Nested affordance-based intuitive design tool: Affordance interaction matrix

Abstract Affordances serve as design cues, facilitating users in effortlessly identifying the intended use of objects. However, due to the phenomenological nature of the affordance concept, its application and understanding in the human-computer interaction (HCI) domain remain uncertain, resulting in limited utilization in design practice. This study introduces the concept of nested affordances, linking affordances more closely and explicitly with perception. We reposition the affordance concept and transform it into a design tool—the Affordance Interaction Matrix (AIM). This matrix captures the nested relationships and perceptual conflicts between target affordances within a product, assisting designers in identifying and eliminating potential confusion for users when facing a design, providing implicit interaction cues. The AIM-based design method proposed in this research addresses the shortcomings in describing product affordance interactions, focusing on the natural guidance of specific behaviors. This approach enables designers to clarify intuitive interaction foundations and make swift, effective decisions. Finally, the paper demonstrates the application and advantages of AIM through a practical case study of accessible kitchen furniture.


PUBLIC INTEREST STATEMENT
Our everyday life is replete with countless interactions between us and the objects we use, from simple kitchen utensils to complex digital devices.These interactions, however, can often be challenging due to design inconsistencies or lack of user-friendly features.This research seeks to improve the experience of human-object interactions by introducing a novel concept termed 'nested affordances'.It suggests a new design tool, the Affordance Interaction Matrix (AIM), that captures the complexities of these interactions and helps designers create products that are more intuitive and user-friendly.Through AIM, designers can identify and eliminate potential confusion for users, making interactions more effortless and satisfying.The paper demonstrates the real-life benefits of AIM through the design of accessible kitchen furniture, showing its potential to enhance everyday life.This study holds significant implications for all of us as it aims to make our interactions with objects around us more enjoyable and efficient.

Introduction
One of the goals of design research is to deeply understand how users establish close interaction relationships with products and effectively control these relationships.Designers face the challenge of creating products that are not only functional but also intuitive to use.
Affordance, as a design concept, describes how objects or environments support human behavior.It is a quality relative to human users, indicating how an object or environment can be used or operated.For example, the affordance of a chair is its sit-ability, and the affordance of a door is its ability to be opened and closed Affordances in design are users' action possibilities when interacting with an artefact.They can be "directly" perceived based on the structural features of the artefact (Kaptelinin & Nardi, 2012).If designed properly, users can effortlessly determine how the product should be used.
However, Gibson's original affordance concept, although influential and considered an ideal mechanism for triggering action, is also deemed too narrow.In practical applications, its use presents certain difficulties and cannot fully satisfy HCI needs (Kaptelinin & Nardi, 2012;Soegaard & Dam, 2012).
To enhance the relevance and practicality of Gibson's original affordance concept in practice, this study develops an intuitive conceptual tool, the Affordance Interaction Matrix (AIM), based on Gaver's nested affordance concept, for practical product technology analysis, design, and evaluation tasks.This tool, used during the conceptual stage for design evaluation and comparison, assists designers in detecting potential action confusion users may encounter.It enables designers to make rapid, effective decisions based on intuitive interaction design principles, allowing for a deeper understanding and application of perceptual information.By systematically modifying product features, it implicitly provides interaction cues, resulting in more intuitive and natural user experiences.
The focus of this study is to create a design tool based on a well-defined theoretical framework.The article is structured as follows: Section 1 systematically reviews HCI affordance research, its development, and limitations.Section 2 provides a detailed overview of the nested affordance framework, repositioning affordances and integrating Gaver's perspective on nested affordances with perception.Section 3 presents design strategies and a corresponding matrix tool, based on the existing nested affordance framework, which unifies intuitive interaction and perception.Section 4 demonstrates the feasibility of the tool through an accessible kitchen example.Lastly, we discuss the tool's strengths, limitations, and future improvements.

