Design and Evaluation of the Interface of Recreational Intelligent Escort Products

In the context of the Internet of Things (IoT), the user interface has become the main means of interaction between the user and the network system, and the increasing variety of ways of interacting with the user interface has created many “digital problems” for the elderly. In order to explore the preferences of elderly people in using smart products and to help designers to objectively and rationally select interface design solutions, to enhance the experience of elderly people in using smart products and the naturalness of the interaction process, and to motivate them to actively participate in Internet life, this study proposes a new approach to interface design solution selection, which reduces the subjectivity of solution selection in the design process. Firstly, the interface was decomposed into 7 components, and the orthogonal experimental design was used to calculate the evaluation indexes and the correlation degree between the objects of 18 typical solutions, and ﬁnally the preferred solution was obtained. Secondly, conjoint analysis was used to obtain the importance that older users attached to the seven interface components and their preferences for the types of elements. The research takes the interface design of an elderly companion robot as an example. The method enables the optimization of the target problem of how to match the interface design elements and the ﬁnal solution preference in IoT systems, enabling designers to use mathematical and rational thinking to study contradictory problems, enhancing the objectivity and scientiﬁcity of interface design and solution selection, providing a more natural and comfortable interaction experience for elderly users, and promoting healthy ageing. M2 Cognitive M3


