A Knowledge Recommendation Method for Product Form Design Integrating Crowd-Intelligence Context Similarity and Trust Relationships in Cloud Environments

Abstract

During the cloud-based product form design process, traditional collaborative-filtering recommendation methods fail to effectively calculate similarity metrics or generate relevant knowledge recommendations for newly joined designers, due to their lack of historical knowledge scores, resulting in inefficient knowledge acquisition. Since designers show a clear tendency of professional trust in the knowledge adoption process, they are more inclined to accept knowledge resources recommended by people with similar professional backgrounds to theirs or by authorities in their fields. Therefore, this paper proposes a knowledge recommendation method for product form design integrating crowd-intelligence context similarity and trust relationships in cloud environments. The method first constructs an ontology model and a product form design knowledge ontology, containing task context, designer’s context, and computational context to facilitate the acquisition, storage, processing, and invocation of contextual information and knowledge. Second, the neighboring set of target designers is determined by calculating the multidimensional contextual similarity and trust relationship between designers. Finally, the missing knowledge score of the target designer is predicted by the knowledge evaluation of the neighboring designers, and the recommendation list is generated. The method’s effectiveness and feasibility are confirmed through a case study of coffee machine product form design.

1. Introduction

Product form design is a complex, knowledge-intensive task that is highly reliant on design knowledge [1]. In the process of product form design, knowledge resources play a crucial role [2]. The utilization of inaccurate knowledge resources can not only disrupt the sequential coherence of design decisions, but also introduce biases in designers’ selection of crucial design parameters [3]. Conversely, accurate knowledge resources can not only facilitate the efficient resolution of problems, but also markedly enhance design efficiency and offer strong support for designers. Consequently, a diverse array of design knowledge recommendation methods have emerged, aiming to better serve the product form design task. Among them, the product form design mode in the cloud environment is favored by the product design field, due to its characteristics of knowledge-sharing, service-orientation, and high efficiency [4,5]. In the cloud environment, the product form design pattern enables online design activities, significantly enhancing the efficiency of product form design through asynchronous and remote collaboration. It achieves this by aggregating personnel from multidisciplinary fields and integrating cross-platform heterogeneous data and knowledge resources, thereby further improving the quality of design services [6]. However, the complexity of cloud-based design activities, the highly collaborative nature of tasks, and designers’ personalized, dynamic demands all influence the form of knowledge recommendation services [7]. In this context, optimizing the knowledge recommendation service and ensuring accurate matching of designers’ knowledge needs with knowledge resources hold extremely important practical significance for enhancing the efficiency and quality of product form design in the cloud environment.

The core of knowledge recommendation technology lies in matching designers’ knowledge needs with vast and diversified knowledge resources, screening out the most suitable design knowledge, and actively pushing it to designers to assist them in completing design tasks quickly and efficiently [8]. Currently, research on knowledge resource recommendation technology by domestic and international scholars mainly falls into four categories: collaborative filtering, content-based recommendation, association rule-based recommendation, and hybrid recommendation algorithms [1,9].

1.

Content-based design knowledge recommendation

Content-based design knowledge recommendation can achieve knowledge recommendation based on the similarity between design tasks, design processes and knowledge items. Xu et al. [10], addressing the issue of low automation in knowledge push for product variant design, proposed a method for variant design based on sequential pattern mining. This method performs knowledge push by calculating the designer’s knowledge usage behavior, the support degree of frequent knowledge, and the similarity between the task knowledge sequence and the frequent knowledge sequence in the current design process. Zhang et al. [11] proposed a map-based knowledge reuse method to assist decision makers in making wise decisions regarding problems encountered in new product development. OWL ontology is utilized to construct the knowledge graph, capture knowledge resources throughout the product lifecycle, and fulfill knowledge requirements during the process of new product design. The PageRank algorithm is employed to calculate the knowledge entities with high correlation to knowledge demand within the knowledge graph and push them to the decision makers. Yu et al. [8], aiming at the dynamic knowledge requirements of product iterative design, proposed a knowledge push model that supports product iterative design. They established the visual expression and structured storage of design knowledge based on a knowledge graph, utilizing the requirement decomposition method of function–behavior–structure mapping. Subsequently, an evaluation method for the iterative design knowledge model was established, based on knowledge similarity. According to the evaluation results, the design knowledge can be promptly updated as the design process evolves. Zhang et al. [12] established a Quality–Function–Knowledge–Deployment model to address various knowledge requirements across different stages of product design. This model maps the knowledge requirements of each design stage to the relevant product design knowledge. It assists designers in tracking the knowledge needed to achieve innovative product design. Li et al. [13] proposed a green conceptual design-based knowledge recommendation model for product conceptual design processes. By constructing an invention principle knowledge space and establishing attribute–principle correlation models, this approach enables conceptual design solutions to simultaneously satisfy both functional requirements and green performance criteria. Liu et al. [14] proposed a knowledge optimization and push model for high-end equipment innovation methods. They established a data model for the knowledge representation of innovation methods in the application context space using structured ontology language. They determined the evaluation indicators and weights for the applicability of innovation methods and established their preferred decision-making model. They implemented an integrated knowledge system for innovation methods and realized the push function of multi-method sequences.

2.

Collaborative-filtering-based design knowledge recommendation

Knowledge recommendation based on collaborative filtering analyzes designers’ historical data and integrates real-time feedback from current design activities to deeply explore knowledge needs, thereby enabling personalized design knowledge recommendation. Zhang et al. [15] proposed a two-stage optimization method for Collaborative Filtering. Firstly, User-based Collaborative Filtering was employed to initially filter out items that align with multiple user-interest points. Subsequently, the final recommendation list is generated, taking into account both user interest and social influence, to achieve a balance between the accuracy and diversity of the recommendations. Zhang et al. [16] proposed a feedback knowledge push method based on CAD and the cosine similarity algorithm within the knowledge vector space model. This method matches the knowledge requirements of designers with knowledge in the knowledge base, and actively pushes ecological knowledge to designers. In follow-up work, the system filters eco-design knowledge twice, using the designer’s feedback record, and then pushes the filtered knowledge to the designer, thereby achieving accurate feedback knowledge push. Wang et al. [17] proposed a topic-diversity knowledge recommendation method aimed at addressing the issue that existing recommendation methods could not simultaneously satisfy both the accuracy and diversity of knowledge recommendations. They improved the user-based collaborative-filtering method by incorporating user-topic expertise information and proposed filtering strategies for diversity by combining context information with user interest models. The goal was to ensure contextual usability and thematic diversity in the knowledge push results. Ji et al. [18] proposed a multi-task context-aware design case knowledge recommendation method to address the issues of pertinence deficiency and accuracy reduction in traditional knowledge recommendation methods within complex, multi-environment collaborative product design scenarios. They adopted a dynamic collaborative-filtering similarity calculation method to achieve efficient design knowledge push.

