An integrated probabilistic linguistic multiple attribute group decision making method for tourism mobile e-commerce service quality evaluation

Abstract

The tourism industry is the business card of a city and an important source of financial revenue. As tourism is becoming increasingly popular, tourism satisfaction has become a key indicator for Yangzhou tourism. As an important business model, e-commerce has developed into a branch of mobile e-commerce. Mobile e-commerce can be combined with the tourism industry to provide services such as information access and city tours for tourism at the city level. The tourism mobile e-commerce service quality evaluation is multiple-attribute group decision-making (MAGDM). In recent times, Exponential TODIM (ExpTODIM) and VIKOR methods were employed to tackle the challenges of MAGDM. To handle uncertain data during the evaluation of tourism mobile e-commerce service quality, Probabilistic Linguistic Term Sets (PLTSs) have been adopted as a valuable tool. This paper presents the Probabilistic Linguistic ExpTODIM-VIKOR (PL-ExpTODIM-VIKOR) method as solution for MAGDM under PLTSs. Additionally, numerical case study is included to validate the proposed method within the context of evaluating the quality of tourism mobile e-commerce services. The primary contributions of this study can be summarized: (1) extension of ExpTODIM technique, based on VIKOR to PLTSs; (2) utilization of information entropy to derive weights based on expected values and deviation degree under PLTSs; (3) introduction of the PL-ExpTODIM-VIKOR technique to effectively manage MAGDM under PLTSs; and (4) execution of numerical study and comparative analysis to verify the effectiveness of PL-ExpTODIM-VIKOR in evaluating the quality of tourism mobile e-commerce services.

Keywords

multiple-attribute group decision-making (MAGDM)probabilistic linguistic term sets (PLTSs)ExpTODIM VIKOR service quality evaluation

1 Introduction

The rapid progress and integration of mobile communication technology and internet technology have created a favorable environment for the widespread adoption of mobile e-commerce in various industries and people's daily lives.^1–3 Over the past few years, there has been a significant increase in the number of mobile users, particularly smartphone users. The 41st Statistical Report on the Development of China's Internet, published by the CNNIC Network Information Center in China,^4–7 provides insightful data in this regard. According to the report, as of December 2017, China had a total of 772 million internet users, with 753 million accessing the internet through mobile devices, representing a staggering 97.5% of the overall internet user base. These statistics clearly indicate a growing inclination towards mobile-oriented lifestyles among individuals, highlighting the increasing importance of mobility in people's lives. Due to the close cooperation between mobile e-commerce and the tourism industry in recent years, the tourism market in recent years has mainly focused on the development of tourism mobile e-commerce.^8–10 More and more enterprises are joining this large market, and in the fiercely competitive environment, service quality issues are beginning to occur frequently. According to the complaint platform of People's Tourism Network 3.15, tourism consumers have many different complaints about the services provided by the tourism mobile e-commerce platform, such as a significant gap between the online description and the provided tourism products, issues with ticket refunds and changes on the website, and failure to fulfill service commitments for fraudulent marketing activities.^11–14 The emergence of these problems has had a negative impact on the user experience, reduced user satisfaction, and placed tourism service enterprises at a disadvantage. Compared to traditional e-commerce services, tourism mobile e-commerce services have more unstable factors and higher requirements for service quality. Therefore, this article constructs an evaluation model for its quality from the perspective of user experience, and conducts a fuzzy comprehensive evaluation of the model through a questionnaire survey. Based on the evaluation results, targeted suggestions are proposed to improve user experience and improve the company's service quality.^15–17 The research on service quality began in the 1980s, and domestic and foreign scholars have conducted comprehensive research on it from different perspectives and industries, producing rich research results. However, with continuous information technology development, the content and methods of services in various industries have undergone significant changes, and new requirements have been put forward for the evaluation and research of service quality.^18,19 Through reading literature and research, it has been found that there is very little research on the tourism mobile e-commerce services evaluation system. Most of the secretaries and materials related to its first study the service quality and then qualitatively and quantitatively analyze various factors that may affect the service, and there are even fewer studies from the perspective of user experience. The current development of tourism mobile e-commerce services in China is not yet mature, but due to the continuous progress of the economy and technology, tourism mobile e-commerce has also undergone significant changes.^20,21 How to grasp user needs and improve enterprise competitiveness in a rapidly changing environment is a continuous and dynamic issue. Therefore, it is necessary to study and analyze the business level of tourism e-commerce based on customer experience, which helps to understand the new situations and potential changes that may occur in the tourism service industry in the future.^22–24