Introduction
With the development of the Internet of ings (IoT) [1], more and more smart devices are connected to the Internet and used in smart homes, smart healthcare, and other fields. Huang et al. [2]. define a smart ageing platform as a technological platform that provides intelligent and personalized services to the elderly by accurately identifying and processing key environmental and human data through technologies, such as the Internet of ings and artificial intelligence. e advantages of IOT applications in the field of smart ageing continue to emerge, with some scholars arguing that intelligent systems based on the Internet of ings (IoT) can help prevent cognitive decline in older people [3]. IoT-based systems for elderly companionship products are constantly being used in smart ageing, where elderly people can control the system through a human-machine interface such as a touch screen to achieve personalized services. Human-machine interface in the traditional sense is divided into human-machine interface (HMI) generated by human-machine interaction and human-computer interface (HCI) generated by human-computer interaction. Humanrobot interface (HRI) is a general term for the physical and information interfaces formed during the interaction between aging people and service robots. Compared to traditional human-machine interfaces, HRIs focus more on the safety and efficiency of human-machine interaction and the friendliness of the interface experience [4]. Intelligent companion products for the elderly are gradually flooding into the market, and with the rise of voice, gestures, and other emerging interaction methods, the research on the interface design of intelligent companion products for the elderly should not be limited to the study of HCI. In order to improve the acceptance and satisfaction of intelligent escort products among the elderly population, HCI and HMI should be studied comprehensively, combined with the different ways of interaction between the elderly and the interface as well as the feedback, to jointly explore the influencing factors of the interface design of intelligent products for elderly escorts.
Numerous scholars have explored HRIs from different perspectives. Yi et al. [5] verified the role played by different interface designs and users' educational backgrounds on task performance and subjective evaluations of mobile terminal customization systems. Reddy et al. [6] investigated whether, for older adults, redundancy in the interface is advantageous over text or symbol-based interfaces during early or intermittent device use. Based on the model of working memory, Xu et al. [7] explored the key points of product interface design elements that affect the memory depth of the elderly in each memory stage from the perspective of caring for the elderly rehabilitation population. Jiang et al. [8] derived three principles for the design of information product interfaces for the elderly based on an experiential perspective through an experiential study of three aspects, including sensory recognition, functional cognition, and behavioral associations. Most of the studies in the above literature explore product interface design and grade evaluation from the point of view of elderly users themselves, ignoring the interaction behavior and interaction mode between users and the interface. Many scholars have since incorporated human-computer interaction behaviors and modalities into their research. For example, Karpov and Yusupov [9] conducted an analytical review of the state-of-the-art and future intelligent interfaces for human-computer interaction, detailing the organizing principles, main features, and types of multimodal user interfaces. Oulasvirta et al.'s [10] layout design problem for graphical user interfaces is defined as an integer programming task that allows to identify the type of problem, analyze its complexity, and utilize known algorithmic solutions. Wang et al. [11] proposed an interactive device with a tangible interface that combines human-computer interaction technology and older adults' life experiences to provide three functions: nostalgia, leisure, and entertainment, in order to help older adults achieve active aging. Wang et al. [12] explored how interface design features affect the gaze behavior and behavioral performance of older users in mobile news applications. In comprehension of the above literature, many researchers have explored the design of humanmachine interface by combining the physiological and psychological characteristics of elderly users and the interaction mode between users and the interface but ignored the evaluation of the preferential link in the design process. While designers propose multiple interface design solutions, they need to make decisions on the optimal solution with a scientific and objective approach. At the same time, the interface components are connected and influenced by each other, and the researcher fails to evaluate the superiority of the object precisely by considering the user and the interface as a whole. Such a problem will lead to the final design solution not meeting the cognitive characteristics of elderly users, reducing the user's experience of using smart products and the naturalness of the interaction process. e combination of different types of each interface component of a recreational intelligent product will result in multiple design solutions, and the evaluation and selection of the solutions requires a more comprehensive evaluation system. Many scholars have been experimenting and summarizing according to the actual practice, while drawing on the knowledge of other disciplines such as operations research, management science, and mathematics to study the evaluation methods, mainly hierarchical analysis [13,14], entropy power method [15,16], the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method [17][18][19], and comprehensive evaluation method [20][21][22]. When these methods are applied, expert interviews and questionnaires are often used to establish evaluation indicators and evaluation systems, and the indicators are often derived based on direct generalization by the researcher, without being able to classify the evaluation indicators of the interface based on scientific logic. e superiority rating of different design solutions is determined only by a single weight, which is more subjective, without theoretical support and more one-sided. Extenics regards the world as a primitive world, a collection of objects or a system of objects, and the interface of recreational intelligent products can be treated as an object, and the comprehensive index of the evaluation interface reflects the overall situation of the interface as its properties. Extenics was introduced to establish a topologic evaluation system to find the evaluation index more accurately by using the topologic performance of the object elements and to establish the degree of association between factors based on the correlation function to evaluate the superiority of the object more accurately, instead of relying on the weights alone to determine the superiority and inferiority levels of different design solutions [23]. Liu et al. [24] proposed a method for configuring complex machine product modules based on extenics-based case reasoning. Liu et al. [25] developed an extenics-based model to formulate a dependence function for measuring the correlation between bus and system performance. Gu et al. [26] used extenics principles to address the choice between color differences (affecting sensitivity and the number of matching colors) and performance timeouts (affecting the degree of fatigue) in the design of human-machine interfaces for nuclear power plants. Yang et al. [27] conducted a comprehensive evaluation of landslide hazards based on extenics principles combined with fuzzy hierarchical analysis. Zhang et al. [28] proposed a method to evaluate the degree of impact on seven damaged mountains in Jinan based on the material element model derived from the extenics theory.
Synthesizing the above literature, there are few studies on the application of extenics to product interface design, and the method can optimize the target problem of how to match the interface design elements and the final solution preference. At the same time, the topologically superior evaluation method is a practical method for comprehensive evaluation, which can combine multiple evaluation indexes to determine the degree of superiority or inferiority of a solution [29]. erefore, the research is based on topologic theory to establish the object-metarelationship of the interface design of recreational smart products in order to obtain the optimal solution and the preference of elderly users for the interface design elements and to provide a theoretical reference for designers to design the interface of recreational smart products.
e key contributions of this study include the following.
(1) We analyze the extenics evaluation system, the interface of smart devices and its components and discuss the interface design evaluation process based on extenics in detail (2) Next, we construct an evaluation hierarchy; four evaluation features were expanded and divided into interrelated levels to make them organized (3) en, we use the Analytic Hierarchy Process (AHP) that combines qualitative and quantitative analyses, construct the fuzzy mutual inverse judgment matrix, and perform a joint analysis of users' preferences for interface elements (4) Finally, 18 sets of elderly companion robot interfaces are designed using the optimized combinations derived from the orthogonal design, and prototypes are made for the research population to operate in the experiments