Wang et al. [19] proposed a knowledge push method for aircraft assembly tooling design based on knowledge graphs and user behaviors. By constructing a knowledge document library, a tag network, and a push context model, they achieved dynamic ranking and personalized knowledge recommendations. Additionally, the recommendation priority is adjusted in real time through user behavior feedback, to enhance the accuracy of push notifications.

3.

Rule-based design knowledge recommendation

Rule-based recommendation is an automated strategy that delivers design knowledge to designers through predefined rules and conditions. Zhang et al. [20] proposed a knowledge push method based on association rules. This method decomposed conceptual design knowledge from coarse-grained to fine-grained, according to the principle of granularity, achieving knowledge refinement and solving the problem of knowledge representation. In addition, the FP-tree algorithm for association rules was used to mine potential connections between knowledge granularity levels and to obtain knowledge items that ultimately met the specified conditions. These items were then pushed to the designer to achieve the goal of knowledge push. Ji et al. [21] established an ontology model of design knowledge, utilizing rough sets and information technology to reveal the correlation between design tasks and design knowledge. They extracted the push rules for design knowledge and, finally, implemented knowledge push based on these rules and the knowledge requirements of designers. Na et al. [22] employed rough set theory to extract push rules from user usage logs, and completed personalized knowledge push for designers based on their knowledge requirements. Shen et al. [23] used the improved interpretive structure model to establish the subdivision-structure association constraint matrix and constraint network. They also designed the performance capture model to realize the active push design of subdivision structures, based on network linkage.

4.

Hybrid-algorithm-based knowledge recommendation

Hybrid-algorithm-based knowledge recommendation integrates two or more techniques to compensate for individual algorithmic limitations and optimize recommendation outcomes. Zhang et al. [24] proposed a knowledge matching method based on a multi-classification radial basis-function neural network, aiming to address the issue that traditional design knowledge-recommendation matching algorithms require repeated computations and suffer from low accuracy. The training set was expanded through two methods: oscillating the feature weights and revising the case features within the case feature vectors. The “nprod” and “comp” components of the neural network were enhanced to adapt to the multi-classification problem in knowledge matching. This allows the method to match knowledge from the knowledge base in a single pass, and ensures the accuracy of the push results. Yu et al. [25], based on the ontology model of automotive product design knowledge, designed a hybrid push algorithm for product design knowledge that considers user preferences. This algorithm pushes product design knowledge to users by calculating the semantic similarity between the user’s knowledge demand vector and the knowledge text vector. Chen [26] proposed a hybrid collaborative-filtering push algorithm that combines item-based and user-based filtering. Zhang et al. [27] introduced a knowledge push technology based on applicable probability matching and multidimensional context-driven methods. They constructed a training sample set consisting of design knowledge representation vectors, design case feature vectors, and mapping Boolean matrices. By applying Bayes’ theorem, they calculated the matching degree between knowledge and content, to filter the knowledge in the push results. Zhao et al. [2] use the multidimensional hierarchical context model to analyze knowledge requirements and characterize the design knowledge modeling according to the characteristics of cloud-based design patterns. They utilize a similarity matching algorithm, combined with the SSA-BPNN model, to calculate the push coefficient for designers. Pei et al. [28] proposed a knowledge push method of complex product-assembly process design based on a distillation model-based dynamically enhanced graph and the Bayesian network, aiming at the problems of low efficiency and inconsistent quality of process documents caused by excessive reliance on manual knowledge in assembly process design. The knowledge graph is constructed through the BERT-BiLSTM-CRF model, which is trained based on expert knowledge, and the large language model, and the knowledge graph update is achieved by adopting the dynamic weighting strategy of confidence. Finally, a Bayesian network model is constructed, based on the relationship among assembly components, assembly features and operations, to achieve the push of assembly process knowledge under different design requirements. Cheng et al. [29] proposed a personalized knowledge recommendation model based on knowledge hierarchy evolution and category awareness in response to the current lack of consideration for user knowledge changes and knowledge item categories in knowledge recommendation performance. First, by using bidirectional GRU and time-adjustment functions, the learning evolution of users is understood through the analysis of their learning trajectory data. Second, based on the multi-head attention mechanism, full-column headings are introduced to capture the information of knowledge items in relevant modules, enhancing the accuracy of knowledge recommendation. Wang et al. [30] proposed a patent knowledge recommendation method for product innovation design, based on few-shot feature extraction and cross-citation networks, to address the issue of low knowledge reuse efficiency in the innovative design of complex industrial products. The fine-tuned BERT model is used to identify and extract the feature entities in the input design problem or task book, vectorize the design problem or task book, and calculate the cosine similarity with the patent to obtain the patent recommendation list, achieving effective knowledge push. Zhao et al. [31] proposed a knowledge recommendation method for the assembly site in response to the insufficiency of knowledge recommendation methods for technical issues during the assembly process of spacecraft. This method establishes an organizational model of technical problem knowledge instances and problem scenarios, achieving standardized expression of technical knowledge. The problem scene features were extracted through the topic model, and the key attributes of the technical problem were screened, based on the scene topic vector, completing the quantitative representation of the technical problem. Ultimately, by integrating the feature recognition of the current problem scenario, knowledge recommendation is achieved through the use of retrieval algorithms.

The above research provides a variety of ideas for the design of knowledge recommendation. However, there are still the following problems:

1.

While collaborative-filtering algorithms depend on explicit designer ratings, they face the cold-start problem in cloud-based design environments: newly added designers lack sufficient historical interaction data for generating accurate recommendations.

2.

Designers’ willingness to adopt knowledge push exhibits a clear trust preference—they are more inclined to accept suggestions from individuals with professional expertise or field authority. Trust relationship-based knowledge recommendation enhances recommendation credibility, while the effectiveness of design knowledge depends critically on its contextual adaptability. However, current hybrid recommendation methods combining multiple techniques have failed to effectively integrate both contextual information and trust relationships in product-form design knowledge recommendation systems.

To sum up, this paper proposes a product form knowledge recommendation method for the cloud environment. This method breaks through the limitations of traditional collaborative-filtering methods in data-sparse scenarios, by mining the multi-dimensional context information and collaborative trust relationship characteristics generated by group interaction in the cloud environment, and improves the accuracy and context reliability of recommendations.