Affordances in HCI research
This section provides an overview of the research achievements, developments, and limitations of affordances in the HCI field.Given that Kaptelinin and Nardi's (2012) paper "Affordances" has already provided a comprehensive and in-depth exploration of the evolution and research results of affordances in the HCI field, this study will introduce key literature directly related to the research topic.In subsequent sections, we will detail our theoretical framework and design tool aimed at filling the research gap and enhancing the value of affordances in HCI practice.
In 1979, Gibson created the term "affordance" and defined it as "the affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or ill" (Gibson, 1979, p. 127).In other words, affordances exist in the environment and can be utilized by animals.Norman (1988) first introduced this term and concept into the design field.He considered affordance as an attribute of things that, if perceived, guides users on how to use the object, and later proposed the term "perceived affordance" to differentiate it from Gibson's affordance concept (Norman, 1999).Gibson emphasizes the possibilities for action as affordances, while Norman focuses on how to communicate these possibilities to users.
McGrenere and Ho further explored design affordances and specifying affordance information, introducing the concept of degrees of affordance (McGrenere & Ho, 2000).They advocated optimizing design in two directions: increasing the capture of affordances at the level of possibilities and enhancing clarity at the level of perceptual information.However, their design framework primarily focused on the affordances of virtual software, rather than physical objects.
Nested and sequential affordances (Gaver, 1992), levels and types of affordance (Hartson, 2003;Vicente & Rasmussen, 1992), and discussions on Gibson affordances have facilitated the further development of the concept, making it a more useful conceptual tool in analysis and design.
In current HCI discussions on affordance, a major issue is the uncertainty of the meaning and role of the affordance concept due to the existence of multiple interpretations of the term (Kaptelinin & Nardi, 2012).To address these issues, Taehyun and Sangwon developed a heterophenomenology framework for user experience analysis, which effectively describes various phenomena related to the concept of affordance occurring in physical, social, and self dimensions, as well as in the design of products and services (Ha & Lee, 2021).
Supporting the direct perception of appropriate user actions was the fundamental reason for introducing the affordance concept into HCI (Norman, 1988;Gaver, 1991).Therefore, this study aims to return to Gibson's original definition of affordance and, combined with the concept of nested affordance, proposes a specific design tool.The goal is to present a new affordance concept positioning and address the limitation of advanced theoretical analysis discussions on affordance within the design research community, ensuring that the concept is relevant and effective in the HCI design process.

Design theory based on nested affordances
In this section, we reposition the concept of affordance by introducing Gibson's theory of affordances, and more closely and explicitly integrate Gaver's perspective on nested affordances with perceptual concepts.

Affordance positioning: Merging perception
In the past two decades, the relationship between affordances and perception has been a highly focused and controversial topic in human-computer interaction (HCI) research (Kaptelinin & Nardi, 2012).Although Gibson's original concept of affordances has provided some guidance for HCI research to some extent, existing research suggests that this concept is too narrow to meet the needs of HCI research and practice (Kaptelinin & Nardi, 2012).
Therefore, we propose to expand Gibson's affordances by integrating them with perceptual research in the field of HCI.As shown in Figure 1, perception serves as a mediation (middle layer) between the basic theoretical tool for design analysis (bottom layer) and the specific affordances discovered and explored by users (top layer), forming a nested affordance relationship.Gaver (1991), points that the main advantage of the ecological perspective is that it "may offer a more succinct approach to the design of artifacts that suggest relevant and desirable actions in an immediate way."Thus, this study views affordances as a conceptual tool under an ecological perspective rather than a design criterion.Our interpretation of affordances is based on Gibson's original concept, "action possibilities provided by the environment," but we do not adopt Gibson's anti-representationalist sense; instead, we apply it to practical perceptual design analysis.
In summary, we use the ecological perspective of affordances to guide perceptual analysis and design decisions.This approach retains Gibson's original concept while integrating perceptual research in the HCI field, enhancing the practical value of affordances in design analysis.We aim to strengthen the connection between affordances and perception, providing more effective theoretical support for HCI research and practice.To this end, we have developed an intuitive conceptual tool suitable for technical analysis, design, and evaluation tasks of actual products, positioned between affordances and perception (see Figure 6 for details).

