A Possible Degree-Based D–S Evidence Theory Method for Ranking New Energy Vehicles Based on Online Customer Reviews and Probabilistic Linguistic Term Sets
Abstract
:1. Introduction
- (1)
- This paper crawls online reviews from multiple websites and transforms them into five-granularity PLTSs. Compared with existing methods on online reviews which are from a single website and transformed into hesitant intuitionistic fuzzy sets and q-rung orthopair fuzzy numbers, the decision information concealed in the online reviews is more plentiful and more clearly express the sentiment orientations, including very positive, positive, neutral, negative and very negative sentiments.
- (2)
- Attribute weights are determined by building a bi-objective programming model based on the maximization deviation and the information entropy, by which the differences between alternatives and uncertainty of decision information on each attribute are both considered. However, in other studies, the attribute weights are assigned by experts subjectively or derived only depending on the maximization deviation. Thus, the attribute weights generated in this paper can more synthetically reflect the quality of the decision information and are more reliable.
- (3)
- A possible degree-based D–S theory method is proposed to rank alternatives. A dominant feature of this method is that it can quantitively measure and decrease uncertainty of decision information. Furthermore, it has a stronger distinguishing power compared with existing D–S theory methods.
2. Literature Review
2.1. Decision Methods for Resolving NEV Selection Problems
2.2. MADM Methods with Online Reviews in the PLTS Environment
3. Preliminaries
3.1. Probabilistic Linguistic Term Sets
3.2. Dempster–Shafer Theory
3.3. Existing D–S Evidence Theory-Based Methods
4. A Possible Degree-Based D–S Evidence Theory Method with Online Reviews in the PLTS Context
4.1. Problem Description
4.2. Determine the Decision Matrix with PLTSs Based on Online Reviews
4.2.1. Data Collection and Preprocessing
4.2.2. Convert Online Reviews into Appropriate Linguistic Terms by Sentiment Analyses
Algorithm 1. Transforming reviews into linguistic terms |
Input: the preprocessed user reviews ; positive word set , negative word set , degree adverb word set and deny word set of the new sentiment dictionary; linguistic term set . Output: the sentimental orientation of . 1: for do 2: for do 3: for do 4: for do 5: let , do 6: if then 7: else if then 8: else if then 9: if then 10: else 11: end if 12: else , 13: end if 14: let , do 15: if then 16: else if then 17: else , 18: end if 19: if then 20: else if then 21: else if then 22: else if then 23: else 24: end if 25: end for 26: end for 27: end for 28: end for 29: end for 30: end for |
Note: is computed by the number of words between positive words and degree adverb words. Similarly, and are calculated. Table 4 illustrates the calculation process. represents the number of elements in . |
4.2.3. Determining the Probability Corresponding to Linguistic Terms
4.3. Determine Attribute Weights by Constructing a Bi-Objective Programming Model
4.3.1. A Minimum Probabilistic Linguistic Entropy Model
4.3.2. Construct a Bi-Objective Programming Model to Determine Attribute Weights
4.4. A Possible Degree-Based D–S Evidence Theory Method for Ranking Alternatives in the PLTS Context
4.4.1. New Confidence and Plausibility Functions
4.4.2. A Confidence–Plausibility-Based Possible Degree for Ranking Alternatives for Each Website
4.4.3. Build a 0–1 Programming Model for Obtaining the Final Alternative Ranking Orders
4.5. The Structure of the Possible Degree-Based D–S Evidence Theory Method in the PLTS Context
5. A Case Study of Selecting New Energy Vehicles
5.1. Description of the Problem
5.2. Solving Process by the Proposed Method
6. Sensitivity Analysis and Comparative Analysis
6.1. Sensitivity Analysis of the Balancing Coefficient
6.2. Comparative Analysis
6.2.1. Comparation with Existing Car Selection Methods Based on Online Reviews
- (1)
- The proposed method crawls online reviews from multiple websites, while existing NEVs selection methods [6,7,21] obtained online reviews from only one website. As different consumers prefer distinct platforms and online reviews in a single platform is limited, it is advisable to derive online reviews from several websites. At this point, the evaluation information collected by the proposed method is more sufficient, which is helpful for determining reasonable decision results.