2. Product-Form Design Knowledge Service in Cloud Environment

2.1. Product-Form Design Knowledge Service Mode in Cloud Environment

As an emerging model, product form design in the cloud environment leverages the advantages of the internet and big data, improves design efficiency by integrating and optimizing public knowledge resources distributed online, and obtains diversified problem-solving ideas and a large number of innovative product form design schemes [32,33]. The cloud platform disassembled the total task of product form design, and handed it over to different designers within the cloud environment. The designers completed the task based on their own knowledge and experience, or with knowledge provided by external sources. By gathering a wide range of product form knowledge resources as the source of innovation for product form designers, the platform enabled them to complete the task of product form design in an asynchronous and remote collaboration mode.

The product-form design knowledge service proposed in this study utilizes cloud computing and virtualization technologies to create unified virtual models of massive, heterogeneous knowledge resources. This service-oriented approach enables resource sharing, complementary advantage integration, and personalized knowledge recommendation for designers.

This knowledge service model encompasses various types of cross-field, multi-disciplinary, and multi-professional knowledge, such as standard specifications, patent literature, document knowledge, case knowledge, expert experience, and model knowledge. It is characterized by complexity, dynamism, and intersectionality [7,34]. In this model, designers work according to their task requirements, while the platform retrieves and matches product form design knowledge using similarity algorithms, optimizes the results based on designer preferences, and proactively delivers relevant design knowledge. The product-form design knowledge service model in the cloud environment is shown in Figure 1.

As illustrated in Figure 1, the application interaction layer, serving as the top-level entry point, receives design requirements, constraints, and real-time feedback input by designers, and facilitates human–computer interaction through an intuitive visual interface. The task management layer involves disassembling the design task into various processes and assigning them, based on an intelligent algorithm. At the designer layer, multi-disciplinary designers are brought together to carry out specific design activities through distributed collaboration. This collaboration dynamically generates design behavior data, interaction data, knowledge requirements, and so forth. In the design activity layer, designers use the knowledge and resources provided by the knowledge service layer to carry out a series of design activities according to the sub-tasks assigned to them. The knowledge service layer recommends relevant knowledge content to designers based on task information and designer knowledge requirements, utilizing functions such as knowledge retrieval, knowledge discovery, and knowledge recommendation. The knowledge resource layer serves as a rich source of knowledge for the knowledge service layer, offering designers a convenient way to obtain knowledge and providing a robust knowledge foundation for product form design.

The entire service process is received by the application interaction layer from the information input by the designers. And the task management layer decomposes design tasks into distinct phases and assigns them to multiple designers at the designer layer. When designers perform specific design activities, they generate diverse knowledge demands, and the knowledge service layer responds by providing matching, recommendation, and consultation services to support these activities. The underlying knowledge resource layer stores and manages a wide array of design knowledge resources, encompassing design drawings, patent documents, and industry standards. Each layer is executed step by step, according to the upper-level task instructions, while low-level knowledge resources are injected back into the design activities through intelligent matching. Additionally, real-time behavioral data is generated, which sustainably optimizes the task allocation strategy and knowledge push algorithm, thereby achieving coordination among demand, task, behavior, and knowledge.

2.2. Product-Form Design Knowledge Service Issues in the Cloud Environment

The cloud environment resource pool stores a large amount of product design knowledge resources. In the design process, the cloud platform divides the design task into different sub-tasks. According to the task requirements of designers, targeted knowledge resources are pushed to assist the realization of product design objectives and schemes. However, in the initial stage of a cloud platform’s development, the lack of sufficient behavioral data and personalized feedback from designers makes it difficult to effectively recommend design knowledge resources that match their needs. At the same time, product form design knowledge encompasses everything from fundamental design principles, shape analysis, and material selection to cutting-edge design trends, user research, and innovative technologies, with each type of knowledge having its specific application contexts. Design knowledge is created and reused within a specific context, and only by placing knowledge resources within their specific design contexts can they fully exert their due value [35]. Because designers engage in different tasks, their knowledge preferences vary, resulting in diverse demands for product form design knowledge. For example, interaction designers may prioritize human–computer efficacy knowledge, while appearance designers tend to seek resources for shape semantics analysis. Therefore, effectively recommending relevant knowledge to designers and enhancing their trust in the usability of knowledge contexts has become critically important.

To sum up, this paper proposes to provide a solution to the cold-start problem of product form knowledge recommendation in the cloud environment by leveraging multi-dimensional contextual information and trust relationships. The main steps are shown in Figure 2.

• Multi-dimensional context-ontology and product-form design knowledge-ontology model construction.

A multi-dimensional context ontology for product form design is constructed using OWL, with task context, designer’s context, and computational context as its primary dimensions. The constructed ontology is subsequently stored in the cloud-based context database within a cloud environment. During the knowledge recommendation process, the contextual information is classified and parsed by the cloud platform, then utilized for calculating inter-designer contextual similarity in the subsequent process. Meanwhile, OWL is employed to formally describe product-form design knowledge resources, and a knowledge ontology model is constructed using Protégé 5.5.0 software. This approach enables standardized representation of product form design knowledge, establishes the foundation for knowledge recommendation, and ultimately achieves efficient knowledge management and rapid recommendation.

2.

Neighboring designer identification.

First, experts evaluate the importance of different situational elements on a scale of 1 to 5. Subsequently, the entropy weight method is employed to calculate and determine the weights, followed by computing the comprehensive contextual-ontology similarity with integrated weighting. Second, a trust mechanism is established by computing both direct- and indirect-trust values. Direct trust is derived from designers’ knowledge evaluation behaviors, while indirect trust is quantified through similarity analysis of their contextual assessment scores. Finally, the target designer’s neighborhood set is identified through combined analysis of contextual similarity and trust relationships.

3.

Target designer rating prediction and recommendation list generation.

From the filtered neighborhood set, the top-N most similar designers to the target are selected as nearest neighbors. Using neighborhood knowledge scores to impute the target designer’s missing data, we then recommend the top-K highest-scored knowledge resources. This method can effectively enhance the accuracy and trustworthiness of cold-start knowledge recommendation.

3. Multi-Dimensional Context and Knowledge Ontology Construction

3.1. Multi-Dimensional Context-Ontology Construction

A context refers to any information characterizing the state of an entity—including persons, places, or interactive objects—and their mutual relationships [36]. Context has the characteristics of objective existence, independence and personalization [10,37], and is an important factor to distinguish different designers and knowledge activities. It can also promptly filter out the information that has a low relevance to the current tasks of the designers, in time [38]. The purpose of knowledge recommendation is to enable designers to obtain the required knowledge more efficiently. Meanwhile, due to the context-dependent nature of knowledge, the value of the same knowledge may vary greatly in different design contexst, so it is necessary to consider the context of knowledge application in the process of knowledge recommendation [39,40]. Therefore, this study constructs a context-ontology model to enable (1) structured storage and management of multi-dimensional context information, and (2) crowd intelligence context-similarity computation, as detailed in Section 4.1.