Concept of nested affordances
Animals and environments are highly nested entities, with components and processes existing simultaneously across multiple spatial and temporal scales; there are no isolated components or processes (Franchak, 2020; J. J. Gibson, 1979;Turvey, 1992;Van Orden et al., 2003;Wagman & Miller, 2003. In Gaver's paper "Technology Affordances" (1991), he explored nested and sequential affordances, dividing them into temporal and spatial dimensions.The temporal dimension focuses on animal behavior, while the spatial dimension focuses on the objective environment.
Sequential Affordances: Gaver (1991) pointed out that "acting on a perceptible affordance leads to information indicating new affordanc" (p.82).As Gibson implied, temporal nesting refers to the nesting of affordances when an action possibility is composed of one or more actions (McGrenere & Ho, 2000).For instance, a door is perceived as openable, and the handle must be perceived as graspable, rotatable, and pullable.This simple task requires three affordance-based interactions (Gaver, 1991).
Nested Affordances: One affordance acts as the context for another affordance (Gaver, 1991).For example, in the calculator shown in Figure 3(a), compared to Figure 3(b), it is more likely to elicit pressing actions because it nests much perceptual information supporting "pressing downward." In Calculator 3a, larger and flat non-slip buttons enhance the tactile affordance, with the pressing affordance nested within the touch affordance.The buttons float above the base, and the gap below is revealed, indicating the direction of pressing.Perceiving the affordance of pressing downward relies on perceiving the floating buttons revealing the gap.The metallic material of the base contrasts with the plastic material of the buttons, highlighting the buttons' lightness.All nested affordance perceptual information, including touch, color, size, shape, position, material, texture, gloss, sound, temperature, weight, etc., is organized into an ordered perceptual hierarchy, making the internal elements of the product tend toward a single action, pressing downward.
Seemingly simple and ordinary actions may be quite complex in their composition, and the selection and control of these actions require gathering information about each nested affordance.Moreover, these activities largely occur outside the conscious cognition of the constituent behaviors, even before the action begins (Warren, 1984).In other words, the perception of this Recognizing that all affordances are nested within the context of other affordances, no affordance is perceived in isolation (Mark et al., 2015;Rietveld & Kiverstein, 2014;Wagman & Stoffregen, 2020).Affordance structures that support goal-directed behaviors are typically composed of multiple interconnected affordances, so the perception of affordances must take into account these nested relationships.Designers need to adopt more precise analysis methods to examine the affordance perceptual information nested throughout the product components.
The temporal dimension of nesting explains the sequential occurrence of affordances in time, focusing more on the implementation of action forms and the perception of objects in psychology and physiology.The spatial dimension of nesting describes the grouping mechanism of affordances in perception.The design tool to be proposed in this study will focus on the efficiency of users' perceptual exploration of specific affordances in physical objects and the ease of information generation.This will help to better understand the role of affordances and their application in the design process.

Conceptual design approach based on nested affordances
This section incorporates the concept of nested affordances into the design process, proposing a design strategy that combines intuitive interaction and perception, as well as the corresponding matrix tool.This approach helps designers better understand and apply perceptual information, providing implicit interaction cues for a more intuitive and natural interaction experience.

Nested affordance design strategy
Affordance refers to an attribute or feature of an object that suggests how to operate it, while nested affordance exists as a property of a system, displaying a series of cues that guide users in achieving interaction.According to Gibson's concept of affordance, designers need to rationally construct the perceptual information required to support specific behaviors.