Decision making always refers to selecting the optimal decision plan from multiple different action plans in order to achieve a certain goal.^25–28 Decision making behavior can be seen everywhere in daily life, such as people's choice of goods when shopping, supplier selection in enterprises, and election voting in government departments.^29–32 MAGDM is human social activity in which DMs provide evaluation information for a limited number of alternative solutions based on different multiple attributes, and process the evaluation information using decision theory and methods to achieve the purpose of ranking and selecting optimal solutions.^33–37 Many real-world decision-making problems can be solved using MAGDM methods. Therefore, it is necessary to manage the MAGDM. Moreover, given the intricacy of decision-making scenarios and the limitations of human cognition, decision-makers often encounter challenges when attempting to precisely describe the evaluation information of solutions using accurate numerical values.^38–42 Language information is more in line with people's expression habits, such as “good”, “moderate”, and “poor”.^43–48 In addition, cognitive differences may lead to deviations in decision-makers’ understanding of the same language information. Different decision-makers have varying degrees of preference for the same language information.^49–53 For example, two decision-makers rated a computer as’ good ‘, but the former had only 80% confidence in believing it was “good”, while the latter had 100% confidence in believing it was “good”. It cannot be generalized that the evaluation information of the two is exactly the same. This is because DMs have different knowledge backgrounds and experiences, and when processing their language evaluation information, they need to consider individual differences and achieve personalized evaluation.^54–58 Therefore, there is a need for a tool that conforms to the expression habits of DMs and can achieve personalized differences to describe the decision information of DMs. The tourism mobile e-commerce service quality evaluation is MAGDM. In recent studies, the ExpTODIM^59,60 and VIKOR^61,62 have been applied to address challenges in MAGDM. To handle the uncertainty present in the evaluation of tourism mobile e-commerce service quality, PLTSs^63–66 have been recognized as valuable tool. Although several techniques have been employed to individually manage the traditional ExpTODIM technique^59,60 and VIKOR^61,62 for selecting the optimal choice, limited attention has been employed to integrating the Entropy technique⁶⁷ with ExpTODIM based on the VIKOR approach under PLTSs. Consequently, this paper constructs integrated approach called probabilistic linguistic ExpTODIM-VIKOR (PL-ExpTODIM-VIKOR) to effectively address MAGDM under PLTSs. To establish the validity and reliability of PL-ExpTODIM-VIKOR technique, an illustrative example is presented, focusing on evaluating the quality of tourism mobile e-commerce services. Additionally, comparative analysis is conducted to further support the proposed technique. The primary objectives and motivations of this study could be summarized: (1) extending ExpTODIM based on VIKOR approach to PLTSs using information entropy; (2) utilizing entropy to derive weights based on expected values and deviation degree under PLTSs; (3) introducing PL-ExpTODIM-VIKOR technique as effective approach for managing MAGDM under PLTSs; and (4) performing numerical study and comparative analysis to verify the effectiveness of the PL-ExpTODIM-VIKOR technique in evaluating the quality of tourism mobile e-commerce services.

To achieve this objective, the study is structured: Section 2 provides an introduction to PLTSs. Section 3 presents the design of PL-ExpTODIM-VIKOR under PLTSs with entropy. In Section 4, illustrative study is presented, focusing on evaluation of tourism mobile e-commerce service quality along with comparative analysis. Finally, Section 5 concludes the paper and outlines future directions.

2 Preliminaries

Pang, Wang⁶⁴ designed the PLTSs.

Definition 1.
⁶⁴ Let $S S = {s s_{α} | α = - θ, \dots, - 2, - 1, 0, 1, 2, \dots θ}$ be LTSs, the linguistic terms $s s_{α}$ express the information to $β$ in light with function $s g$ :
$s g : [s s_{- θ}, s s_{θ}] \to [0, 1], s g (s s_{α}) = \frac{α + θ}{2 θ} = β$
(1)

$β$ has equivalent information to $s s_{α}$ through function $s g^{- 1}$ :
$s g^{- 1} : [0, 1] \to [s s_{- θ}, s s_{θ}], s g^{- 1} (β) = s s_{(2 β - 1) θ} = s s_{α}$
(2)
Definition 2.
⁶⁴ Given the LTS $S S = {s s_{α} | α = - θ, \dots, - 2, - 1, 0, 1, 2, \dots θ}$ , a PLTS is expressed:
$S S (p) = {s s^{(s ϕ)} (s p^{(s ϕ)}) | s s^{(s ϕ)} \in L, p^{(s ϕ)} \geq 0, s ϕ = 1, 2, \dots, # S S (p), \sum_{s ϕ = 1}^{# S S (p)} p^{(s ϕ)} \leq 1}$
(3)
where $s s^{(s ϕ)} (p^{(s ϕ)})$ is $s ϕ th$ for $s s^{(s ϕ)}$ with probability information $p^{(s ϕ)}$ , and $# S S (p)$ is length of $S S (p)$ . The given $s s^{(s ϕ)}$ in $S S (p)$ are constructed through ascending order.

Pang, Wang⁶⁴ normalized the PLTS $S S (p)$ as
$\begin{aligned} S S (s p) & = {s s^{(s ϕ)} (s p^{(s ϕ)}) | \begin{array}{l} s s^{(s ϕ)} \in S S, s p^{(s ϕ)} \geq 0, s ϕ = 1, 2, \dots, # S S (s p), \\ \sum_{s ϕ = 1}^{# S S (s p)} s p^{(s ϕ)} = 1 \end{array}}, \\ s p^{(s ϕ)} & = s p^{(s ϕ)} / \sum_{s ϕ = 1}^{# S S (s p)} s p^{(s ϕ)} for all s ϕ = 1, 2, \dots, # S S (s p) . \end{aligned}$

In order to manage two PLTSs, Pang, Wang⁶⁴ construct the method to make two PLTSs with same length numbers.
Definition 3.
⁶⁴ Let $S S = {s s_{α} | α = - θ, \dots, - 2, - 1, 0, 1, 2, \dots θ}$ be an LTSs, $S S_{1} (s p) = {s {s_{1}}^{(s ϕ)} (s {p_{1}}^{(ϕ)}) | s ϕ = 1, 2, \dots, # S S_{1} (s p)}$ and $S S_{2} (s p) = {s {s_{2}}^{(s ϕ)} (s {p_{2}}^{(s ϕ)}) | s ϕ = 1, 2, \dots, # S S_{2} (s p)}$ be PLTSs, $# S S_{1} (s p)$ and $# S S_{2} (s p)$ are length of PLTS $S S_{1} (s p)$ and $S S_{2} (s p)$ . If $# S S_{1} (s p) > # S S_{2} (s p)$ , then add $# S S_{1} (s p) - # S S_{2} (s p)$ linguistic terms to $# S S_{2} (s p)$ . The added LTSs are smallest LTSs in $# S S_{2} (s p)$ and probabilities information are zero.