Relevant studies generally summarize the context into the description of information in five dimensions: Who, When, Where, What and How [41], indicating that designers engage in design activities at a specific time, place, and with a certain method, as well as the implementation content and results of the activities. For product form design in the cloud environment, the context determines and affects the changes in designers’ needs, as well as the status during the completion of tasks. Its main characteristics are as follows:

1.

Designer relevance: personal characteristics of designers, such as age, occupation, knowledge level, interests, and preferences, influence their knowledge needs.

2.

Diversity: contexts arise from designers, task characteristics, business processes, equipment resources, and the external environment, which are complex, diverse, and heterogeneous.

3.

Dynamic: it changes with designers, tasks, etc. However, the knowledge requirements of designers in the cloud environment are less affected by factors such as time and place, and are closely related to designer characteristics, task characteristics, data, and equipment resources.

In order to more accurately describe the design context in the cloud environment, based on summarizing relevant studies and combining the characteristics of the cloud environment, this paper proposes a multidimensional context model for product design in the cloud environment, and constructs the ontology through Protégé, as shown in Figure 3.

The Multidimensional Context-Ontology model for product design in a cloud environment is categorized into three contexts: Task Context, Designer’s Context, and Computational Context, as shown in Equation (1).

$$\mathrm{M}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}=\left\{\mathrm{T}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{r}’\mathrm{s}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t},\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}\right\}$$

(1)

1.

Task Context. The knowledge needs generated by designers are generally closely related to the product form design tasks they perform and the problems they encounter in those tasks. Therefore, modeling the task context is beneficial for effectively exploring the knowledge needs of designers. Based on a summary of related research, the product form design process can be divided into five key stages: demand analysis, conceptual design, preliminary design, detailed design, and process design [42]. Different stages possess distinct design goals, and each goal can be associated with specific tasks and objects. For each task, designers employ various design methods and tools to execute and complete it. Consequently, the scenario of a product design task in the cloud environment can be expressed as shown in Equation (2):

$$\mathrm{T}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}=\left\{\begin{array}{c}\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d}\mathrm{O}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{P}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{G}\mathrm{o}\mathrm{a}\mathrm{l},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{T}\mathrm{a}\mathrm{s}\mathrm{k},\\ \mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{o}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{y},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{T}\mathrm{o}\mathrm{o}\mathrm{l}\end{array}\right\}$$

(2)

The specific content is shown in

Table 1. Task Context description.

Context Elements	Specific Description
Design Object	The design object currently targeted by the design activity.
Design Phase	The different stages of the product design task.
Design Goal	The objectives required to execute the current design task.
Design Task	The design objective of the current activity.
Design Method	The design methodologies employed during design activities.
Design Aid	The design software and equipment utilized for the current design activity.

.

2.

Designer’s Context. The designer context is used to describe the attributes of the designer himself. The knowledge requirements of designers in the cloud environment are uncertain and domain-specific. Their educational background, professional background, and skill proficiency determine their knowledge level and learning ability. Meanwhile, historical service experience, working time, and task role will also affect designers’ knowledge interests [26]. Thus, the designer’s context in a cloud environment can be expressed as shown in Equation (3).

$$\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{r}’\mathrm{s}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}=\left\{\begin{array}{c}\mathrm{E}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d},\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d},\mathrm{S}\mathrm{k}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y},\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{T}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{r}\mathrm{e},\\ \mathrm{H}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{S}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{s},\mathrm{T}\mathrm{a}\mathrm{s}\mathrm{k}\mathrm{R}\mathrm{o}\mathrm{l}\mathrm{e}\end{array}\right\}$$

(3)

The specific content is shown in

Table 2. Designer’s Context description.

Context Elements	Specific Description
Educational Background	Designers’ educational qualifications (e.g., Bachelor’s degree, Master’s degree).
Professional Background	Designers’ professional backgrounds.
Skill Proficiency	Designers’ skill proficiency levels.
Professional Tenure	Designers’ relevant work-experience duration.
Historical Service	Designers’ prior project experience.
Task Role	Designers’ roles in the design process.

.

3.

Computational Context. The computational context can be described as the utilization or creation of relevant data resources and websites by designers in the execution of design activities. These contents also reflect the knowledge needs of designers, which can be documented and analyzed, utilizing cloud platform big data. Consequently, the computing scenario within the cloud environment can be expressed as shown in Equation (4).

$$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}=\left\{\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e},\mathrm{W}\mathrm{e}\mathrm{b}\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s},\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{s}\right\}$$

(4)

The specific content is shown in

Table 3. Computational Context description.

Context Elements	Specific Description
Data Resource	Designers’ utilized/generated database resources (e.g., market trends, industry standards, design sketches).
Web Resources	Web resources and associated data utilized by designers during project execution.
Computing Resources	Designers’ hardware/software infrastructure (computing devices, design applications, and cloud platforms).

.

3.2. Product Form Design Knowledge Ontology Construction

The types of knowledge involved in the field of product form design encompass design drawings, patents, research reports, industry standards, product specifications, design tools, inspirational texts, symbolic elements, color schemes, and other relevant information. At the same time, owing to the characteristics of cloud design and the interdisciplinary nature of product form design, the knowledge of product form design is complex, dynamic, and intricate. In order to enhance the utilization rate of product form design knowledge, we build a knowledge ontology model using OWL, thereby facilitating the standardized representation of product form design knowledge and enabling efficient management and rapid push, as shown in Figure 4.

In this paper, the product-form design knowledge ontology is represented as a quadruple KO,

$$\mathrm{K}\mathrm{O}=\left\{\mathrm{E}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y},\mathrm{A}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{e},\mathrm{R}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n},\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{t}\right\}$$

(5)

In Equation (5), Entity represents the product-form design knowledge-resource entity, which can be formalized as

$$\mathrm{E}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}=\left\{\begin{array}{c}\mathrm{I}\mathrm{d},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{O}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t},\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a},\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e},\mathrm{K}\mathrm{n}\mathrm{o}\mathrm{w}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}\mathrm{T}\mathrm{y}\mathrm{p}\mathrm{e},\\ \mathrm{K}\mathrm{n}\mathrm{o}\mathrm{w}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e},\mathrm{K}\mathrm{n}\mathrm{o}\mathrm{w}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\end{array}\right\}$$

(6)

In Equation (6), ID is the unique identifier for knowledge resources. Design Object is the target product object to which the knowledge is applied. Discipline Area represents the subject area of the knowledge, encompassing design, psychology, materials science, management, mechanical engineering, user research, and so on. Design Stage indicates the stage of knowledge application, which includes demand analysis, conceptual design, preliminary design, detailed design, and process design. Knowledge Type signifies the type of knowledge, such as patent reports, 2D drawings, 3D models, design materials, color schemes, expert experience, data parameters, design rules, inspirational texts, design examples, formulas, and so on. Knowledge Source specifies the sources of the knowledge, including design manuals, national standards, market reports, journals, monographs, user feedback, and other relevant sources. Knowledge Content provides a specific description of the knowledge content.

In Equation (5), Attributes constitute a concept set that represents certain attribute features of knowledge entities, encompassing domain attributes, phase attributes, object attributes, and product feature attributes. The product feature attributes represents the characteristic information of the design object, comprising five subclasses: shape, color, material, interaction, and process. Relation is a set of association relations between concepts, representing all other attribute relations except hierarchical relation and autocorrelation relation. The formal expression is $〈{\mathrm{K}\mathrm{O}}_1,{\mathrm{K}\mathrm{O}}_2,\mathrm{y}〉$, where ${\mathrm{K}\mathrm{O}}_1,{\mathrm{K}\mathrm{O}}_2\subseteq \mathrm{E}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}\bigcup \mathrm{A}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{e}$ and $\mathrm{y}$ represents the attribute relationship between concepts. Part is a set of hierarchical relationships between concepts, representing relationships between superclass and subclass.

4. Product-Form Design Knowledge Recommendation Based on Crowd Intelligence Context-Trust Relationship

Collaborative filtering is an algorithm for personalized content push, the core of which lies in using crowd intelligence to predict and recommend content that aligns with individual preferences. Especially in the field of design, it can effectively mine designers’ potential knowledge preferences [43]. Traditional collaborative-filtering algorithms primarily rely on designers’ ratings of common knowledge resources to compute the similarity between designers [44]. However, in a cloud environment, new designers may be scarce, due to the lack of historical data, rendering it impossible to accurately compute designer-to-designer similarity. Therefore, this paper has improved the traditional collaborative-filtering algorithm. By introducing a multi-dimensional context similarity calculation model and a designer-trust relationship calculation model, the recognition probability of similar designers and the reliability of score completion have been enhanced. Compared with other hybrid recommendation algorithms, the credibility of the recommended content has been improved by analyzing the similarity of designers’ knowledge scoring behavior and situational preferences.

The context-ontology similarity computation involves three steps: (1) context element weights are determined through expert scoring and entropy weighting. (2) Individual similarity calculations are performed for text, attribute, numerical, vector, and fuzzy classes. (3) These results are integrated with context weights, to derive the comprehensive multi-dimensional similarity metric.

The trust-value calculation involves two components: (1) direct trust derived from designers’ scoring behavior, and (2) indirect trust computed through context-based scoring similarity. These values are then synthesized, via linear weighting, to obtain the comprehensive-trust metric.

Finally, the target designer’s nearest neighbors are identified by combining comprehensive contextual similarity and trust metrics. These neighbors’ knowledge scores then impute missing values for the target, enabling personalized knowledge recommendations through a generated prediction list. The algorithm framework is shown in Figure 5.

4.1. Crowd-Intelligence Context Similarity Calculation

The multi-dimensional context information stored in the cloud environment context-ontology repository serves as the foundation for computing designers’ context-ontology similarity. Given that designers’ knowledge usage behaviors and preferences are context-dependent, their similarity must be computed by incorporating situational information. This paper employs context-ontology similarity computation [45], incorporating textual, attribute-based, numerical, vector-space, and fuzzy-class similarity measures $\mathrm{S}\mathrm{I}\mathrm{M}\left({\mathrm{M}\mathrm{C},\mathrm{M}\mathrm{C}}^{\prime }\right)$. Meanwhile, context weights reflect the relative importance of different context elements for accurate neighbor identification. Therefore, experts assess the importance of different contextual elements, and the entropy weight method is employed to calculate and determine their weights, effectively mitigating subjectivity. Ultimately, the calculated weights are integrated into the context similarity calculation model. The entropy weight method is an objective weighting approach grounded in information entropy theory. This method assigns higher weights to context elements exhibiting smaller entropy values, making it particularly suitable for addressing weight distribution challenges in multi-dimensional, heterogeneous datasets. Its applicability extends to critical scenarios including, but not limited to, design context analysis and knowledge recommendation systems. The specific calculation formula for context weight is as follows.

1.

Information entropy calculation.

$${Entropy}_j=\frac{1}{\ln \left(g\right)}\sum _{i=1}^m{\mathrm{p}}_{ij}\ln \left({\mathrm{p}}_{ij}\right)$$

(7)

$${\mathrm{p}}_{ij}={\displaystyle \frac{x_{ij}^{\prime }}{{\sum }_{i=1}^g{x}_{ij}^{\prime }}}$$

(8)

In Equations (7) and (8), ${Entropy}_j$ represents the information entropy of the $j$ context element, ${\mathrm{p}}_{ij}$ is the proportion of the score of the $i$ expert to the $g$ context element $j$, $x_{ij}^{\prime }$ is the standardized score, $\ln \left(g\right)$ is the normalized factor, and $g$ is the total number of experts.

2.

Weight calculation.

$${\mathrm{D}}_j=1-{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}}_j$$

(9)

$$W_j={\displaystyle \frac{{\mathrm{D}}_j}{\sum _{i=1}^n{\mathrm{D}}_j}}$$

(10)

In Equations (9) and (10), ${\mathrm{D}}_j$ represents the difference coefficient of the $j$ context element, $W_j$ represents the weight of the $j$ context element, and $n$ is the total number of context elements.

3.

Calculation of comprehensive context similarity by integrating context weights.

$${SIM}_{\mathrm{M}\mathrm{C}}=\sum _{j=1}^n{W}_{j}SIM\left({\mathrm{M}\mathrm{C},\mathrm{M}\mathrm{C}}^{\prime }\right)$$

(11)

In Equation (11), ${SIM}_{\mathrm{M}\mathrm{C}}$ is the comprehensive context similarity that incorporates context weights, and $SIM\left({\mathrm{M}\mathrm{C},\mathrm{M}\mathrm{C}}^{\prime }\right)$ is the ontological similarity of scenarios $\mathrm{M}\mathrm{C}$ and ${\mathrm{M}\mathrm{C}}^{\prime }$.

4.2. Trust-Relationship Value Calculation

Trust relationship refers to the degree of mutual trust between designers, based on knowledge evaluation, common interests, and other relevant factors. This relationship is indicative of a process through which more reliable designers are selected within a designer’s community or neighborhood. It is assumed that if Designer a (${\mathrm{D}}_a$) is interested in the knowledge resources that Designer b (${\mathrm{D}}_b$) has liked or endorsed, it indicates the existence of a trust relationship between them. In the process of recommending product form design knowledge, calculating the trust value between designers can enrich the neighborhood information, enhance the reliability of the push, and address the issue of sparse data. In this paper, direct-trust value ${\mathrm{T}}^{\mathrm{i}\mathrm{m}}$ and indirect-trust value ${\mathrm{T}}^{\mathrm{i}\mathrm{n}}$ are calculated comprehensively, to better reflect the trust relationship between designers. The designer-trust relationship is shown in Figure 6.

4.

Direct-trust value calculation.

Direct trust indicates the existence of a direct connection or relationship between the target designer and other designers. If designers have jointly rated a project, a direct-trust relationship between them is considered to exist. The designer-trust matrix is constructed based on these direct-trust relationships, where, typically, the number 1 indicates trust and 0 indicates distrust. An example of a designer-trust matrix, denoted as T, is shown in

Table 4. Designer-trust matrix.

	$D_1$	$D_2$	…	$D_m$
$D_1$	$1$	$1$	…	1
$D_2$	$0$	$1$	…	$0$
…	…	…	…	…
$D_m$	$1$	$0$	…	1

.

When $\mathrm{T}\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)=1$, it indicates that there is a trust relationship between ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$. Conversely, when $\mathrm{T}\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)=$ 0, it indicates that there is no trust relationship between ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$. The calculation method of direct trust of designers is shown in Equations (12) and (13).

$${\mathrm{T}}_{im}\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)={\displaystyle \frac{M-L_{{\mathrm{D}}_a,{\mathrm{D}}_b}+1}{M}}$$

(12)

$$M={\displaystyle \frac{\ln m}{\ln Q}}$$

(13)

In Equations (12) and (13), $L_{{\mathrm{D}}_a,{\mathrm{D}}_b}$ represents the shortest trust propagation distance between ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$. M represents the maximum trust propagation distance between all designers, m represents the total number of user nodes, and Q represents the average of designer node access.

5.

Indirect-trust value calculation.

In the initial stage of a cloud environment, direct-trust data may also be very sparse. If only direct trust between designers with common scoring behavior is considered, and when there is no common scoring knowledge shared between two designers, it can easily result in an inability to accurately determine the trust relationship between them. A designer’s rating metric can directly reflect a designer’s personal preferences. The closer the knowledge score measures between two designers, the higher the similarity between them, and consequently, the higher their indirect trust. Therefore, this paper uses the Pearson correlation coefficient to calculate the similarity of context score measures between designers, and obtains the indirect trust between designers ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$.

$${\mathrm{T}}_{in}(a,b)={\displaystyle \frac{{\sum }_{K_q\in \mathrm{K}}(r_{a,K_q,c}-\overline{r_{a,c}})(r_{b,K_q,c}-\overline{r_{b,c}})}{\sqrt{{\sum }_{K_q\in \mathrm{K}}{(r_{a,K_q,c}-\overline{r_{a,c}})}^2{(r_{b,K_q,c}-\overline{r_{b,c}})}^2}}}$$

(14)

In Equation (14), ${\mathrm{T}}_{in}(a,b)$ represents the indirect trust of the designer. $r_{a,K_q,c}$ represents designer a’s rating of knowledge resource $K_q$ under context c. $r_{b,K_q,c}$ represents designer b’s rating of knowledge resource $K_q$ under context c. $r_{a,c}$ and $r_{b,c}$ represent, respectively, the evaluation value of knowledge resources that ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$ have jointly rated under the same context c.

6.

Comprehensive-trust value calculation.

Based on Equations (11) and (14), a linear weighting method is adopted to calculate the comprehensive trust of ${\mathrm{D}}_{\mathrm{a}}$ and ${\mathrm{D}}_{\mathrm{b}}$. The calculation is shown in Equation (15).

$${\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}\left(a,b\right)=\theta {\mathrm{T}}_{in}(a,b)+\left(1-\theta \right){\mathrm{T}}_{im}\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)$$

(15)

In Equation (15), $\theta$ is the adjustable weight coefficient. When $\theta$ is 0, the algorithm only calculates the direct trust between designers. When $\theta$ is 1, the algorithm only considers the indirect trust of the designer.

4.3. Prediction of Knowledge Score Based on Crowd Intelligence Context-Trust Relationship

1.

Calculation of Neighboring designers.

According to the calculations above, we have obtained the multi-dimensional context similarity and the designer’s trust value. These values are then integrated to more accurately calculate the comprehensive-similarity value of the designer. The calculation formula is presented in Equation (16).

$$SIM\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)=\left\{\begin{array}{c}{\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}\left(a,b\right),{\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}\left(a,b\right)\ge \eta \\ \lambda {\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}\left(a,b\right)+(1-\lambda ){SIM}_{\mathrm{M}\mathrm{C}},0<{\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}\left(a,b\right)<\eta \\ 0,\mathrm{else}\end{array}\right.$$

(16)

In Equation (16), $\eta$ is the designer’s trust threshold. If the trust value between a and b is greater than $\eta$, it indicates that a and b have a high degree of trust in each other. Even if ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$ do not have similar knowledge scores, they can still fully trust and accept each other’s preferred knowledge resources. If the trust value between ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$ is less than $\eta$, it indicates that the two designers have no similar knowledge rating behavior, and the context similarity between them needs to be further considered. $\lambda$ is the weight coefficient for calculating the designer’s comprehensive similarity.

2.

Score prediction.

Through the above calculations, a comprehensive value is obtained that combines the trust value of the fusion designer and the similarity of the multi-dimensional context. The Top-N designers with the highest similarity to the target designer are selected as the nearest neighbors of the target designer to participate in the score prediction. Additionally, TOP-K knowledge items are recommended to the designer. The score prediction is calculated as follows.

$$P_{\mathrm{a},K_q}=\overline{r_a}+{\displaystyle \frac{{\sum }_{b\in \mathrm{N}}SIM\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)(r_{b,K_q}-\overline{r_b})}{{\sum }_{b\in \mathrm{N}}SIM\left({\mathrm{D}}_a,{\mathrm{D}}_b\right)}}$$

(17)

In Equation (17), ${\mathrm{P}}_{\mathrm{a},K_q}$ represents the score predicted by ${\mathrm{D}}_a$ on knowledge resource $K_i$, $\overline{r_a}$ and $\overline{r_b}$ represent the average score of ${\mathrm{D}}_a$ and ${\mathrm{D}}_b$ respectively, $r_{b,K_q}$ represents the score of neighboring person ${\mathrm{D}}_b$ on knowledge resource $K_i$, and N is the neighboring set of designer ${\mathrm{D}}_a$.