Decomposition of Interface Components.
By observing and analyzing the interface design of most smart devices on the market (especially for elderly companion robots), then consulting professional evaluation websites, consulting interface design experts, and also interviewing elderly users, the collected information and the records of interviews with elderly people and experts were compiled, and the seven constituent elements and the types of each element that need attention in the interface design of recreational smart products were determined as shown in Table 1.

Orthogonal Experimental Design.
Orthogonal experimental design is a design method to conduct experiments with multiple factors and multiple levels according to an orthogonal table for three or more experimental factors, which is characterized by using the results of partial experiments to analyze the situation of the full experiment, with the aim of finding the optimal combination of levels.
According to the numbering of each element type in Table 1 to arrange the combination, if a full-scale experiment is conducted, there are 1458 possible scenarios, but doing so is not only a large amount of work, and there is duplication, and the optimallevel combination needs to be found. erefore, the orthogonal design module in SPSS 26.0 was used to conduct orthogonal experiments on the constituent elements, and 18 typical combination schemes could be obtained, as shown in Table 2. [30][31][32] is a discipline founded in 1983 by Chinese scholars led by researcher Wen Cai from Guangdong University of Technology, and is also known as the method of physical meta-analysis. e primitive theory is one of its three pillars, which suggests that the basic elements of things include the thing element, the matter element, and the relationship element. After establishing the evaluation indexes, the final correlation degree of each solution is determined through the calculation of the weight and the correlation function, and then the solution is preferred. e interface design evaluation process based on extenics is shown in Figure 1.

Determine the Object Element.
e expression of the object element theory is an ordered triple: R � (N, c, v), where N stands for the name of the thing, c stands for its characteristic value, and v stands for the quantity of c. If R is a multidimensional object element, then there are multiple features and the corresponding quantity values, and then R can be represented by the matrix column: Let U be a theoretical domain, and if x is any element in U, then the extension set A in U is where y � k(x) is the correlation function of A and k(x) is the correlation degree.
According to the research question, the name of the target product, that is, the thing to be evaluated, is determined to be the interface design, and a comprehensive   Figure 1: Interface design evaluation process.
analysis is conducted from functional, user, and experience aspects using the primitive method. e three design experts collate the information to obtain the interface design evaluation datum and then establish the interface evaluation target primitives according to the formal description in the theory of expandable innovation as follows:

Evaluation Hierarchy Construction.
e interface evaluation target primitives have been constructed, but the evaluation indexes of the interface design of recreational and intelligent products involve multilevel and multicriteria, and in deciding the criterion layer and subcriteria layer, the factors affect or constrain each other, and at the same time, the elderly should be considered as a special group of people to reduce their cognitive difficulty, and the evaluation criteria should be selected to ensure their comprehensiveness and representativeness. erefore, the four evaluation feature values were expanded by combining the topologic topology and the hierarchical clarity of hierarchical analysis and divided into interrelated and ordered levels to make them organized.
(1) Target layer: e only and definitive one, that is, the wellness smart product interface design. (2) Guideline layer: To ensure the comprehensiveness of the scope of the evaluation criteria design, the interface needs to be evaluated in a multifaceted manner. e four first-level criteria are interaction mode M 1 , interface quality M 2 , cognitive support M 3 , and user experience M 4 , then the set of first- rough the questionnaire method of the literature [33,34] and by integrating the opinions of experts and designers, and using the expanded method of the topologic theory, the scientific, comprehensiveness, and objectivity of the evaluation index establishment are ensured. e finalized 14 evaluation indexes for the interface design of recreational and intelligent products are shown in Table 3. From this, the set of secondary subcriteria is constructed: (3) Program level: 18 typical combination programs. (4) e construction of the evaluation hierarchy for the interface design of recreational and intelligent products is shown in Figure 2.

