheng (2005) took bus passengers as the investigation object in Guangzhou city, collected and sorted out the questionnaire, obtained the evaluation result of the passenger satisfaction of conventional bus transit, and proposed improvement measures based on the dissatisfaction factors such as the first and last shift, ticket price, and driving speed [30]. Guobing Hu, Sun, etc. (2011) [31] uses the four points graph model, and, from the perspective of passengers, determines the score of evaluation index and its weights, finds the root cause of passenger dissatisfaction and puts forward related suggestions, the feasibility, effectiveness, and extensibility of the index system, the analysis method and the related suggestions are proved by the case study of public transport in Nanchang city. Xiuzhen Guo and Xiaoxiong Weng (2014) [32] used the analytic hierarchy process (AHP) to determine the weight of indicators, and evaluated the level of public transport service with the method of fuzzy comprehensive evaluation. The AHP method represents a formal framework for solving complex multiatributive decision making problems, as well as a systemic procedure for ranking multiple alternatives and/or for selecting the best from a set of available ones [33]. In reference to the American customer satisfaction index (ACSI) model, based on the quality of service, service facilities, service, safety, environment and other four aspects, Lili Jiao (2012) [34] established the index system, built the customer satisfaction index model of urban rail transit of China, and used partial least square method to estimate the model, with the practicability of the model verified by an example.

From the above research status, it can be seen that studies on customer satisfaction are mostly based on practical cases, and different countries have their satisfaction measurement models. Most scholars concentrated on the study of satisfaction factors, models, and the construction of an evaluation index system, focusing on how to build a satisfaction evaluation model for a single-mode public transport, such as bus lines and bus transfers in different cities and carry out case verification. Each study has a certain theoretical and practical value. However, there are still deficiencies in theoretical and practical studies, which are mainly reflected in the following two aspects:

First, the current literature on passenger satisfaction of urban public transport service is not comprehensive enough, and the indicator system needs to be further improved. In particular, the analysis of factors affecting passenger satisfaction of public transport service is not thorough enough in terms of passengers’ demands for comfort, convenience, waiting time, and accessibility.

Second, the existing research is limited to the single-mode evaluation of the passenger satisfaction: urban conventional bus transit or rail transit, and pays less attention to the overall satisfaction evaluation of urban public transport that includes multiple modes.

A. Determining the weight vector by AHP

Based on the actual data obtained from the questionnaire survey, this paper evaluates the annual urban multi-model public transport service in Ningbo city and puts forward corresponding countermeasures and suggestions according to the problems shown in the evaluation results.

Based on the AHP method, the weight vector W_si (see step 3 in subsection A) determined by conducting empirical and/or field studies of transportation professionals reflects the intention of decision-makers, which is the subjective weight from consulting expert opinions. One advantage of the AHP method is that it provides both an elicitation method as well as a strong theoretical framework that allows precise quantitative calculations. The procedures of the AHP method can be illustrated step by step as follows:

1. Step 1: Structure a hierarchy of the criteria based on the evaluated factors.
   Passenger satisfaction of public transport is obtained under the influence of multi-dimensional psychological factors, and the factors are related to each other in a complex way. A hierarchical evaluation model is established based on the principle of giving priority to passengers:
   First, state an overall objective for the problem and list factors that affect the objective. In this case, evaluation target O = {passenger satisfaction with urban public transport service}, according to the evaluation object O, the evaluation criteria set B = {B1, B2 …, Bn}and sub-criteria set C = {C1, C2 …, Cn}. In the case of this paper, B = {waiting time B1, transfer convenience B2, service B3, information B4, passenger comfort B5, station environment B6, interior sanitation B7}. Then structure a hierarchy of criteria for the problem: for each cluster or level in the hierarchy, some factors will be subjected to a corresponding evaluated objective.
2. Step 2: Construct a pairwise comparison matrix.
   The major advantage of the AHP method is that, instead of asking experts to directly give a weight for a particular evaluation factor, they will be asked to rate the relative importance of the different factors. The expert group composed of transportation professionals, through the process of integration, communication, and feedback, uses scaling law proposed by Thomas L. Saaty [36], assuming that there are n evaluation factors, the importance intensity of factor i over factor j can be represented by Aij. A complete pairwise comparison matrix A can, therefore, be obtained.
3. Step 3: Calculate the priority vectors of evaluated factors.
   To calculate the weight vectors of evaluated factors, we used the common method of ANC (average of normalized columns). ANC can be presented as: (1)
   The weight vector can therefore be obtained from matrix A by normalizing the vector in each column and then averaging over the rows of the resulting matrix.
   The weight determined based on the AHP method reflects the intention of decision-makers, so it is a subjective weight: W_si is the subjective weight. Determine the weight vector of the evaluation index, and make the weight distribution set Wi to the index set B or C is W_si, then the subjective weight set of all levels of the index is W = {W_s1, W_s2…, W_sn}.
4. Step 4: Check the consistency of human judgments (consistency check of single-sorting).
   From Step 3, the numerical subjective weights = {W_s1, W_s2…, W_sn} of the factors from the numerical judgments matrix A can be obtained. It is important to check that the human judgments are internally consistent. One method is to calculate the consistency ratio (CR)to reduce the possibility of consistent random deviation, the maximum eigenvalue λ_max and the consistency index CI of the judgment matrix are calculated of the matrix, then calculate the consistency ratio CR which is a measure of how a given matrix compares to a purely random matrix in terms of their consistency indices: (2) (3) Where, RI is the average random index, which is computed and tabulated as shown in Tables [36], If a value of the consistency ratio CR <0.1, the numerical judgments will be considered to be acceptable [36], and the comparison matrix corresponding to the hierarchical index has passed the consistency check. Otherwise, it is necessary to readjust the index value of the matrix to achieve consistency.
5. Step 5: Check the consistency of human judgments(consistency check of total-sorting).
   The total-sorting of all levels refers to the sorting weight value of the indexes of each level relative to the indexes of the highest level. Assuming that there are n elements in k layer, when CR(k)<0.1, the whole judgment matrix is considered to pass the consistency check.

B. Determining the comprehensive weight vector by AHP-EWM

The basic idea of the entropy weight method (EWM) is to determine the objective weight according to the index variability. Compared with various subjective weighting models, the biggest advantage of the EWM is the avoidance of the interference of human factors on the weight of indicators, thus enhancing the objectivity of the comprehensive evaluation results [37,38]. Generally speaking, the smaller the information entropy of an index is, the greater the degree of variation of the index value will be, the more information it provides, the greater the role it can play in the comprehensive evaluation, and the greater its weight will be, and vice versa.

The weight determined based on the AHP method reflects the intention of decision-makers, so it is a subjective weight. However, the weight determined by the entropy weight method does not consider the intention of decision-makers, but has a strong mathematical theoretical basis and purely reflects the relationship between data. The two kinds of weights have some limitations, so they are combined organically to give a comprehensive weight that reflects both objective information and subjective information.

Information entropy can be used to measure the amount of information. The indexes under each criterion layer form an evaluation matrix. EWM calculates each weight according to the evaluation matrix, which reflects the influence of the index data itself on the weight in the objective information of evaluation, and is an objective weight.

Formulas are as follows: (4) (5) (6) Where, x_ij is the value of the jth index of the ith sample; P_ij is the proportion of the ith sample of the jth index; e_j is the entropy value of the jth index, and k is related to the number of samples. Generally, let k = 1/ lnm, and 0<e<1. W_oi is the objective weight of the jth index; g_j is the differential coefficient of the jth index, and. g_j = 1 − e_j (j = 1,2,…, n).

Combining the subjective and objective information, determine the comprehensive weight, that is: (7) Where, W is the combined weight, W_si, W_oi respectively is the subjective weight and the objective weight. The weights of the criteria and sub-criteria in the case are obtained by formula (7).