Affordance perception through exploration
The basis for acquiring affordances is the combination of information provided by the world and human action capabilities, and the perception of affordances carries behavior, especially exploratory behavior (Gibson, 1979;Neisser & Becklen, 1975).Increasingly, research evidence shows that affordances are not passively perceived but are obtained through exploration (Stoffregen & Mantel, 2015).
Individuals who are motivated to perform certain actions under specific circumstances engage in behaviors, or movements, that generate perceptual information about affordances.Some exploratory actions are deliberate and conscious, while others are implicit and occur outside of intentional awareness.Both types are important and can influence design (Wicker, 1984).
Perception-driven active exploration can involve various types of interaction with the environment or objects, encompassing motor, cognitive, and sensory processes.These may include: tactile exploration: Involving whole-body movements, such as using hands to touch and inspect texture, shape, and temperature, to gather information about affordances of objects or surfaces (Lederman & Klatzky, 1987).Visual scanning: Involves head and eye movements to systematically observe the environment or objects, to collect information and identify affordances (Treisman & Gelade, 1980).Auditory exploration: Actively listening for auditory cues that provide information about objects or the environment, such as echoes or sounds produced by interaction with surfaces or materials (Bregman, 1994).Olfactory exploration: Utilizing the sense of smell to identify specific characteristics of the environment or objects, such as detecting odors that indicate the presence of particular materials or substances (Anderson et al., 2003).Gustatory exploration: Tasting objects or substances to gather information about their properties, such as edibility or chemical composition (Bartoshuk et al., 1994).
These perception-driven active explorations facilitate the recognition of affordances, enabling users to better understand how to interact with their environment and objects within it.

Reserving exploration space for users
Recognizing that the affordances within products often exist in nested structures, users perceive these affordances through exploration.Therefore, the concept of affordances involves not only the costs associated with execution or operation but also the costs associated with exploratory actions related to affordances (Mantel et al., 2012).To account for this, designers should not only create products that meet users' needs but also optimize exploratory actions and the resulting perceptual information to reveal corresponding affordances.
In this context, encouraging users to perform information-generating actions in design can be regarded as adding information to the product (Mantel et al., 2012).However, more importantly, the concept of affordances is often misunderstood as a "stimulus" that triggers reflexive behavior, and this type of information is not imposed on users, such as printed labels.Instead, product design should enable users to generate and obtain information optimally.In fact, affordances are attributes valuable to individuals in certain contexts, with their objective characteristics and subjective experiences being almost unconsciously acquired from the environment.Affordances are the product of the interaction between objective characteristics and subjective experiences in the interaction process.
Considering the proactivity of human perception, designers need to be aware that a portion of the information in products should not be imposed on users but should be generated and picked up by users unconsciously (Naoto et al., 2004).To leave room for active exploratory actions in the product, designers should reduce the difficulty of generating information, allowing users to easily generate information as needed and focusing on providing ambiguous information (as shown in Figure 4).
The perception formed by the product does not provide enough information for users, instead promoting more efficient information acquisition from the environment, thus achieving information balance (Zipoli Caiani, 2014).The matrix tool proposed in this study aims to eliminate redundant elements unrelated to the target action, creating a positive exploration space for users rather than adding extra perceptual information.This tool employs a reverse design approach based on user needs, facilitating information gathering from the external world.

Optimizing nested affordance perception information
Theoretical discussions on affordances seldom address the fact that multiple affordances coexist in any given situation, requiring users to make choices regarding affordances and potentially needing to distinguish between affordances consistent with a specific behavioral goal and those that are not (Stoffregen, 2003).