Correlation Function Determination.
e association function is calculated using the following method: let X 0 � a, b, X � a p , b p , X 0 ∈ X, the primary association function can be obtained as follows.where X 0 is the classical domain, X is the nodal domain, p(x, X 0 ) denotes the value of the association function of an element under the classical domain, and D(x, X 0 , X) denotes the value of the association function of an element under the nodal domain; then, the functional relationship equation is To select the optimal solution among multiple solutions, the set F � F 1 , F 2 , . . . , F m can be chosen by the device, and the object element model matrix is where F i represents multiple scenarios, C j (i � 1, 2, . . . , n) represents the impact characteristics of multiple scenarios, and V ij represents the quantity value of the ith scenario corresponding to C j , that is, the specific data collected from the experts.
In the evaluation process, we also need to give the object element model of the ideal solution as a basis to judge whether the evaluated solution meets the requirements, and the expression is where F * represents the ideal solution, C j represents the impact characteristics of the evaluated solution, V j represents the domain of the ideal solution corresponding to the quantity of C j , that is, V j � a j , b j , is the range given about the characteristics (C 1 , C 2 , . . . , C n ) T , that is, classical domain, which is determined by the decision maker according to the real life situation.
In multiple evaluated solutions, (C 1 , C 2 , . . . , C n ) T represents the feature indicators, (V 1 , V 2 , . . . , V n ) T represents the score given to each indicator by the decision maker, and note that V pj � a pj , b pj is the range allowed by the feature set (C 1 , C 2 , . . . , C n ) T , that is, the nodal domain, determined by Scientific Programming the maximum range of quantitative values scored by the decision maker for each feature value. e expression of the association function of the evaluated scheme, obtained from the primary association calculation, is where V j � a j , b j , V pj � a pj , b pj .

Calculation of Indicator Weights. Analytic Hierarchy
Process (AHP) combines qualitative and quantitative analysis but is more subjective and susceptible to the influence of extreme values in the judging process. Triangular fuzzy analytic hierarchy process (TFAHP) is a study of mathematical problems with vagueness using triangular fuzzy numbers, which can combine multiple elements and attributes to solve vagueness and subjectivity [35][36][37], and its main calculation steps are as follows.

Construction of Fuzzy Mutual Inverse Judgment Matrix
for Two-by-Two Comparison of Criterion Layers. First, the first-level evaluation criterion is scored in two comparisons for the target layer to construct a first-level fuzzy mutual inverse judgment matrix. Secondly, the subcriteria are scored in two comparisons for the first-level criterion to construct a fuzzy mutual inverse judgment matrix for the second-level subcriteria. Judges are required to use a scale of 1 to 9 for judging decisions, and the quantification and meaning of the defined terms are shown in Table 4. Take the target layer element Q and its corresponding firstlevel criterion M 1 , M 2 , . . ., M n of the criterion layer as an example, and construct the fuzzy mutual inverse judgment matrix A: where the fuzzy set of r ij is (l ij , m ij , u ij ), and the nth-term criterion is compared for judgment; then, we get e criteria of each level of each scheme are scored by z experts, and the fuzzy comprehensive mutual inverse judgment matrices of Q − M level and M − N level are established, respectively. Assuming that similar scorers have similar levels of knowledge as well as judgment, an arithmetic average is used to combine the scoring information.

Calculation of Weight Values
(1) Defuzzification of the Matrix. Firstly, the fuzzy judgment matrix needs to be transformed into the judgment matrix of exact figures, and the mean area method is generally used, as shown in equation (4), followed by the consistency test.
(2) Weight Value Calculation. After the defuzzification process, the calculation of the weight vectors of each matrix begins, and the usual methods are least squares, arithmetic averaging, and geometric averaging. In this paper, the geometric mean method is used, and the specific steps are as follows [39].
Step 1. Calculate the product of each row of the judgment matrix where r ij denotes the element of the ith row and jth column of the matrix and n is the number of elements.
Step 2. Find the geometric mean of M i Step 3. Normalization process

Consistency Check.
Due to the ambiguity and limitations of human thinking and the complexity of judging things, there may be inconsistencies in the judgments given by decision makers in the judging process, so the consistency of the matrix needs to be checked. If the tested judgment matrix possesses consistency, then it can be assumed that the original triangular fuzzy matrix can also pass the consistency test [40]. First, the matrix is input into MATLAB software to find the maximum eigenvalue λ max , and then the consistency of the matrix is tested by combining the consistency criterion CI and the random consistency criterion RI. e selection of the mean random consistency criterion RI is shown in Table 5. e CI as well as the consistency ratio CR is calculated as follows: (1) Calculate the degree of inconsistency CI: where λ max is the maximum eigenvalue of the matrix and n is the matrix order. Extremely important e extreme importance of one metric over another 8, 9, 10 1/10, 1/9, 1/8 Note: 2, 4, 6, and 8 are the compromise values, r ij � r −1 ij . One indicator is less important than the other, using the reciprocal representation.

Scientific Programming 7
(2) Calculate the consistency ratio CR: When CR < 0.1, the judgment matrix is considered to have good consistency; otherwise, the matrix needs to be adjusted until good consistency is achieved.

Calculation of the Final Weights of Each Evaluation
Index at the Criterion Level. After completing the consistency test, the total hierarchical ranking needs to be obtained as a reference for the final program evaluation. In this paper, there are two levels of criterion level and subcriteria level, and the weights of the subcriteria need to be multiplied with the weights of the corresponding criterion when calculating the final weights of the indicators. For example, to calculate the final weight of indicator N 1 , the weight of N 1 is multiplied by the weight of the corresponding criterion M 1 .

Final Correlation Calculation and Solution Preference.
In the evaluated scenario, each feature has a different degree of influence on the scenario; therefore, the weights of the features need to be combined; then, the correlation between the evaluated scenario and the ideal scenario is A larger λ i means that the evaluated solution is closer to the ideal solution and also closer to the decision maker's expectation, and the correlation value is used as a reference to rank and prefer the solution.

Joint Analysis of Older Users' Preference for Interface
Design Elements. Based on the topology primitive theory, a topology evaluation system can be constructed for 18 typical solutions, and the best combination can be selected. To obtain the preference of elderly users for each type of interface components, the utility value and importance of each element should be calculated by joint analysis. Positive and negative validity values can reflect whether the research population holds a preference for the type of element, and the magnitude of the value can reflect the degree of preference or dislike. Importance reflects the degree to which the element is valued in the overall interface design. Not only can we get the preferences of elderly users, but also can help designers to grasp the design focus and at the same time can support the correctness of the above solution preferences. e preferences of elderly users for the interface design of recreational smart products were obtained from the analysis of both the combination of overall design elements and the calculation of the importance of single design elements.

Collection of Scoring Data.
A random sampling method was used to select z elderly users with experience in using wellness smart products as the research population, covering different occupations, genders (differences between men and women are not discussed in the text), and ages, and 18 typical combination scenarios were scored using a 7-point Likert scale, and reliability was calculated after the questionnaires were collected.

Overall Utility Value and Importance Calculation.
Once the questionnaire had qualified reliability, the collated data were imported into SPSS 26.0 and the conjoint analysis module was used to calculate statistics such as individual and overall utility values as well as importance values. e utility and importance values provide statistics on the overall intention of the research population, that is, the user's preferences.

T-Test.
In addition, u elderly users were selected to evaluate the survey of the same judging scheme, and their results were used as actual values; the results of the survey of z elderly users in the previous period were used as predicted values, and the confidence level of the experiment or model was captured by calculating the correlation between the two values.