C. Comprehensive evaluation of passenger satisfaction based on FCE

1. Step 1:Determining the set of evaluation factors.
   Evaluation factors can be defined according to the objectives of the satisfaction evaluation process. A set of n evaluation factors can be represented as a vector C = {C1, C2, …., Cn}. For example, one can define C = {C1, C2, …., C20} = {waiting time, punctuality of first and last shift. …, Sanitary facilities in the vehicle}such that different measurements will be conducted to evaluate the public transport service based on these 20 factors.
2. Step 2:Determining the set of appraisal grades.
   The evaluation criteria of each evaluation index are divided into 4 grades, namely: satisfaction, comparative satisfaction, basic satisfaction and dissatisfaction, and these grades are assigned to 100, 80, 60 and 0, so the evaluation set V = {V1,V2,V3,V4} = = {100,80,60,0}.
3. Step 3: The questionnaire survey.
   The actual FCE questionnaire was generated based on the evaluation indexes of the hierarchical model. For conventional bus transit and rail transit, passengers were asked to fill in the FCE questionnaire. The FCE questionnaire was collected and preliminary survey results were analyzed.
4. Step 4: Setting the fuzzy mapping matrix.
   The goal of the evaluation process is to provide a mapping from C to V. For a specific factor Ci, the fuzzy mapping to the appraisal vector V can be represented by the vector R_i = {r_i1,  r_i2, …, r_ik, …, r_im}, in which m represents the number of levels in the appraisal (see step 2), and r_ik represents the fuzzy membership degree of appraisal factor i to grade k. In the Ningbo city case, single factor evaluation of the single factor Ci(i = 1,2,…,n) was made in the indicator set C, and then according to the proportion of people with grade V_m in the total people in the ith index, the single factor evaluation set of the ith factor is obtained, and the evaluation membership matrix R is obtained: r_i = (r_i1, r_i2, Λ, r_nm). In general, the fuzzy appraisal matrix of all n factors can be derived and represented as a matrix R, such that if there are n factors and m levels of appraisal grades:
   In the above matrix notation for R, each row represents the set of appraisal membership degrees to the corresponding appraisal vector V for each evaluation factor C_i in the evaluation vector C.
   Take the overall evaluation result B, that is, the membership vector of the evaluation index element set to the evaluation grade set.
5. Step 5: Determining the weight of each evaluation factor.
   To obtain a comprehensive passenger satisfaction evaluation, the relative importance of each evaluation factor on the overall grading of public transport should be quantified. The weight vector can be represented by W, which can be formulated by the AHP method, as described in the A subsection. As above, for n evaluation factors, the weight can be represented by the vector W = (W₁, W₂, …, W_n), in which the sum of all elements equal 1. From the example discussed later, if it is determined that W_B = (0.22, 0.24, 0.15, 0.14, 0.08, 0.08, 0.09), then the relative weights satisfaction will be (0.22, 0.24, 0.15, 0.14, 0.08, 0.08, 0.09) for B = {waiting time B1, transfer convenience B2, service B3, information B4, passenger comfort B5, station environment B6, interior sanitation B7} respectively.
6. Step 6: Getting the overall appraisal result.
   The overall appraisal result can be obtained by considering the relative weights of each evaluation factor, such that a single vector with the same level of appraisal grades m (see step 2) can be represented by: Where ‘∘’ is a composition operator.
   According to the questionnaire results, the weights of evaluation indexes determined by AHP-EWM and the scores of each grade, the comprehensive evaluation results of conventional bus transit and rail transit were calculated respectively. Take the conventional but transit for example:
7. Step 7: Synthesizing the result vector of fuzzy synthetic evaluation.
   The comprehensive passenger satisfaction evaluation on public transport in the whole city was obtained by combined the evaluate results of conventional bus and rail transit. The formula is as follows:

A. Overview

This paper takes public transport of Ningbo city as a case to verify and the research scope mainly includes the conventional bus transit and rail transit services in Haishu District, Jiangbei District, Beilun District, Zhenhai District, and Yinzhou District. The research objective is to evaluate the passenger satisfaction with public transport service in Ningbo in 2019.