- (2)
- The evaluation information extracted from online reviews by the proposed method is more precise and reliable because it is represented as PLTSs with five-granularity linguistic terms. The method [7] applied q-rung orthopair fuzzy sets (q-ROFSs) to express evaluation information. However, q-ROFSs only express the proportions of positive and negative sentiments but failed to distinguish comments which are neutral sentiments or do not provide any evaluation. Although the method [6] can handle comments without any evaluations by hesitant intuitionistic fuzzy sets (HIFSs), it is unable to express the strength of positive and negative sentiments. Converting sentiment scores into memberships of alternatives, Ref. [21] delt with online reviews into hesitant probabilistic fuzzy sets (HPFSs). Compared with methods [6,7], the method [21] represented online reviews more smoothly. Nevertheless, the decision information may be distorted when online reviews are transformed into sentiment scores. The proposed method describes evaluation information by five-granularity PLTSs, including very positive, positive, neutral, negative and very negative linguistic terms, which can not only retain natural language forms of sentiment orientations in online reviews, but also reflex strengths of different sentiments with their proportions. Hence, evaluation information derived by the proposed method is more precise and reliable.
6.2.2. Comparison with MADM Methods in the PLTS Environment
- (1)
- The decision information in the proposed method is more reliable because it is extracted from user online reviews on products. However, decision information in methods [37,38] are provided by several DMs. Due to the limited knowledge and experiences of DMs, the provided decision information may be limited and unable to represent general evaluations of most users.
- (2)
- The attribute weights in the proposed method are obtained by minimizing the uncertainty degrees of attributes as well as maximizing deviations between alternatives with respect to attributes. The method [37] gave attribute weights subjectively, which may greatly impact on alternative ranking orders. For example, when the attribute weights are assigned as the ones obtained by the proposed method, alternatives are sorted as . However, when attribute weights are given as , the ranking order is and the best alternative changes from . Although method [38] objectively determined attribute weights by maximizing deviation and method [39] fused AHP and deviation, they both neglected the uncertainty degrees of attributes. As decision information is based on online reviews in which there exists much uncertainty, it is more reasonable to consider uncertainty besides deviations between alternatives while deriving attribute weights.
- (3)
- The proposed method is feasible and has a stronger distinguishing power while ranking alternatives. It can be seen from Table 13 the that alternative ranking order by the proposed method is similar with those derived by methods [37,38,39] and the best alternative is . Furthermore, Observing Table 14, the Pearson correlation coefficients of alternative ranking orders are all greater than 0.9, which verifies the similarity of alternative ranking orders between the proposed method and existing ones. This illustrates the feasibility of the proposed method. Moreover, the distinguishing power of the proposed method is stronger, which can be described in Figure 5.
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Alternatives | Online Reviews |
---|---|
AION S () | In terms of space, it is very spacious for household use. As a Class A car, it doesn’t look large visually, but the overall space utilization is excellent. Even with five people seated, it doesn’t feel crowded. |