In order to compare two PLTSs, Pang, Wang⁶⁴ construct the method to compare two PLTSs in light with expected values and deviation degree.
Definition 4.
⁶⁴ For the PLTS $S S = {s s_{α} | α = - θ, \dots, - 2, - 1, 0, 1, 2, \dots θ}$ , the expected values $P L E V (S S (s p))$ and deviation degree $P L D D (S S (s p))$ is:
$\begin{aligned} P L E V (S S (s p)) & = \sum_{s ϕ = 1}^{# S S (s p)} s g (S S (s p)) s p^{(s ϕ)} / \sum_{s ϕ = 1}^{# S S (s p)} s p^{(s ϕ)} \end{aligned}$
(4)

$\begin{aligned} P L D D (S S (s p)) & = \frac{\sqrt{\sum_{s ϕ = 1}^{# S S (s p)} {(s g (S S (s p)) s p^{(s ϕ)} - P L E V (S S (s p)))}^{2}}}{\sum_{s ϕ = 1}^{# S S (s p)} s p^{(s ϕ)}} \end{aligned}$
(5)

By Eqs. (4)–(5), order for two PLTSs is conducted: (1) if $P L E V (S S_{1} (s p)) > P L E V (S S_{2} (s p))$ , $S S_{1} (s p) > S S_{2} (s p)$ ; (2) if $P L E V (S S_{1} (s p)) = P L E V (S S_{2} (s p))$ , if $P L D D (S S_{1} (s p)) = P L D D (S S_{2} (s p))$ , then $S S_{1} (s p) = S S_{2} (s p)$ ; if $P L D D (S S_{1} (s p)) < P L D D (S S_{2} (s p))$ , then, $S S_{1} (s p) > S S_{2} (s p)$ .

In order to compare two PLTSs, Lin and Xu⁶⁸ construct the Euclidean distance to measure closeness degree for two PLTSs.
Definition 5.
⁶⁸ Let $S S = {s s_{α} | α = - θ, \dots, - 2, - 1, 0, 1, 2, \dots θ}$ be LTS. Let $S S_{1} (s p) = {s {s_{1}}^{(s ϕ)} (s {p_{1}}^{(ϕ)}) | s ϕ = 1, 2, \dots, # S S_{1} (s p)}$ and $S S_{2} (s p) = {s {s_{2}}^{(s ϕ)} (s {p_{2}}^{(s ϕ)}) | s ϕ = 1, 2, \dots, # S S_{2} (s p)}$ be PLTSs with $# S S_{1} (s p) = # S S_{2} (s p) = # S S (s p)$ , then Euclidean distance $P L E D (S S_{1} (s p), S S_{2} (s p))$ is designed:
$\begin{aligned} P L E D (S S_{1} (s p), S S_{2} (s p)) \\ = \sqrt{\sum_{s ϕ = 1}^{# S S_{1} (s p)} {(s {p_{1}}^{(s ϕ)} s g (s {s_{1}}^{(s ϕ)}) - s {p_{2}}^{(s ϕ)} s g (s {s_{2}}^{(s ϕ)}))}^{2} / # S S (s p)} \end{aligned}$
(6)
3 PL-ExpTODIM-VIKOR technique for MAGDM with entropy weight

3.1 PL-MAGDM issues

Then, PL-TODIM-VIKOR approach is administrated for MAGDM. Let $D A = {D A_{1}, D A_{2}, \dots, D A_{m}}$ be alternatives, and attributes set $D G = {D G_{1}, D G_{2}, \dots, D G_{n}}$ with weight $s w$ , where $s w_{j} \in [0, 1]$ , $\sum_{j = 1}^{n} s w_{j} = 1$ and a set of experts $D E = {D E_{1}, D E_{2}, \dots, D E_{q}}$ . The decision evaluation is administrated with linguistic information $s s_{i j}^{k}$ . Then, PL-TODIM- VIKOR approach is administrate for MAGDM with entropy (See Figure 1).

Step 1. Transform cost attribute into beneficial one. If the cost information is $s s_{τ}$ , then the beneficial one is $s s_{- τ} (τ = - 3, - 2, - 1, 0, 1, 2, 3)$ .

Step 2. Transform the linguistic information $s s_{i j}^{k}$ into PLTs $s s_{i j}^{(s ϕ)} (p_{i j}^{(s ϕ)}), s ϕ = 1, 2, \dots, # S S_{i j} (s p)$ and build the PL-matrix $S S = (S S_{i j} (s p))_{m \times n}$ , $S S_{i j} (s p) = {s s {_{i j}}^{(s ϕ)} (p {_{i j}}^{(s ϕ)}) | s ϕ = 1, 2, \dots, # S S_{i j} (s p)}$ .

Step 3. Obtain the normalized PL-matrix $S S = (S S_{i j} (s p))_{m \times n}$ , $S S_{i j} (s p) = {s s {_{i j}}^{(s ϕ)} (p {_{i j}}^{(s ϕ)}) | s ϕ = 1, 2, \dots, # S S_{i j} (s p)}$ . Thus, PLTs for $S A_{i}$ is depicted as: $P L S A_{i} = (s s_{i 1}^{(s ϕ)} (p_{i 1}^{(s ϕ)}), s s_{i 2}^{(s ϕ)} (s p_{i 2}^{(s ϕ)}), \dots, s s_{i n}^{(s ϕ)} (s p_{i n}^{(s ϕ)}))$ , $s ϕ = 1, 2, \dots, # S S_{i j} (s p)$ .

Figure 1.

PL-ExpTODIM-VIKOR technique is administrated for MAGDM with entropy weight.

3.2. Construct the attributes weight with entropy

Step 4. Entropy⁶⁷ is constructed to derive weight. The normalized PL-matrix $N S S_{i j} (s p)$ is administrated:

N S S_{i j} (s p) = \frac{P L E V (S S_{i j} (s p)) + P L D D {S S_{i j} (s p)}}{\sum_{i = 1}^{m} (P L E V (S S_{i j} (s p)) + P L D D {S S_{i j} (s p)})},

(7)

The fuzzy Shannon entropy values (FSEV) are obtained:

F S E V_{j} = - \frac{1}{\ln m} \sum_{i = 1}^{m} N S S_{i j} (s p) \ln N S S_{i j} (s p)

(8)

and

N S S_{i j} (s p) \ln N S S_{i j} (s p) = 0

N S S_{i j} (s p) = 0

Then, the weights $s w = (s w_{1}, s w_{2}, \dots, s w_{n})$ is obtained:

s w_{j} = \frac{1 - F S E V_{j}}{\sum_{j = 1}^{n} (1 - F S E V_{j})}, j = 1, 2, 3, \dots, n .

(9)

3.3 PL-ExpTODIM-VIKOR approach for PL-MAGDM

The PL-ExpTODIM-VIKOR approach is constructed for MAGDM.

Step 5. Administrate relative weight:

r s w_{j} = s w_{j} / s w_{j}^{*},

(10)

s w_{j} * = max_{j} s w_{j}

, and

0 \leq s w_{j} \leq 1

Step 6. Construct the dominance degree information through ExpTODIM technique.

(1) The dominance degree $ϕ ϕ_{j} (D A_{i}, D A_{t})$ of $D A_{i}$ over $D A_{t}$ for $D G_{j}$ is obtained.

ϕ ϕ_{j} (D A_{i}, D A_{t}) = {\begin{cases} \frac{r s w_{j} \times (1 - 10^{- ρ P L E D (S S_{i j} (s p), S S_{t j} (s p))})}{\sum_{j = 1}^{n} r s w_{j}} & if P L E V (S S_{i j} (s p)) > P L E V (S S_{t j} (s p)) \\ 0 & if P L E V (S S_{i j} (s p)) = P L E V (S S_{t j} (s p)) \\ - \frac{1}{θ} \frac{\sum_{j = 1}^{n} r s w_{j} \times (1 - 10^{- ρ P L E D (S S_{i j} (s p), S S_{t j} (s p))})}{r s w_{j}} & if P L E V (S S_{i j} (s p)) < P L E V (S S_{t j} (s p)) \end{cases}

(11)

where

θ

is constructed according to the Tversky and Kahneman⁶⁹ and

ρ \in [1, 5]

.⁷⁰

The $ϕ ϕ_{j} (D A_{i}) (j = 1, 2, 3, \dots, n)$ for $D G_{j}$ is defined:

\begin{aligned} ϕ ϕ_{j} (D A_{i}) & = [ϕ ϕ_{j} (D A_{i}, D A_{t})]_{m \times m} \\ \begin{array}{cccc} D A_{1} & D A_{2} & \dots & D A_{m} \end{array} \\ = \begin{matrix} D A_{1} \\ D A_{2} \\ ⋮ \\ D A_{m} \end{matrix} [\begin{array}{ccccc} 0 & ϕ ϕ_{j} (D A_{1}, D A_{2}) & \dots & ϕ ϕ_{j} (D A_{1}, D A_{m}) \\ ϕ ϕ_{j} (D A_{2}, D A_{1}) & 0 & \dots & ϕ ϕ_{j} (D A_{2}, D A_{m}) \\ ⋮ & ⋮ & \dots & ⋮ \\ ϕ ϕ_{j} (D A_{m}, D A_{1}) & ϕ ϕ_{j} (D A_{m}, D A_{2}) & \dots & 0 \end{array}] \end{aligned}

(2) Produce the $ϕ ϕ_{j} (D A_{i})$ of alternative $D A_{i}$ for other alternatives under $D G_{j}$ :

ϕ ϕ_{j} (D A_{i}) = \sum_{t = 1}^{m} ϕ ϕ_{j} (D A_{i}, D A_{t})

(12)

(3) Construct the dominance matrix $ϕ ϕ = (ϕ ϕ_{i j})_{m \times n}$ :

ϕ ϕ = (ϕ ϕ_{i j})_{m \times n} = [\begin{array}{ccccc} D G_{1} & D G_{2} & \dots & D G_{n} \\ D A_{1} & \sum_{t = 1}^{m} ϕ ϕ_{1} (D A_{1}, D A_{t}) & \sum_{t = 1}^{m} ϕ ϕ_{2} (D A_{1}, D A_{t}) & \dots & \sum_{t = 1}^{m} ϕ ϕ_{n} (D A_{1}, D A_{t}) \\ D A_{2} & \sum_{t = 1}^{m} ϕ ϕ_{1} (D A_{2}, D A_{t}) & \sum_{t = 1}^{m} ϕ ϕ_{2} (D A_{2}, D A_{t}) & \dots & \sum_{t = 1}^{m} ϕ ϕ_{n} (D A_{2}, D A_{t}) \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ D A_{m} & \sum_{t = 1}^{m} ϕ ϕ_{1} (D A_{m}, D A_{t}) & \sum_{t = 1}^{m} ϕ ϕ_{2} (D A_{m}, D A_{t}) & \dots & \sum_{t = 1}^{m} ϕ ϕ_{n} (D A_{m}, D A_{t}) \end{array}]

