Rapid advances in drone technology and improvements in size, cost, and intelligence have led to a gradual lowering of the threshold for the use of consumer-grade drones, extending their utility in communications, photography, agriculture, surveillance, and various public services71. They are also widely sought after in major e-commerce platforms. Therefore, we choose a consumer-grade aerial photography drone as the product for our case study to validate the practicability of the proposed product design concept evaluation model.

Corresponding to the product concept design evaluation framework (Fig. 1), firstly, we crawled and analyzed the reviews of drone consumers from e-commerce platforms to construct a targeted evaluation criteria system, i.e., the content of “Get data sources” section. Second, experts in the field are invited to make independent judgments on the constructed evaluation criteria, and the relative importance of the evaluation criteria is calculated according to PFAHP, i.e., the content of “Weighted calculation of assessment criteria using PFAHP” section. Finally, the three existing drone conceptual design assessment schemes with the constructed assessment criteria system were prepared as online questionnaires and published on the Internet in anonymous form to collect questionnaire data from drone consumers, and the obtained questionnaire data were calculated using the PFTOPSIS method, i.e., the content of “Prioritization of product design concepts using PFTOPSIS” section. An illustrative numerical example is added to “Explanatory numerical examples” section to further illustrate the practicality of the method used. The example study described in detail in this section provides a clear understanding of how the proposed method works in the big data environment based on Pythagorean fuzzy set quantification for the product concept design evaluation process.

Get data sources

We collect user text data on consumer-grade aerial drones from JD.COM, one of the largest e-commerce websites in China. First, we use a crawler to crawl JD’s high-selling consumer-grade aerial drone reviews, collecting a total of 6741 web text reviews, and then process the data as described in “Text data mining and clustering” section. “Like”, “good”, “received”, “satisfied”, “Buy” and other words are high-frequency words for reviews (n = 1199; 1122; 835; 823 and 432) but they do not reflect users’ preferences for products and are not meant for the actual evaluation. Therefore, in order to avoid their interference with the final statistical results, we added the above words to the deactivated word list for secondary cleaning of the original data, and the total number of valid comments after secondary cleaning was 5697. We conducted a frequency analysis of online reviews of drones to obtain words that clearly express user preferences, and the results of the frequency analysis are summarised in Table 3. There are 24 words with high frequencies that clearly express user preferences, and they appear in the text a total of 9549 times, and the most frequent words are “texture”, “cheap”, “simple” and “clear”.

Table 3 Results of frequency analysis of users’ preferred terms from online reviews.

Taking effective reviews as the source of corpus data, the bag-of-words model selects the top 54 feature words (such as textured, simple, clear, and technology) that have a large TFIDF weight and can centrally reflect user preferences as the k-means clustering basis. The number of k-means user preference optimal clusters is found by the SSE standard between the cluster value of 2 and 11, as shown in Fig. 2. The abscissa of Fig. 2 is the number of clusters, and the ordinate is the average distance of each corpus, and its value can reflect the degree of aggregation of each type. It can be seen from Fig. 2 that when the review samples are divided into 8 categories, the broken line tends to be stable, so we choose 8 as the number of clusters. After determining the number of clusters, we obtained the number of clusters and their central words and sorted the results into Table 4. According to Table 4, we eliminate the comment text in category 1, which has a large amount of data and cluttered categories and merge the comment data in categories 2 and 3, which all point to operability. According to the most representative words of each category and combined with the original corpus, word frequency, and design dimensions, the results are summarized as the design concept evaluation criteria, as shown in Fig. 3.

Figure 2
figure 2
Table 4 K-means clustering results.
Figure 3
figure 3

Consumer drone concept design evaluation criteria system.

Evaluation of target product design concept solutions

Weighted calculation of assessment criteria using PFAHP

Ten experts in the field were invited to pairwise compare the assessment criteria system shown in Fig. 3 using the language terms of PFS (shown in Table 2). The ten experts (including five males and five females with an average age of 35.1) are engineers from different departments with a deep knowledge base in the fields of equipment manufacturing, smart technology, and product design, and they have 9 years (mean) of experience in product development to provide a valid assessment of the evaluation criteria system for this study.