The cost-performance ratio of AION S is very high. I only spend 20 to 30 yuan each week on charging outside. Such travel costs are really attractive for an average family. | |
Tesla Model Y () | The car has a large mouse-like body, providing a very spacious interior. It is evident that this car has been meticulously designed. The interior space is surprisingly large, especially in the front row, where you can stretch your legs straight out. However, the armrest box is too small, which is quite inconvenient. |
With increased features at no additional cost, the cost-performance ratio is very high. It excels in all aspects and is also very good compared to others in the same class. | |
Great Wall Euler Good Cat () | The interior space is very large. Compared to other models in the family, it is not inferior to other cars with larger exteriors. However, correspondingly, the large interior space has compressed the trunk space, making the trunk not very spacious. |
However, after looking at three or four models, Euler Good Cat is the best choice within my acceptable range, in every aspect. Not only are the promotional activities substantial, but the service is also excellent. | |
BYD Han () | Overall, I am quite satisfied with the space. It meets the needs for daily commuting and holiday trips. Especially the front row space and the legroom in the back row are quite spacious. |
At this price, buying a BYD Han is a no-brainer, highly recommended. The driving comfort is truly on par with Mercedes. Now, 4S shops have test drive cars available, so you can experience it yourself. The power response is immediate, the soundproof glass is indeed quiet, and the rear space is ample. There are no discounts on the price, but this car is worth the price. | |
BYD Qin PLUS () | The space is very large, enough for a family of four. The headroom in the back row is also very good, and even with a height of 1.78 m, it doesn’t feel cramped. The seats are very comfortable, with good softness and excellent support. |
The overall cost-performance ratio is very high. After all, the price is quite reasonable, and the configurations in all aspects are very good compared to cars in the same class. |
Alternatives | ||||||||
---|---|---|---|---|---|---|---|---|
2 | 0 | 2 | 1 | 0 | 3 | 0 | ||
3 | 4 | 1 | 4 | 4 | 6 | 5 | ||
13 | 10 | 7 | 5 | 7 | 14 | 22 | ||
19 | 14 | 15 | 17 | 10 | 16 | 23 | ||
48 | 57 | 38 | 58 | 64 | 46 | 35 | ||
0 | 0 | 22 | 0 | 0 | 0 | 0 | ||
3 | 3 | 1 | 2 | 3 | 3 | 2 | ||
9 | 3 | 7 | 7 | 8 | 10 | 11 | ||
34 | 21 | 27 | 15 | 24 | 29 | 27 | ||
24 | 24 | 26 | 25 | 25 | 35 | 42 | ||
63 | 81 | 69 | 83 | 73 | 55 | 51 | ||
1 | 2 | 4 | 2 | 1 | 2 | 1 | ||
1 | 2 | 1 | 0 | 1 | 2 | 1 | ||
6 | 1 | 2 | 2 | 0 | 2 | 8 | ||
18 | 6 | 12 | 9 | 7 | 13 | 16 | ||
14 | 15 | 19 | 13 | 8 | 26 | 15 | ||
49 | 64 | 53 | 63 | 71 | 44 | 47 | ||
0 | 0 | 1 | 1 | 1 | 1 | 1 | ||
2 | 1 | 1 | 0 | 1 | 0 | 2 | ||
4 | 2 | 2 | 2 | 3 | 2 | 12 | ||
9 | 7 | 10 | 9 | 6 | 9 | 25 | ||
16 | 10 | 15 | 12 | 9 | 24 | 24 | ||
73 | 84 | 73 | 82 | 86 | 67 | 41 | ||
1 | 1 | 4 | 0 | 0 | 3 | 1 | ||
1 | 0 | 2 | 2 | 1 | 3 | 7 | ||
1 | 5 | 5 | 1 | 0 | 2 | 8 | ||
13 | 3 | 7 | 8 | 9 | 9 | 19 | ||
23 | 17 | 21 | 22 | 9 | 14 | 23 | ||
67 | 79 | 69 | 72 | 86 | 77 | 48 | ||
0 | 1 | 1 | 0 | 0 | 0 | 0 |
Alternative | Sentiment | |||||||
---|---|---|---|---|---|---|---|---|
0.0235 | 0.0000 | 0.0235 | 0.0118 | 0.0000 | 0.0353 | 0.0000 | ||
0.0353 | 0.0471 | 0.0118 | 0.0471 | 0.0471 | 0.0706 | 0.0588 | ||
0.1529 | 0.1176 | 0.0824 | 0.0588 | 0.0824 | 0.1647 | 0.2588 | ||
0.2235 | 0.1647 | 0.1765 | 0.0200 | 0.1176 | 0.1882 | 0.2706 | ||
0.5647 | 0.6706 | 0.4471 | 0.6824 | 0.7529 | 0.5412 | 0.4118 | ||
0.0000 | 0.0000 | 0.2588 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||
0.0224 | 0.0224 | 0.0075 | 0.0149 | 0.0224 | 0.0224 | 0.0149 | ||
0.0672 | 0.0224 | 0.0522 | 0.0522 | 0.0597 | 0.0746 | 0.0821 | ||
0.2537 | 0.1567 | 0.2015 | 0.1119 | 0.1791 | 0.2164 | 0.2015 | ||
0.1791 | 0.1791 | 0.1940 | 0.1866 | 0.1866 | 0.2612 | 0.3134 | ||
0.4701 | 0.6045 | 0.5149 | 0.6194 | 0.5448 | 0.4104 | 0.3806 | ||
0.0075 | 0.0149 | 0.0299 | 0.0149 | 0.0075 | 0.0149 | 0.0075 | ||
0.0114 | 0.0227 | 0.0114 | 0.0000 | 0.0114 | 0.0227 | 0.0114 | ||
0.0682 | 0.0114 | 0.0227 | 0.0227 | 0.0000 | 0.0227 | 0.0909 | ||
0.2045 | 0.0682 | 0.1364 | 0.1023 | 0.0795 | 0.1477 | 0.1818 | ||
0.1591 | 0.1705 | 0.2159 | 0.1477 | 0.0909 | 0.2955 | 0.1705 | ||
0.5568 | 0.7273 | 0.6023 | 0.7159 | 0.8068 | 0.5000 | 0.5341 | ||
0.0000 | 0.0000 | 0.0114 | 0.0114 | 0.0114 | 0.0114 | 0.0114 | ||
0.0190 | 0.0095 | 0.0095 | 0.0000 | 0.0095 | 0.0000 | 0.0190 | ||
0.0381 | 0.0190 | 0.0190 | 0.0190 | 0.0286 | 0.0190 | 0.1143 | ||
0.0857 | 0.0667 | 0.0952 | 0.0857 | 0.0571 | 0.0857 | 0.2381 | ||
0.1524 | 0.0952 | 0.1429 | 0.1143 | 0.0857 | 0.2286 | 0.2286 | ||
0.6952 | 0.8000 | 0.6952 | 0.7810 | 0.8190 | 0.6381 | 0.3905 | ||
0.0095 | 0.0095 | 0.0381 | 0.0000 | 0.0000 | 0.0286 | 0.0095 | ||
0.0095 | 0.0000 | 0.0190 | 0.0190 | 0.0095 | 0.0286 | 0.0667 | ||
0.0095 | 0.0476 | 0.0476 | 0.0095 | 0.0000 | 0.0190 | 0.0762 | ||
0.1238 | 0.0286 | 0.0667 | 0.0762 | 0.0857 | 0.0857 | 0.1810 | ||
0.2190 | 0.1619 | 0.2000 | 0.2095 | 0.0857 | 0.1333 | 0.2190 | ||
0.6381 | 0.7524 | 0.6571 | 0.6857 | 0.8190 | 0.7333 | 0.4571 | ||
0.0000 | 0.0095 | 0.0095 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
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0.2031 | 0.0950 | 0.1901 | 0.1067 | 0.2016 | 0.1231 | 0.0804 | |
0.1611 | 0.0934 | 0.2090 | 0.2208 | 0.1167 | 0.1092 | 0.0898 |
0.4131 | 0 | 0.1950 | 0.1469 | 0 | 0.1531 | 0.0919 | |
0.2730 | 0 | 0.1751 | 0.2707 | 0 | 0.2192 | 0.0620 |
Notation | Explanation |
---|---|
The set of linguistic term. where . | |
The th review from the th website revaluating the th alternative with respect to th attribute. | |
The number of positive sentiment words in the th reviews for attribute of alternative for website . | |
The number of negative sentiment words in the th reviews for attribute of alternative for website . | |
The number of positive degree adverb words in the th reviews for attribute of alternative for website . | |
The number of negative degree adverb words in the th reviews for attribute of alternative for website . | |
The number of users who have missing evaluations the attribute of alternative for website . |
Review | Classification of Words | The Examples of Degree Words | The Sentimental Orientation of Words |
---|---|---|---|
The space inside the car is quite spacious. As soon as you get into the car, you will feel very light and bright. Whether you sit in the front or the back, the useful space is very gelivable and very large. I, 1.78 m, can have such experiences, so it is no problems for other people. It is not crowded at all for three people sitting in the back. | Positive sentiment words: spacious, light and bright, gelivable, large. Negative sentiment words: problem, crowded Degree words: quite, very1, very2, very3. | : , , , | The degree adverb “quite” is regarded as a positive degree () word |
: , |
Review Symbols | Review | The Sentiment Orientation of Word | Quantity Comparison | Review Orientation |
---|---|---|---|---|
The space inside the car is quite spacious. As soon as you get into the car, you will feel very light and bright. Whether you sit in the front or the back, the useful space is very gelivable and very large. I, 1.78 m, can have such experiences, so it is no problems for other people. It is not crowded at all for three people sitting in the back. | : spacious, light and bright, gelivable, large : problem, crowded : quite, very1, very2, very3 : at all : no, not | (more like) | ||