In 2019, 7 conventional bus transit companies were operating in the five Districts of Ningbo, with 6,484 operating vehicles and 1,250 routes. There are 1,140 standard vehicles in operation on rail lines 1, 2, and 3, with a total number of 456 vehicles and 76 groups. The total length of the lines in operation is 91 kilometers. There are 66 stations on the lines, and the rated capacity of passengers is 110,960.

B. The data processing

2) Survey implementation.

The cycle of passenger satisfaction evaluation of public transport in the downtown area of Ningbo in 2019 is from January to December. The survey is conducted in the following two ways:

1. Conventional bus transit.
   Ningbo south railway station, Gulou bus station, Ningbo passenger transport center station, Youngor Stadium station, Dongmen station, Baisha central station, Gaoqiao station, Donghuan south road station, etc.
2. Rail transit:
   Stations of line 1: Gaoqiao station, Daqingqiao station, Gulou station, Dongmen station, Sakura park station, Fuqing north road station.
   Stations of line 2: Yinzhou Avenue station, Light textile city station, Passenger transport center station, Railway station, Bund bridge station, Lulin station.

After eliminating waste, abnormal and incomplete volumes, this survey obtained 6728 valid questionnaires, including 5046 for conventional bus transit and 1682 for rail transit. The proportion of indicator C_i choosing V_n in the questionnaire is shown in Tables 1 and 2.

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Table 1. Passenger evaluation of index of passenger satisfaction of conventional bus transit.

https://doi.org/10.1371/journal.pone.0241004.t001

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Table 2. Passenger evaluation of index of passenger satisfaction of rail transit.

https://doi.org/10.1371/journal.pone.0241004.t002

A. Evaluation model

For the multi-mode public transport of Ningbo city, the passenger satisfaction model was established from the perspective of people, vehicles, environment, and facilities and equipment used most frequently, to determine the passenger satisfaction evaluation index system of public transport service in Ningbo city in 2019.

B. Hierarchical evaluation index matrix and consistency check

The results of the consistency check for both single-sorting and total-sorting of the comparison matrix for each level of indexes were calculated. According to formula (7), the weights of the criteria and sub-criteria of conventional bus transit and rail transit can be calculated and obtained, as shown in Table 3.

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Table 3. Consistency check of the overall sorting of public transport in Ningbo city.

https://doi.org/10.1371/journal.pone.0241004.t003

1) Conventional bus transit.

Through the expert scoring of public transport professionals to the indicators in Ningbo city, consistent opinions were obtained after many times, the results of the statistics were in the comparison matrix, and comprehensive check indicators of the overall sorting are:

Therefore, the overall sorting of passenger satisfaction of conventional bus transit in Ningbo passed the consistency check.

According to formula (7), the weight of criteria and the weight of sub-criteria of the comprehensive index system for conventional bus transit can be calculated, as shown in Table 4.

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Table 4. Overall sorting and weight calculation of conventional bus transit.

https://doi.org/10.1371/journal.pone.0241004.t004

2) Rail transit.

The comprehensive check indicators of the total sorting is:

In the same way, unanimous opinions can be obtained through expert scoring. According to formula (7), the weight of the criteria and the weight of the sub-criteria of the comprehensive index system for rail transit can be calculated, as shown in Table 5.

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Table 5. Total sorting and weight calculation of rail transit.

https://doi.org/10.1371/journal.pone.0241004.t005

C. Fuzzy comprehensive evaluation

D. Analysis of evaluation results

E. Suggestions for improvement

From the analysis of the results, two suggestions on multi-mode public transport in Ningbo city are given: