## 3 Materials and Methods
### Extenics-Based Perceptual Imagery Mining  
(1) Imagery Descriptor Extraction  
Product competitiveness and user acceptance critically depend on accurately translating imagery characteristics into design elements. However, the complexity and diversity of perceptual imagery pose significant challenges for precise extraction and representation. Traditional approaches relying on designers' subjective intuition lack systematic objectivity; this can misalign designs with user needs and compromise market performance. To address these limitations, this study employed a web crawler methodology to acquire imagery descriptors. Subsequent Extenics-based semantic analysis ensured scientifically objective evaluation and screening of perceptual features, providing a verifiable theoretical foundation for design practice. Using Python-driven web crawlers, we extracted 612 valid perceptual descriptors for industrial cleaning robots from relevant websites, forums, social media (Weibo), and e-commerce platforms. The data underwent preprocessing--including cleaning, tokenization using the Jieba algorithm, and frequency analysis. A bar chart (Figure 2) displays these terms in descending order of occurrence. We identified the 12 highest-frequency descriptors: mechanical, minimalist, dynamic, technological, dignified, modern, delicate, elegant, fashionable, austere, robust, and agile. These descriptors form the foundational lexicon for subsequent analysis. (2)  
Extenics Semantic Representation and Quantification Matrix  
Extenics theory fundamentally addresses contradictory problems through qualitative-quantitative transformation and inference, utilizing matter-element theory and extension set theory [16]. By integrating domain-specific methodologies, it achieves problem-solving and innovation. Extenics semantic analysis--a creative design methodology combining diagrammatic reasoning with Extenics matter-element theory and extension innovation methods [17; 18]--quantifies symbolic characteristics. This approach formalizes and quantifies contradictions inherent in creative thinking processes, transforming subjective symbolic features into computable data. This conversion provides foundational support for subsequent analysis while reducing decision biases from cognitive ambiguity and strengthening the semantic precision between design elements and imagery characteristics. Consequently, the approach has been widely adopted in product design research across diverse industries [19; 20]. Figure 2: Frequency ranking of perceptual imagery descriptors for industrial cleaning robot form design. This study applies matter-element theory to conduct extension analysis of imagery characteristics for product styling requirements. Through extension transformation and analysis, we rationally convert subjective elements into quantitative data formats, resulting in structured semantic lexicons. These lexicons provide methodological pathways for design practice. Building on this foundation, this phase employs Extenics semantics to evaluate and screen perceptual imagery descriptors, ultimately constructing a semantic keyword repository. Per matter-element theory, a matter-element \(B\) is defined by object \(O\), characteristic \(C\), and value \(V\) (the extension field). Their relationship is quantified as a triad: \(B=(O,\,C,\,V)\) where: O: Object under study (extensible object) \(C=(V_{x},\,V_{\gamma})\):\(V_{x}\in(0,1]\) with \(\Sigma V_{x\gamma}=1\) (\(n\geq 1\)) denotes relevance intensity between required imagery and object ontology (higher values indicate stronger association). \(V_{\gamma}\) represents imagery valuation of characteristic C (higher values indicate greater imagery significance). \(V\): Value information of characteristic comnotation, defined as the extension field. The Extenics semantic construction proceeds as follows:  
\[B=(O,C,V)=\left[ \begin{array}{c}C_{1}V_{1}\\ C_{2}V_{2}\\ \vdots\vdots\\ C_{n}V_{n}\end{array}