Design Application: Example of Interface Design for Elderly Escort Robots
Using the typical optimized combinations derived from the orthogonal design described above, 18 sets of elderly companion robot interfaces were designed and high-fidelity prototypes were made for the research population to operate in the experiments. e prototype is defined as a master controller as a client and connects to the server side via the ESP8266 Wi-Fi module, which is in station mode. e server side uses PHP to provide socket support and uses the unofficial PHP extension Swoole to build the socket communication server. e high-fidelity interface is shown in Figures 3(a)-3(r).

Object-Ordered Triad Construction.
N is the interface design, c is the 14 secondary subcriteria evaluation indexes identified in Table 3, and v represents the quantity value of c. en, a matrix column of ordered triads is obtained as follows: Naturalness v 2

⋮ ⋮
Caring and friendly v 14

Classical Domain and Section Domain
Determination. e evaluation indexes for the interface design of the elderly companion robot were distributed to three experts, who were asked to score the 18 options to be selected as shown in Figure 3 according to the four primary and 14 secondary evaluation indexes identified in Table 3 on a percentage scale. e final scores of the indicators were obtained by taking the arithmetic average of the scores of the three experts, and the results are shown in Table 6.
Evaluation scoring is conducted on a percentage system, and the evaluation results can be divided into four levels: excellent (75-100), good (50-74), moderate , and poor (0-24). After consulting with the evaluation experts, it is known that the expected range of the evaluation indicators of the evaluated program metamodel, that is, the classical domain, should be within 75-100 is a good and reasonable level, and the maximum range of all evaluation indicators, that is, the nodal domain, can be taken as 0-100; then the classical domain and the nodal domain are as follows.
Classical domain: Section domain: Scientific Programming

Final Correlation Calculation.
e correlation degree and optimal order of each evaluated solution were calculated according to equations (3)- (8) and (20), and the results are shown in Table 12.

Calculating Utility Values and T-tests.
According to the steps of utility value calculation in Section 3.4, 60 elderly users with experience in using recreational smart products were selected as the research population for scoring. e alpha coefficient of the questionnaire was 0.827 and the Kaiser-Meyer-Olkin (KMO) was 0.776, indicating that the questionnaire has good reliability and can be used as a basis for the next analysis. e research data were imported into SPSS 26.0 software, and the overall utility and importance values could be obtained by using the conjoint analysis module, and the results are shown in Table 13.
In addition, 15 elderly users were selected to rate the same evaluated program, and their results were used as the actual values, and the data from 60 users in the previous period were used as the predicted values, and the correlation between the two values was calculated by paired-sample ttest, and their analytical data are shown in Table 14.
As can be seen from Table 14, the p value is 0.588, which is greater than 0.01, and there is no significant difference between the two samples. It indicates that the predictive ability of this joint analysis is better and can truly reflect the degree of users' preferences.