Step 7. Construct the maximum group utility $P L S_{i}$ , minimum individual regret $P L R_{i}$ and relationship degree $P L Q_{i}$ between $P L S_{i}$ and $P L R_{i}$ in light with VIKOR technique.

\begin{aligned} P L S_{i} & = \sum_{j = 1}^{n} s w_{j} \frac{H D (d ϕ ϕ_{j}^{+}, ϕ ϕ_{i j})}{H D (d ϕ ϕ_{j}^{+}, d ϕ ϕ_{j}^{-})} \end{aligned}

(13)

\begin{aligned} P L R_{i} & = {max}_{j = 1}^{n} s w_{j} \frac{H D (d ϕ ϕ_{j}^{+}, ϕ ϕ_{i j})}{H D (d ϕ ϕ_{j}^{+}, d ϕ ϕ_{j}^{-})} \end{aligned}

(14)

\begin{aligned} P L Q_{i} & = v \times \frac{P L S_{i} - P L S_{i}^{-}}{P L S_{i}^{+} - P L S_{i}^{-}} + (1 - v) \times \frac{P L R_{i} - P L R_{i}^{-}}{P L R_{i}^{+} - P L R_{i}^{-}} \end{aligned}

(15)

where

P L S_{i}^{+} = {max}_{i = 1}^{m} P L S_{i}

P L S_{i}^{-} = {min}_{i = 1}^{m} P L S_{i}

P L R_{i}^{+} = {max}_{i = 1}^{m} P L R_{i}

and

P L R_{i}^{-} = {min}_{i = 1}^{m} P L R_{i}

v = 0.5

H D (d ϕ ϕ_{j}^{+}, d ϕ ϕ_{i j})

is Hamming distance between

d ϕ ϕ_{j}^{+} = {max}_{i = 1}^{m} ϕ ϕ_{i j}

and

ϕ ϕ_{i j}

H D (d ϕ ϕ_{j}^{+}, d ϕ ϕ_{j}^{-})

is Hamming distance between

d ϕ ϕ_{j}^{+} = {max}_{i = 1}^{m} ϕ ϕ_{i j}

and

d ϕ ϕ_{j}^{-} = {min}_{i = 1}^{m} ϕ ϕ_{i j}

Step 8. Three sequences are obtained by $P L S_{i}$ , $P L R_{i}$ and $P L Q_{i}$ with ascending order.

4 Numerical example and comparative analysis

4.1 Numerical example

In recent years, with rapid development of China's economy and continuous improvement of residents’ consumption levels, tourism has gradually become a widely accepted form of leisure and entertainment, and the scale of tourism consumption in China has been increasing year by year. According to authoritative statistics from the National Tourism Administration, in 2017, the number of domestic tourists is 5.001 billion with increase of 12.8% compared to same period last year; The annual revenue of tourism industry reached 5.40 trillion yuan with increase of 13.6% compared to same period last year. Analyzing the composition of GDP this year, the tourism industry contributed 9.13 trillion yuan which accounting for 11.04% of total GDP. Tourism consumers’ demand for tourism is becoming increasingly diverse and self-service, starting to choose tourism products based on their preferences, time, cost, and other factors. Especially in the context of mobile e-commerce, information acquisition is more convenient, and the personalization of tourism groups is becoming increasingly prominent. The rapid development of mobile communication technology and popularity of mobile terminals (such as mobile phones, personal digital assistant, etc.) have made people's lives and consumption habits tend to be mobile; At the same time, with improvement of people's living standards and increasing pressure of work and life, the demand for tourism among the people is becoming increasingly strong, and diversified and personalized requirements are constantly being put forward. Tourism mobile e-commerce, with its platform and technological advantages, has been recognized and used by more and more citizens, and has become a development trend in the tourism industry. The key to the success of tourism mobile e-commerce lies in providing perfect services. However, a series of factors such as the constantly changing environment and frequently updated technology have made tourism consumers demand higher service quality. Only by providing perfect services and meeting consumer needs can enterprises better compete and survive. Therefore, it is necessary to administrate research and evaluation on service quality of domestic tourism mobile e-commerce. The tourism mobile e-commerce service quality evaluation is MAGDM. Five tourism mobile e-commerce platforms $D A_{i} (i = 1, 2, 3, 4, 5)$ are chosen in line with four different attributes: ① DG₁ is reliability of tourism mobile e-commerce. ② DG₂ is tourism mobile e-commerce cost. ③ DG₃ is convenience of mobile e-commerce for tourism. ④ DG₄ is tourism mobile e-commerce security. The DG₂ is cost attribute. Five potential tourism mobile e-commerce platforms $D A_{i} (i = 1, 2, 3, 4, 5)$ are assessed by linguistic terms through different experts which are from tourism management department, university professors and tourism decision consulting department:

\begin{aligned} S S & = {s s_{- 3} = e x t r e m e l y p o o r (D E P), s s_{- 2} = v e r y p o o r (D V P), \\ s s_{- 1} = p o o r (D P), s s_{0} = m e d i u m (D M), s s_{1} = g o o d (D G), \\ s s_{2} = v e r y g o o d (D V G), s s_{3} = e x t r e m e l y g o o d (D E G)} \end{aligned}

by five DMs, as constructed in Tables 1–5.

Table 1.
Linguistic terms from DM_1.

Alternatives DG₁ DG₂ DG₃ DG₄

DA₁ DM DM DVG DVG

DA₂ DEP DVG DM DEP

DA₃ DVG DVP DEG DVG

DA₄ DM DG DM DG

DA₅ DVG DEP DEP DVG

Table 2.

Linguistic terms from DM_2.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DEG	DM	DEG	DG
DA₂	DVP	DG	DVP	DEP
DA₃	DEG	DP	DG	DEG
DA₄	DP	DVG	DP	DG
DA₅	DVG	DP	DVP	DVG

Table 3.

Linguistic terms from DM_3.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DG	DVP	DEG	DG
DA₂	DEP	DVG	DP	DEP
DA₃	DEG	DEP	DVG	DEG
DA₄	DVP	DVG	DP	DM
DA₅	DG	DM	DP	DEG

Table 4.

Linguistic terms from DM_4.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DM	DP	DEG	DVG
DA₂	DVP	DVG	DP	DEP
DA₃	DEG	DEP	DEG	DEG
DA₄	DP	DEG	DVG	DP
DA₅	DM	DM	DEG	DEG

Table 5.

Linguistic terms from DM_5.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DM	DVP	DEG	DM
DA₂	DP	DM	DM	DEP
DA₃	DEG	DEP	DEG	DG
DA₄	DP	DEG	DVG	DP
DA₅	DG	DM	DEG	DEG

Then, the PL-TODIM-VIKOR approach is constructed for selecting the potential tourism mobile e-commerce platforms.

Step 1 Transform DG₂ into beneficial attribute. If cost information is $s s_{τ}$ , then corresponding beneficial one is $s s_{- τ} (τ = - 3, - 2, - 1, 0, 1, 2, 3)$ (See Tables 6–10).

Step 2 Transform linguistic terms into PL-matrix (See Table 11).

Step 3 Administrate the normalized PL-matrix (See Table 12).

Step 4 Administrate the weight: $s w_{1} = 0.1743, s w_{2} = 0.4272, s w_{3} = 0.1759, s w_{4} = 0.2226$ .

Step 5 Administrate relative weight: $r s w = {0.4080, 1.0000, 0.4118, 0.5211}$

Step 6 Administrate the $ϕ ϕ = (ϕ ϕ_{i j})_{5 \times 4}$ (Table 13):

Step 9 Calculate the $P L S_{i}$ , $P L R_{i}$ and $P L Q_{i}$ .

\begin{aligned} P L S_{i} & = {0.4397, 0.3653, 0.7879, 0.2218, 0.7121} \end{aligned}

\begin{aligned} P L R_{i} & = {0.2548, 0.1776, 0.3789, 0.1426, 0.2643} \end{aligned}

\begin{aligned} P L Q_{i} & = {0.3128, 0.2453, 1.0000, 0.0000, 0.7605} \end{aligned}

Step 10 Sort different alternatives through $P L S_{i}$ , $P L R_{i}$ and $P L Q_{i}$ .

\begin{aligned} P L S_{4} < P L S_{2} < P L S_{1} < P L S_{5} < P L S_{3} \\ P L R_{4} < P L R_{2} < P L R_{1} < P L R_{5} < P L R_{3} \\ P L Q_{4} < P L Q_{2} < P L Q_{1} < P L Q_{5} < P L Q_{3} \end{aligned}

Table 6.

Linguistic terms from DM_1.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DM	DM	DVG	DVG
DA₂	DEP	DVG	DM	DEP
DA₃	DVG	DVP	DEG	DVG
DA₄	DM	DG	DM	DG
DA₅	DVG	DEP	DEP	DVG

Table 7.

Linguistic terms from DM_2.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DEG	DM	DEG	DG
DA₂	DVP	DG	DVP	DEP
DA₃	DEG	DP	DG	DEG
DA₄	DP	DVG	DP	DG
DA₅	DVG	DP	DVP	DVG

Table 8.

Linguistic terms from DM_3.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DG	DVP	DEG	DG
DA₂	DEP	DVG	DP	DEP
DA₃	DEG	DEP	DVG	DEG
DA₄	DVP	DVG	DP	DM
DA₅	DG	DM	DP	DEG

Table 9.

Linguistic terms from DM_4.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DM	DP	DEG	DVG
DA₂	DVP	DVG	DP	DEP
DA₃	DEG	DEP	DEG	DEG
DA₄	DP	DEG	DVG	DP
DA₅	DM	DM	DEG	DEG

Table 10.

Linguistic terms from DM_5.

Alternatives	DG₁	DG₂	DG₃	DG₄
DA₁	DM	DVP	DEG	DM
DA₂	DP	DM	DM	DEP
DA₃	DEG	DEP	DEG	DG
DA₄	DP	DEG	DVG	DP
DA₅	DG	DM	DEG	DEG

Table 11.

PL-matrix.

Alternatives	DG₁	DG₂
DA₁	${s s_{0} (0.6), s s_{2} (0.2), s s_{3} (0.2)}$	${s s_{- 2} (0.4), s s_{- 1} (0.2), s s_{0} (0.4)}$
DA₂	${s s_{- 3} (0.4), s s_{- 2} (0.4), s s_{- 1} (0.2)}$	${s s_{0} (0.2), s s_{1} (0.2), s s_{2} (0.6)}$
DA₃	${s s_{2} (0.2), s s_{3} (0.8)}$	${s s_{- 3} (0.6), s s_{- 2} (0.2), s s_{- 1} (0.2)}$
DA₄	${s s_{- 2} (0.4), s s_{- 1} (0.4), s s_{0} (0.2)}$	${s s_{1} (0.2), s s_{2} (0.4), s s_{3} (0.4)}$
DA₅	${s s_{0} (0.2), s s_{1} (0.4), s s_{2} (0.4)}$	${s s_{- 3} (0.2), s s_{- 1} (0.2), s s_{0} (0.6)}$
Alternatives	DG₃	DG₄
DA₁	${s s_{2} (0.2), s s_{3} (0.8)}$	${s s_{0} (0.2), s s_{1} (0.4), s s_{2} (0.4)}$
DA₂	${s s_{- 2} (0.2), s s_{- 1} (0.4), s s_{0} (0.4)}$	${s s_{- 3} (1.0)}$
DA₃	${s s_{1} (0.2), s s_{2} (0.2), s s_{3} (0.6)}$	${s s_{1} (0.2), s s_{2} (0.2), s s_{3} (0.6)}$
DA₄	${s s_{- 1} (0.4), s s_{0} (0.2), s s_{2} (0.4)}$	${s s_{- 1} (0.4), s s_{0} (0.2), s s_{1} (0.4)}$
DA₅	${s s_{- 3} (0.2), s s_{- 1} (0.2), s s_{0} (0.6)}$	${s s_{2} (0.4), s s_{3} (0.6)}$

Table 12.

Normalized PL-matrix.

Alternatives	DG₁	DG₂
DA₁	${s s_{0} (0.6), s s_{2} (0.2), s s_{3} (0.2)}$	${s s_{- 2} (0.4), s s_{- 1} (0.2), s s_{0} (0.4)}$
DA₂	${s s_{- 3} (0.4), s s_{- 2} (0.4), s s_{- 1} (0.2)}$	${s s_{0} (0.2), s s_{1} (0.2), s s_{2} (0.6)}$
DA₃	${s s_{2} (0.0), s s_{2} (0.2), s s_{3} (0.8)}$	${s s_{- 3} (0.6), s s_{- 2} (0.2), s s_{- 1} (0.2)}$
DA₄	${s s_{- 2} (0.4), s s_{- 1} (0.4), s s_{0} (0.2)}$	${s s_{1} (0.2), s s_{2} (0.4), s s_{3} (0.4)}$
DA₅	${s s_{0} (0.2), s s_{1} (0.4), s s_{2} (0.4)}$	${s s_{- 3} (0.2), s s_{- 1} (0.2), s s_{0} (0.6)}$
Alternatives	DG₃	DG₄
DA₁	${s s_{2} (0.0), s s_{2} (0.2), s s_{3} (0.8)}$	${s s_{0} (0.2), s s_{1} (0.4), s s_{2} (0.4)}$
DA₂	${s s_{- 2} (0.2), s s_{- 1} (0.4), s s_{0} (0.4)}$	${s s_{- 3} (0.0), s s_{- 3} (0.0), s s_{- 3} (1.0)}$
DA₃	${s s_{1} (0.2), s s_{2} (0.2), s s_{3} (0.6)}$	${s s_{1} (0.2), s s_{2} (0.2), s s_{3} (0.6)}$
DA₄	${s s_{- 1} (0.4), s s_{0} (0.2), s s_{2} (0.4)}$	${s s_{- 1} (0.4), s s_{0} (0.2), s s_{1} (0.4)}$
DA₅	${s s_{- 3} (0.2), s s_{- 1} (0.2), s s_{0} (0.6)}$	${s s_{2} (0.0), s s_{2} (0.4), s s_{3} (0.6)}$

Table 13.

The $ϕ ϕ = (ϕ ϕ_{i j})_{5 \times 4}$ information.

	DG₁	DG₂	DG₃	DG₄
DA₁	−0.1988	1.0235	0.2037	−0.4785
DA₂	0.2307	0.3581	−1.0441	0.4043
DA₃	−0.9614	−0.8123	0.4873	−1.0549
DA₄	0.6862	−0.4458	−0.2677	0.8752
DA₅	−0.8706	−1.3037	−0.3218	−0.0312

Thus, the best comprehensive university is $D A_{4}$ .

4.2 Comparative analysis

Then, the PL-ExpTODIM-VIKOR is compared with PLWA operator,⁶⁴ PL-TOPSIS approach,⁷¹ PL-CODAS approach,⁷² PL-WDBA approach,⁷³ PL-MULTIMOORA approach⁷⁴ and PL-EDAS approach.⁷⁵ The comparative results are administrated in Table 14.

Table 14.
Order for different approaches.

Order

PLWA operator⁶⁴ $S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

PL-TOPSIS approach⁷¹ $S A_{4} > S A_{1} > S A_{2} > S A_{5} > S A_{3}$

PL-CODAS approach⁷² $S A_{4} > S A_{1} > S A_{2} > S A_{5} > S A_{3}$

PL-WDBA approach⁷³ $S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

PL-MULTIMOORA approach⁷⁴ $S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

PL-EDAS approach⁷⁵ $S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

PL-ExpTODIM-VIKOR approach $S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

	Order
PLWA operator⁶⁴	$S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$
PL-TOPSIS approach⁷¹	$S A_{4} > S A_{1} > S A_{2} > S A_{5} > S A_{3}$
PL-CODAS approach⁷²	$S A_{4} > S A_{1} > S A_{2} > S A_{5} > S A_{3}$
PL-WDBA approach⁷³	$S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$
PL-MULTIMOORA approach⁷⁴	$S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$
PL-EDAS approach⁷⁵	$S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$
PL-ExpTODIM-VIKOR approach	$S A_{4} > S A_{2} > S A_{1} > S A_{5} > S A_{3}$

In accordance with WS coefficients,^76,77 WS coefficient between the PLWA operator,⁶⁴ PL-TOPSIS approach,⁷¹ PL-CODAS approach,⁷² PL-WDBA approach,⁷³ PL-MULTIMOORA approach⁷⁴ and PL-EDAS approach⁷⁵ and PL-ExpTODIM-VIKOR is 1.0000, 0.7917, 0.7917, 1.0000, 1.0000, 1.0000. Based on the comparative analysis conducted above, it is evident that order of these models may vary slightly, but all techniques yield same optimal comprehensive university and worst comprehensive university. This finding confirms the reasonableness and effectiveness of PL-ExpTODIM-VIKOR approach. Additionally, the PL-ExpTODIM-VIKOR approach provides more reliable analysis compared to other methods. Therefore, the main advantages of PL-ExpTODIM-VIKOR approach are summarized: (1) PL-ExpTODIM-VIKOR approach effectively addresses uncertainty in real MAGDM while capturing the psychological behavior of DMs during the evaluation of tourism mobile e-commerce service quality; (2)PL-ExpTODIM-VIKOR approach allows for the analysis of behavior of ExpTODIM and VIKOR techniques as MAGDM approaches when they are combined. However, it is important to note that main disadvantage of PL-ExpTODIM-VIKOR technique is the lack of attention given to group consensus issues under PLTSs for evaluating the quality of tourism mobile e-commerce services.

5 Conclusion and future directions

Mobile e-commerce refers to various activities carried out through wireless networks, relying on mobile communication network devices such as mobile phones, tablets, laptops, etc. Traditional e-commerce is mainly carried out through the Internet and computer terminals, while mobile commerce focuses on mobile devices and terminals. There are differences in technical characteristics, terminal capabilities, application environments, and other aspects between the two. Mobile e-commerce technology and platforms are of great significance to the tourism industry, as although the tourist location remains unchanged, tourists are constantly changing and their travels are changing. Under these conditions, mobile e-commerce will locate target consumers anytime and anywhere, establish dialogue, generate interaction, and through efficient interaction, win over tourists, thus effectively improving the quality of tourism services. The tourism mobile e-commerce service quality evaluation is MAGDM. In this research paper, we propose the PL-ExpTODIM-VIKOR model as a solution to address MAGDM under PLTSs. To validate the effectiveness of PL-ExpTODIM-VIKOR, we provide numerical study specifically focused on evaluating the quality of tourism mobile e-commerce services. The main contributions of this study are summarized: (1) Extension of ExpTODIM technique based on VIKOR to PLTSs using information entropy, enabling a more comprehensive evaluation approach; (2) Utilization of information entropy technique to derive weights based on expected values and deviation degrees under PLTSs, enhancing the accuracy of the decision-making process; (3) Introduction of PL-ExpTODIM-VIKOR technique as robust framework to manage MAGDM under PLTSs, integrating the advantages of both ExpTODIM and VIKOR techniques; (4) Conducting a numerical study for evaluating the quality of tourism mobile e-commerce services along with comparative analysis to demonstrate the effectiveness and reliability of PL-ExpTODIM-VIKOR. Overall, this paper contributes to advancing the field of MAGDM by providing a novel approach that effectively handles MAGDM under PLTSs, resulting in improved decision-making outcomes in the context of evaluating tourism mobile e-commerce service quality.

Based on extensive research, this paper introduces the PL-ExpTODIM-VIKOR technique as a novel approach for evaluating tourism mobile e-commerce service quality under PLTSs. The application of this technique to address the problem of tourism mobile e-commerce service quality evaluation demonstrates its rationality and practical significance. However, there are still several areas within tourism mobile e-commerce service quality evaluation that require further exploration in future research: (1) Construction of Evaluation System: Although some evaluation indicators have been developed for tourism mobile e-commerce service quality evaluation, it is important to consider additional indicators in practical applications to ensure a more comprehensive and scientifically grounded evaluation. This will enhance the overall rationality of the tourism mobile e-commerce service quality evaluation process. (2) Integration of Techniques: In our future studies, we aim to establish connections between the ExpTODIM technique and VIKOR technique for tourism mobile e-commerce service quality evaluation. This can be achieved by incorporating techniques such as RANCOM approach,⁷⁸ CRITIC approach,⁷⁹ COMET approach,^80–82 MAIRCA approach^83,84 and QUALIFLEX approach.^85,86 Such integration will further enhance the effectiveness and accuracy of the evaluation process. By addressing these areas of improvement in future research, we can advance the field of tourism mobile e-commerce service quality evaluation and enhance the overall understanding and application of the PL-ExpTODIM-VIKOR technique.

Footnotes

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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An integrated probabilistic linguistic multiple attribute group decision making method for tourism mobile e-commerce service quality evaluation

Abstract

Keywords

1 Introduction

2 Preliminaries

3.1 PL-MAGDM issues

4.1 Numerical example

Table 1. Linguistic terms from DM1. Alternatives DG1 DG2 DG3 DG4 DA1 DM DM DVG DVG DA2 DEP DVG DM DEP DA3 DVG DVP DEG DVG DA4 DM DG DM DG DA5 DVG DEP DEP DVG

Footnotes

Funding

Declaration of conflicting interests

References

Table 1.
Linguistic terms from DM_1.

Alternatives DG₁ DG₂ DG₃ DG₄

DA₁ DM DM DVG DVG

DA₂ DEP DVG DM DEP

DA₃ DVG DVP DEG DVG

DA₄ DM DG DM DG

DA₅ DVG DEP DEP DVG