5. The Case Study Results and Analysis

The product form design of a household coffee machine involves numerous aspects, such as modeling design, CMF (Color, Material, and Finish) design, and human–computer interaction, among others. This requires the collaboration of multidisciplinary knowledge, while market demands are diversified, necessitating a balance between functional practicality, aesthetic value, and intelligent experience. Therefore, this paper takes the conceptual design activity of an intelligent home coffee machine’s product form as an example to analyze and verify the effectiveness of the method proposed herein.

This paper collects heterogeneous multi-dimensional contextual data from cooperative enterprises’ work logs, structurally describes it using the method proposed in Section 3.1, and stores the processed information. The entire case process simulates a cloud environment, and designers use PCs to simulate design task execution in the cloud environment. The specific knowledge push process is as follows.

5.1. Target Designer Context Data Acquisition

Firstly, extract the multi-dimensional context instance ${\mathrm{D}}_1$ of the target designer a in the context library, as shown in

Table 5. Coffee-machine task context example.

Context Element	Specific Description
Design Phase	Conceptual design
Design Goal	Draw preliminary concept sketches, based on user requirements
Design Task	Clarify the preliminary design style of a home smart coffee machine, and design its appearance and color matching style
Design Object	Smart home coffee machine
Design Method	Competitive product analysis, conceptual sketch drawing method
Design Tool	Photoshop, SPSS

,

Table 6. Designer’s context example.

Context Element	Specific Description
Educational Background	Master
Professional Background	Product design, with product design theory and practice basis
Skill Proficiency	Drawing, modeling, rendering
Professional Tenure	Three years
Historical Services	Participated in several home-appliance product design projects
Task Role	Industrial Designer (responsible for conceptual design)

and

Table 7. Computational context example.

Context Element	Specific Description
Data Resource	Input: market research data (user demand, competitive product analysis) Output: design sketch, model drawing, product effect drawing
Web Resources	Pinterest, Behance, Zcool
Computing Resource	Laptop, cloud storage service

.

5.2. Product-Form Design Knowledge Push Based on Crowd Intelligence Context-Trust Relationship

1.

Crowd-intelligence context similarity calculation.

Twenty experts used a Likert scale ranging from 1 to 5 to evaluate the importance of context elements, and calculated the context weights based on Equations (7) through (10), as shown in

Table 8. Context weights.

Task Context	Designer’s Context	Computational Context
0.4403	0.4478	0.1119

.

Then, the weighted comprehensive context similarity between target designer $D_1$ and other designs is calculated by Equation (11), as shown in

Table 9. Weighted Multi-Dimensional Context-Ontology Similarity.

	${MC}_2$	${MC}_3$	${MC}_4$	${MC}_4$	${MC}_5$	…	${MC}_{47}$	${MC}_{48}$	${MC}_{49}$	${MC}_{50}$	…
${MC}_1$	0.293	0.272	0.081	0.293	0.409	…	0.326	0.389	0.323	0.165	…

.

2.

Direct-trust value calculation.

Based on the calculations above, a trust matrix between target designer D₁ and the other 49 designers was constructed, with their rating behaviors extracted. The direct-trust values were computed using Equations (12) and (13), as shown in

Table 10. Direct-trust value.

	$D_1$	$D_2$	$D_3$	$D_4$	$D_5$	…	$D_{47}$	$D_{48}$	$D_{49}$	$D_{50}$
$D_1$	1	0.162	1	0.162	1	…	0.162	1	0.162	1

.

3.

Indirect-trust value calculation.

In order to ensure the timeliness and representativeness of the scores, this paper extracts the latest score data for 100 knowledge items from the recent score records of each designer, and calculates the indirect trust among 49 designers based on Equation (14), as shown in

Table 11. Indirect-trust value.

	$D_1$	$D_2$	$D_3$	$D_4$	$D_5$	…	$D_{47}$	$D_{48}$	$D_{49}$	$D_{50}$
$D_1$	1	0	0.249	0.227	0.209	…	0.190	0	0.400	0

.

4.

Comprehensive-trust value calculation.

Based on Equation (15), the comprehensive-trust value between the target designer and other designers is calculated using linear weighting, as shown in

Table 12. Comprehensive-trust value.

	D1	D2	D3	D4	D5	…	D47	D48	D49	D50
D1	1	0	0.625	0.194	0.604	…	0.176	0.398	0.281	0.358

.

5.

Identification of neighboring designers.

According to Equation (16), the top five neighboring designers with the highest comprehensive similarity to ${\mathrm{D}}_1$ are calculated, and the order, according to the similarity of designers, is ${\mathrm{D}}_9>{\mathrm{D}}_{21}>{\mathrm{D}}_3>{\mathrm{D}}_{16}>{\mathrm{D}}_{24}$.

6.

Knowledge resource score prediction.

The missing score of ${\mathrm{D}}_1$ is predicted according to Equation (17), as shown in

Table 13. ${\mathrm{D}}_1$ knowledge resource score prediction.

K1	3.674	K29	1.864	…	…
K2	2.798	K32	2.736	K75	3.799
K5	2.550	K36	3.770	K76	2.639
K4	3.452	K42	2.403	…	…
K27	1.580	K44	2.370	K100	2.456

.

7.

Recommendation list generation.

According to the above calculations, the knowledge resources with the top five scores are outputted as the final push result, which is ${\mathrm{K}}_{91}$ > ${\mathrm{K}}_{89}$ > ${\mathrm{K}}_{43}$ > ${\mathrm{K}}_{81}$ > ${\mathrm{K}}_{96}$, and the specific scores are shown in

Table 14. D₁ final recommendation list.

Sort	Number	Knowledge Source	Knowledge Content	Score
TOP 1	$K_{91}$	Design example	The coffee machine measures 25.4 cm in length, 38.5 cm in width, and 44 cm in height. Its appearance is simple yet fashionable, featuring a combination of silver and black. The main functions encompass automatic bean grinding, intelligent brewing, temperature control, and heat preservation. In terms of layout, the operation panel is situated at the top of the machine for convenient user operation.	4.271
TOP 2	$K_{89}$	Design example	The espresso machine boasts a matte case adorned with metal trim, a sleek and streamlined surface, and a circular display perched atop, guiding the user through the espresso-making process. It performs the functions of grinding beans, extracting espresso, and frothing milk, clearly delineating these three functions into distinct zones from left to right. This linear layout optimizes and streamlines the coffee-making ‘workflow’, while preserving the artistic authenticity of a barista-crafted espresso.	4.149
TOP 3	$K_{43}$	Docu	Based on the high-frequency keywords mentioned in the user interviews, the frequency, from highest to lowest, is as follows: advanced sense (encompassing expressions such as ‘advanced dark texture’ and ‘luxury feel’), higher aesthetic value (including phrases like ‘the brewing process is ornamental’, ‘humanistic atmosphere’, ‘rigid and soft contrast’, ‘not monotonous’, and ‘wood and metal combination’), CMF with texture, and making coffee an enjoyable experience.	4.064
TOP 4	$K_{81}$	Design example	(1) The overall image of the coffee machine’s product modeling elements is clear, featuring long straight lines, parts with small rounded corners, and an overall closed-block structure. (2) The overall color elements are relatively simple, with the overall appearance being gray, silver, and black. It mainly presents two dominant colors, resulting in a unified product color image, where the main color is primarily silver gray. (3) The decorative color part is the high-saturation red light, which not only serves as a decorative color breaking the overall tone, but also appears lively and dynamic, while also functioning as a signal indicator. (4) The discharge port part of the component is made of stainless steel, exhibiting a bending effect. Both horizontal and vertical screen forms exist, and the same-colored external glass material is used to enhance the visual effect of the screen.	3.985
TOP 5	$K_{96}$	Docu	The design elements of the capsule coffee machine’s form can be categorized into five key features: the body, the coffee outlet, the cup holder, the machine base, and the control pane	3.960