The technology configuration is average, but the screen resolution is okay. While surfing the internet, the configuration is not smooth enough, and it is stuck sometimes. But the navigation is more convenient than that of the mobile phone. | : is okay, smooth, convenient : stuck : not | (general) | ||
The space in the front row is good, but the back row is very crowded. It is hard for adults to sit in the back row. The trunk is so small that some gift boxes cannot be held during the Chinese New Year. | : good : crowded, so small, can’t be held : very, hard | (more annoying) |
0.2522 | 0.1151 | 0.2522 | 0.1884 | 0.4744 | 0.5105 | 1 | |
0.3745 | 0.2374 | 0.3373 | 0.2735 | 0.4896 | 0.5257 |
Alternatives | |||||||
---|---|---|---|---|---|---|---|
85 | 85 | 63 | 85 | 85 | 85 | 85 | |
133 | 132 | 130 | 132 | 133 | 132 | 133 | |
88 | 88 | 87 | 87 | 87 | 87 | 87 | |
104 | 104 | 101 | 105 | 105 | 102 | 104 | |
105 | 104 | 104 | 105 | 105 | 105 | 105 |
Attribute | |||||
---|---|---|---|---|---|
Alternative | |||||||
---|---|---|---|---|---|---|---|
0.1672 | 0.1628 | 0.1473 | 0.1683 | 0.1722 | 0.1635 | 0.1651 | |
0.1432 | 0.1494 | 0.1536 | 0.1549 | 0.1330 | 0.1358 | 0.1557 | |
0.1636 | 0.1749 | 0.1743 | 0.1757 | 0.1828 | 0.1587 | 0.2028 | |
0.1976 | 0.1896 | 0.1958 | 0.1889 | 0.1843 | 0.1909 | 0.1565 | |
0.1856 | 0.1805 | 0.1862 | 0.1694 | 0.1847 | 0.2084 | 0.1769 | |
0.1428 | 0.1429 | 0.1428 | 0.1429 | 0.1428 | 0.1428 | 0.1429 |
Value | |||||
---|---|---|---|---|---|
0.1612 | 0.1071 | 0.2119 | 0.2640 | 0.2550 | |
0.1620 | 0.1078 | 0.2127 | 0.2648 | 0.2558 |
Parameter Settings | Attribute Weights | Alternative Rankings |
---|---|---|
Methods | Expression Forms | Rank Methods | The Number of Websites |
---|---|---|---|
Yang’s method [7] | q-ROFS | Prospect theory | Single |
Tian’s method [6] | HIFS | ORESTE | Single |
Liu’s method [21] | HPFS | TODIM-MULTIMOORA | Single |
The proposed method | PLTS | Possible degree-based D–S evidence theory | Multiple websites |
Methods | Decision Information | Determination of Attribute Weights | Attribute Weights | Decision Methods | Alternatives Ranking Orders |
---|---|---|---|---|---|
Du’s method [37] | Provided by DMs | Given subjectively | Prospect theory | ||
Li’s method [38] | Provided by DMs | Maximizing deviation | Operator based on D–S evidence | ||
Liang’s method [39] | Online reviews | AHP and deviation | Fuzzy comprehensive evaluation | ||
The proposed method | Online reviews | Uncertainty degree and maximum deviation | Possible degree-based D–S evidence |
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Share and Cite
Zhang, Y.; Xu, G. A Possible Degree-Based D–S Evidence Theory Method for Ranking New Energy Vehicles Based on Online Customer Reviews and Probabilistic Linguistic Term Sets. Mathematics 2025, 13, 583. https://doi.org/10.3390/math13040583
Zhang Y, Xu G. A Possible Degree-Based D–S Evidence Theory Method for Ranking New Energy Vehicles Based on Online Customer Reviews and Probabilistic Linguistic Term Sets. Mathematics. 2025; 13(4):583. https://doi.org/10.3390/math13040583
Chicago/Turabian StyleZhang, Yunfei, and Gaili Xu. 2025. "A Possible Degree-Based D–S Evidence Theory Method for Ranking New Energy Vehicles Based on Online Customer Reviews and Probabilistic Linguistic Term Sets" Mathematics 13, no. 4: 583. https://doi.org/10.3390/math13040583
APA StyleZhang, Y., & Xu, G. (2025). A Possible Degree-Based D–S Evidence Theory Method for Ranking New Energy Vehicles Based on Online Customer Reviews and Probabilistic Linguistic Term Sets. Mathematics, 13(4), 583. https://doi.org/10.3390/math13040583