Discussion
e orthogonal design was used to obtain 18 typical solutions for the optimal combination of the constituent elements of the interface design of the recreational intelligent products, after which the correlation degree of each solution was calculated based on the primitive theory, and the different importance of the elderly users to the constituent elements of the interface and the preference of each element type were obtained by the joint analysis method. e following conclusions can be drawn from the data in Tables 12  and 13. (1) Of the 18 optimized typical combinations, the 13th package was the most preferred by elderly users. Due to ageing, the physiological and psychological functions of the elderly are gradually fading. In the home recreation environment, intelligent products should not only help the elderly to complete their tasks, but also establish emotional care and help and guide the elderly to use modern intelligent products more conveniently from the design level. e 13th solution helps seniors to wake up the operation interface or companion robot more conveniently through voice so as to complete the user's commands. e Windows-style interface layout and the icon style with graphics and text can reduce the cognitive load of elderly users and enhance the care for them.
(2) According to the importance data in Table 13, it can be seen that among the seven components of the interface design of recreational smart products, elderly users attach the most importance to the information input method, followed by the feedback method; then the interface layout method, touch area and wake up method, and the overall design of icons and color settings are relatively less important,  3.293 1 17 Table 8: Interaction mode criterion judgment matrix consistency ratio and its weights.  Table 9: Interface quality criteria judgment matrix consistency ratio and its weights.   indicating that elderly users favor the convenience of operation, the accuracy of information feedback, and the visibility of information. (3) In the interface layout mode element, older users prefer Windows phone type. e interface is visually the most unified and simple, and the icons are large enough to be easily operated and recognized. e voice method is undoubtedly the most popular among the wake-up elements. e voice method can wake up the smart products faster and more conveniently so that they can receive information or instructions quickly. e icon design with graphics and text is preferred by users more than pure pattern or pure text design, which has much to do with the cognitive ability of elderly users, as pure text or pattern is not enough for elderly users to understand the functions represented by the icons. In the color setting, older users prefer warm colors; the reason is that cold colors give users a cold, unfeeling feeling, and older people need more emotional care, so cold colors have the lowest utility value. For the touch area is undoubtedly the larger the better, because the elderly physiological function and normal people have obvious differences in the operation process is likely to point or click unresponsive, moderate increase in touch area can be more convenient for elderly users to operate. In terms of information input and information feedback, elderly users prefer voice input and voice feedback because the elderly group is unfamiliar with smart devices and visual fading, so voice input is faster and more direct, and auditory feedback is also more effective than visual feedback, but visual and haptic feedback should also be incorporated in the design process to create a multisensory, multichannel interaction mode so as to enhance user experience.

Conclusion
Under the IoT system, the elderly face many "digital divide" problems in the use of smart products, especially in the design of the interface of recreational smart products ignore the impact of the interaction between the elderly user and the interface, interaction mode. e method used for the selection of multiple design solutions is also subjective and one-sided, and designers do not have a comprehensive evaluation system as a reference in the process of solution evaluation and selection and fail to evaluate the user and the  interface as a whole to accurately evaluate the merit of the object. Based on this, the study uses topology as the theoretical basis, divides the seven constituent elements of the interface and the types of each element according to the needs and characteristics of elderly users, calculates the final correlation degree of 18 typical solutions based on the correlation function in primitive theory to obtain the final correlation degree, and realizes the ranking and preference of solutions. Finally, the joint analysis was applied to obtain the preference degree of elderly users for the interface design of recreational smart products, which broadened the research ideas of interactive interface design and optimized the target problem of how to match the interface design elements and the final solution preference. e use of mathematical and rational thinking to study contradictory problems enables the objectivity and scientific nature of interface design and solution selection to be improved, indirectly enhancing the naturalness and comfort of the interaction experience of elderly users and promoting the development of the Internet of ings in the cause of smart ageing. ere are also limitations in the study: the evaluation process is more subjective and the sample size is limited, so the follow-up study will consider using eye-tracking technology to obtain rigorous experimental data and combine subjective and objective evaluation statistical methods for further in-depth exploration.

Data Availability
e data used to support the findings of this study are included within the article.

Consent
Informed consent was obtained from all subjects involved in the study

Conflicts of Interest
e authors declare that they have no competing interests regarding the publication of this paper.

Authors' Contributions
Lulu Jiao, Baohua Tan, and Fang Tian contributed equally to this work. Xu Han contributed the central idea, analysed most of the data, and wrote the initial draft of the paper. e remaining authors contributed to refining the ideas, carrying out additional analyses and finalizing this paper. Lulu Jiao designed research, performed research, analyzed data, and wrote the paper. Baohua Tan is responsible for drafting and modifying the contents of important research knowledge. Fang Tian makes substantial contributions to the conception or design of the research, to the collection, analysis, and interpretation of research data; Wenbin Zhao analysed the data and were involved in writing the manuscript. Hua Yu developed the idea for the study, did the analyses, and involved in writing the manuscript.