.

5.3. Recommendation Result Analysis

Recommendation accuracy is the most important index in a recommendation system. In this paper, we use the MAE and RMSE to measure the recommendation accuracy of the proposed algorithm. MAE and RMSE are the most commonly used metrics, where MAE represents the average of the absolute differences between the predicted scores of the target designer for knowledge resources in the training set and their actual scores in the test set. RMSE, on the other hand, represents the square root of the average of the squares of these differences between the target designer’s predicted values and the actual scores in the test set. The smaller the MAE and RMSE values, the higher the performance of the algorithm.

8.

Influence of designer-trust threshold $\eta$.

The size of the designer’s trust threshold will affect the division of trust among designers. An $\eta$ value that is too high or too low is not conducive to the designer’s selection of the nearest neighbors, and, to a certain extent, it affects the accuracy of the final comprehensive-similarity calculation. The designer-trust threshold ranges from 0 to 1, with increments of 0.1. As the $\mathsf{\eta }$ value increases, the variation trends of the MAE and RMSE values respond as shown in Figure 7.

As can be seen from Figure 6, when $\eta >0.5$, the calculated MAE and RMSE values gradually decrease. Conversely, when the $\eta <0.5$, the MAE and RMSE values of the algorithm gradually increase. This is because, when the designer-trust threshold is too low, designers with lower trust values are included in the comprehensive-similarity calculation, thereby reducing accuracy. When the trust threshold is too high, while a set of designers with high trust can be screened out, the number of such designers becomes sparse, leading to less effective information being utilized. Notably, when $\eta =0.5$, the MAE and RMSE values of the algorithm are the smallest. Therefore, the optimal value for the designer-trust threshold $\eta$ is 0.5.

9.

The influence of comprehensive-similarity weight coefficient $\lambda$.

A more accurate measure of comprehensive similarity can be obtained through the weighted combination of designers’ trust relationships and situational similarity. When $\lambda$ = 0, the similarity among designers is purely based on situational similarity. When $\lambda$ = 1, the similarity among designers is solely determined by the trust value. The comprehensive-similarity weight coefficient a ranges from 0 to 1, with increments of 0.1. As the value of a increases, the variation trends of the MAE and RMSE values are shown in Figure 8.

As can be seen from Figure 7, with the increase in the value of $\lambda$, the MAE and RMSE values tend to decrease initially and then increase overall. When $\lambda <0.5$, the MAE and RMSE values gradually decrease. When $\lambda >0.5$, the MAE and RMSE values gradually increase. When $\lambda =0.5$, the MAE and RMSE values are the smallest, indicating that the algorithm performs best at this point. Therefore, the optimal value for the comprehensive-similarity weight coefficient $\lambda$ is 0.5.

10.

Comparative analysis.

In order to test the effectiveness of the proposed method, we take the traditional collaborative-filtering algorithm as a reference, which uses the Pearson coefficient to measure similarity. The algorithms presented in this paper address the “cold start” phenomenon in the cloud environment, with the primary purpose of the test being to design and evaluate the performance of push when there are a limited number of items.

It can be seen from

Table 15. Comparison with traditional collaborative-filtering algorithm.

Algorithm	MAE	Improve
Traditional collaborative-filtering algorithm	0.7337	11.18%
The method proposed in this paper	0.6517	/

that the MAE value of the traditional collaborative-filtering recommendation algorithm is 0.7337, whereas the MAE value of the proposed method is 0.6517, indicating a higher push accuracy. In addition, compared with the traditional collaborative-filtering recommendation algorithm, the recommendation accuracy of the proposed method is improved by 11.18%. The primary reason for this improvement is that the traditional collaborative-filtering algorithm relies heavily on the designer-knowledge scoring matrix, and its recommendation effectiveness diminishes significantly when the data is sparse. By introducing dynamic context factors such as task context, designer’s context, and computational context into the cloud environment, and by expanding the information dimension of similarity calculation through the designer of direct- and indirect-trust relationships between designers, the proposed method maintains a high recommendation accuracy, even in cases of data scarcity. Compared with existing research, the method proposed in this paper demonstrates stronger adaptability in specific scenarios within the field of product form design.

6. Conclusions

This paper addresses the cold-start recommendation problem for product form design knowledge in cloud environments, proposing a knowledge recommendation method for product form design integrating crowd-intelligence context similarity and trust relationships in cloud environments. First, multidimensional context-ontology and product-form design knowledge-ontology models are constructed to facilitate the acquisition, storage, processing, and invocation of contextual information and knowledge. Second, the neighboring set of target designers is determined by calculating the multidimensional contextual similarity and trust relationship between designers. Finally, the missing knowledge score of the target designer is predicted by the knowledge evaluation of the neighboring designers, and the recommendation list is generated. This method effectively alleviates designer data sparsity issues, while significantly enhancing recommendation accuracy and result credibility.

Although there are some deficiencies regarding the proposed methods, the overall train of thought is feasible. First, the recommendation method proposed in this paper can quickly locate relevant knowledge and reduce repetitive exploration, but may constrain innovative potential. Therefore, subsequent research will explore a hybrid recommendation mechanism incorporating dynamic diversity assessment to balance content innovation and usability. Second, the current study primarily relies on small-sample validation. While demonstrating promising preliminary results, its generalizability across broader design domains and larger user populations requires further verification. Finally, the current simulation-based results from the cloud environment require validation in real-world applications. Future work will involve verification through deployment on production cloud platforms. Furthermore, in real cloud environments, the intelligent representation of multi-dimensional scenarios and other elements will be considered, along with the collection of designers’ behavioral feedback. This will facilitate timely updates of the data model, better meet their knowledge needs, and enable higher-quality context-based recommendations.