In this process, linguistic terms are converted to the corresponding Pythagorean fuzzy interval values. Since these experts make different ratings, their subjective judgments need to be aggregated into a compromise pairwise comparison matrix. In this paper, the most representative data (Tertiary criteria assessment C111–C116) are used as an example to provide the relevant calculation results. Table 5 shows the compromise pairwise comparison matrices of the assessment criteria, and the compromise pairwise matrices of Table 5 are next calculated according to steps 2–6 described in “Product concept evaluation weights combined with PFAHP” section, and the results obtained are the difference matrix (Fig. 4a), the interval multiplication matrix (Fig. 4b), the deterministic value matrix (Fig. 4c), and the pre-normalization weight matrix (Fig. 4d). Figure 5 gives the final weight values calculated by the PHAHP method for C111–C116. The same calculation steps are performed in other evaluation criteria to calculate the local weights and global weights of the evaluation criteria, and the results are listed in Table 6.

Table 5 The compromise pairwise comparison matrix of C111–C116.
Figure 4
figure 4

Matrix diagram: (a) difference matrix, (b) interval multiplication matrix, (c) deterministic value matrix, (d) weight matrix before normalization.

Figure 5
figure 5

The weights of C111–C116.

Table 6 Local and global weights for consumer drone design concept evaluation criteria.

Table 6 shows the weight values of each evaluation criterion. The results show that the five most important criteria for evaluating consumer drone design concepts are: durable (C321), cheap (C311), ingenious (C212), superior (C322), and cost performance (C312). The five least important The evaluation criteria are: textured (C113), Exquisite (C112), portable (C222), stable (C221) and professional (C125).

Prioritization of product design concepts using PFTOPSIS

An anonymous online questionnaire was published via the Internet, which was designed according to the language scale of Pérez-Domínguez et al.72 (Table 7), and three prone design concept plans were evaluated using a system of evaluation criteria, which are briefly described in Table 8. A total of seven prone consumer responses were collected. The collected response data were collated, the linguistic variables were converted to Pythagorean fuzzy numbers, and then the criteria weights calculated in the PHAHP method were applied to the calculation of the PFTOPSIS analysis. The decision matrix constructed for this evaluation is shown in Fig. 6.

Table 7 Pythagorean fuzzy linguistic scale used in PFTOPSIS.
Table 8 Basic information on three aerial drone design concept plans.
Figure 6
figure 6

Decision matrix for three design concept plans.

Using Eqs. (19) and (20), the Pythagorean fuzzy PIS and Pythagorean fuzzy NIS values are determined and the obtained results are as follows:

$$x^{ + } = { p(0.{629}, , 0.{484}),p(0.{643}, , 0.{462}), p(0.{600}, , 0.{513}),p(0.{643}, , 0.{462}),p(0.{529}, , 0.{600}),p(0.{600}, , 0.{520}),p(0.{715}, , 0.{570}),p(0.{715}, , 0.{560}),p(0.{657}, , 0.{634}),p(0.{557}, , 0.{552}),p(0.{629}, , 0.{65}0),p(0.{514}, , 0.{444}),p(0.{715}, , 0.{57}0),p(0.{657}, , 0.{647}),p(0.{572}, , 0.{559}),p(0.{543}, , 0.{399}),p(0.{600}, , 0.{523}),p(0.{629}, , 0.{647}), p(0.{579}, , 0.{693}), p(0.{629}, , 0.{670}),p(0.{643}, , 0.{660})} .$$

$$x^{ – } = { p(0.{55}0, , 0.{719}),p(0.{536}, , 0.{742}), p(0.{564}, , 0.{713}),p(0.{457}, , 0.{643}),p(0.{479}, , 0.{627}),p(0.{464}, , 0.{643}),p(0.{643}, , 0.{637}),p(0.{657}, , 0.{624}),p(0.{614}, , 0.{676}),p(0.{529}, , 0.{597}),p(0.{55}0, , 0.{7}0{6}),p(0.{443}, , 0.{512}),p(0.{564}, , 0.{7}0{6}),p(0.{572}, , 0.{73}0),p(0.{464}, , 0.{782}),p(0.{557}, , 0.{7}00),p(0.{557}, , 0.{737}),p(0.{422}, , 0.{796}), p(0.{429}, , 0.{8}0{2}), p(0.{529}, , 0.{726}),p(0.{464}, , 0.{643})} .$$

Using Eqs. (21) and (22), the distances of the alternatives to the Pythagorean fuzzy PIS and NIS are calculated, and the results are provided in Table 9. In addition, the revised closeness values are calculated using Eq. (23), and the results are also shown in Table 9.

Table 9 Closeness coefficients of design concept plans.

According to the PFTOPSIS method, the evaluated solution with modified discount progress (xi) closest to 1 is the solution closest to the positive ideal solution and far from the negative ideal solution. Therefore, having the largest (xi) value means that the drone solution that is considered by the user to performs best in the conceptual design phase. According to Table 9, Plan 2 is the best conceptual design solution.

Explanatory numerical examples

Case 1: evaluation of the design concept of a garbage container for a kitchen

The characteristics of the kitchen waste container are in some way consistent with the evaluation criteria shown in Fig. 3, such as “the shape is exquisite”, “the structure is clear”, “the material is durable”, etc. We will follow the evaluation criteria shown in Fig. 3 and their weight values (Table 6) to apply the PFTOPSIS model to the conceptual design of kitchen waste containers discussed by Liu et al.18. Ten participants were appointed randomly to form a decision panel to express their viewpoints on the conceptual design options in linguistic terms (Table 7) after learning about the four conceptual design options for kitchen waste containers shown by Liu et al.18. Table 10 presents the collated decision matrix, Table 11 shows the corresponding Pythagorean fuzzy PIS and NIS, and Table 12 provides the distances of the conceptual design solutions from the Pythagorean fuzzy PIS and NIS, along with the revised closeness of the conceptual design solutions and the final ranking of the solutions.

Table 10 Decision matrix.
Table 11 Pythagorean fuzzy PIS and NIS.
Table 12 PFTOPSIS calculation results for the conceptual design solution.

The outcomes in Table 12 reveal that Design 2 is the best design and Design 1 is the second best one, which is consistent with Liu et al.’s18 ranking of the conceptual design after increasing the confidence level of managers, which indicates the universality of the method proposed in this paper. And there are many potential reasons for the inconsistent ranking of Design 3 and Design 4, for example, changes in the assessment criteria, changes in the relative importance of the assessment criteria, etc.

The method proposed by Liu et al.18 requires an extended linguistic scale (from three to five levels) if one wants to consider managers’ influence factors (self-confidence), which undoubtedly increases the subjectivity and ambiguity of the assessment process and increases the probability of distortion of the assessment results, the method proposed in this paper, which uses a uniform linguistic scale for all decision makers, ensures the uniformity of the assessment environment and attenuates the “human influence factors”, and the assessment results are more objective and reasonable.

Case 2: conceptual design selection of a smart logistics transport vehicle

At present, traditional logistics vehicles can no longer meet the operational needs of logistics enterprises, so the development of intelligent logistics transport vehicles is very necessary, and the evaluation results have a certain orientation for the development of enterprise products. Therefore, we constructed six evaluation criteria from the perspective of market demand: F1 motor-rated power, F2 wearing parts, F3 aesthetic shape, F4 operation, and maintenance cost, F5 storage capacity, and F6 distribution security. A decision team of 10 people with backgrounds in research and development, manufacturing, and use evaluated the four available options, using linguistic variables to express their views on the evaluation criteria, and the options are chosen.

The weight values θ = (0.135, 0.148, 0.132, 0.150, 0.203, 0.231) were calculated by the PFAHP model, and the final results were obtained by the PFTOPSIS model, and the best intelligent logistics transport vehicle concept design option was Option 4, and the specific calculated values are shown in Table 13.

Table 13 Ranking of smart logistics transport vehicle concept design options.

The drone example and two illustrative numerical cases demonstrate the practicality of the approach proposed in this paper.

The decision model generated based on Pythagorean fuzzy sets can be applied in product design not only for conceptual design evaluation, but also for product sustainability selection, product modularity decision, product color evaluation, and other stages of the full product life cycle. In addition to product design, it can be applied to other fields such as material selection, robot selection, and machine tool selection in manufacturing and mechanical engineering, performance and benchmarking evaluation, personnel selection, and business investment decisions in business management, supplier selection and site selection in logistics and supply chain, wastewater management in natural environment and resources, software evaluation, network selection, and website evaluation in information science, website evaluation, etc.

Although Big Data can provide powerful data support for decision making, it cannot avoid the defects of the data itself. Pythagorean fuzzy sets, due to their own characteristics, provide a precise and superior mathematical-logical framework for expressing fuzzy information, which far exceeds the performance of fuzzy sets and intuitionistic fuzzy sets, while also excelling in handling multidimensional data. In short, the integrated method retains the advantages of the approach itself while increasing the scope of its use, and these features prove it to be a reliable method for solving multi-criteria decision problems.

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