Figure 4. Information balance between product and user.
In product design, designers inevitably need to provide multiple affordances (functions) within the same interaction interface, constructing several goal-oriented actions with varying importance (priority levels).Neglecting the possibility of interference between affordance-based interactions may lead to user confusion during product use.
As shown in Figures 1-5, A, B, and C represent three target affordances (anticipated actions).For each target behavior, redundant and diverse perceptual information exists externally.Moreover, these affordances are often not mutually supportive, and the perceptual information between affordances may overlap, leading to friction.
To address these issues, we propose two aspects for optimizing the perceptual information of nested affordances within products under the nested affordance perception approach: (1) Remove erroneous, redundant perceptual information external to the target behavior (as shown in Figure 5-2): People subconsciously pick up various affordances in their environment, not limited to the initially specified functional requirements.Designers need to eliminate detrimental perceptual information, ensuring that perceptual information related to the target behavior is clear and easy for users to capture.This helps users generate information quickly when needed and enhances the affordance's ease of pickup at the level of possibilities.For numbered lists (2) Construct nested affordances that support the actions required by users (as shown in Figures 5-3): The perceptual information of each affordance may be part of the affordance structure for other goal-oriented activities.Designers should adjust the interactions between affordances, forming mutually guiding and supportive relationships, reducing the cost of exploring target actions and improving the system's discoverability.Optimize the smooth connections between affordances, paving an unobstructed path for user operations.
By following these two design directions, the aim is to achieve the design framework proposed by Grenere, which emphasizes enhancing the ease of pickup of affordances and the clarity of perceptual information.

Affordance Interaction Matrix (AIM)
This study, based on the ASM matrix proposed by (Maier & Fadel, 2009) and the FTIM matrix proposed by (Galvao & Sato, 2005), has developed the Affordance Interaction Matrix (AIM).Created on the foundation of nested affordance theory, AIM provides analysis for each task component and target affordance in product design.

Behavioral and anticipated function
First and foremost, it is essential to clarify that not all product functions can be explained or practiced through the concept of affordance.The term "function" in design, due to varying semantic levels, can be roughly divided into two categories: "behavioral function" and "anticipated function" (Djajadiningrat, 1998).For example, each button on a remote control directly provides users with "pressability."Therefore, each button can be pressed, and the occurrence and perception of pressing behavior are based on affordance relationships.However, the anticipated functions) produced after pressing different buttons are entirely different, and the association between these functions and the buttons can be arbitrarily assigned by the designer.
In Maier's ASM matrix, needs are translated into different types of affordances (Maier & Fadel, 2009b).However, in this study, needs are converted into different actions (behavioral functions).Unlike the anticipated functions in the ASM matrix, the AIM matrix uses behavioral functions for needs, as show in Table 1.This research focuses on people using subliminal consciousness to pick up various nested affordances within products, emphasizing Gibson's action possibilities rather than the initially designed anticipated functions.

AIM matrix example
To implement the design strategy proposed in Section 4.1 and to help designers maximize design improvements, we introduce the Affordance Interaction Matrix (AIM) (see Figure 6).The AIM is based on the nested affordance approach presented in Section 3.1 and has two main functions: (1) connecting different target affordances to consider nesting issues; (2) relating the product's physical structure to the user's expected actions for perceptual conflict assessment.The affordances that the product should provide, i.e., the user's target behaviors, are listed on the left side of the AIM.Meanwhile, AHP was used to calculate the weight of user's intended actions.The Analytic Hierarchy Process (AHP) is a widely used quantitative method for decisionmaking problems.This approach decomposes complex problems into hierarchical structures, conducts pairwise comparisons of elements within each level, and subsequently calculates their respective weights (Lin et al., 2008).
The left-side structure matrix is used to capture the linkage relationships between target affordances.The main components of user interaction with the product are listed at the top of the matrix.The matrix is filled by identifying two types of interaction conflicts between target affordances and components, represented by two different symbols (square and triangle) for two different values (1 and 2).All physical conflicts between components and actions = 2, and all perceptual conflicts = 1.
At the bottom of the matrix, the degree of conflict each component has with affordances is tallied.The higher the score, the more harmful factors the corresponding component generates for affordances, and the greater the opportunity for design improvement.On the right side of the matrix, the total number of harmful components for each affordance is counted.The larger the value is, the poorer the product affordance quality, indicating that more components are impairing the realization of the affordance.

Purpose of AIM matrix
The purpose of constructing matrices is to establish the correlation between the positive attributes (goals) of a product and the required product features.The aim is to eliminate detrimental information within the product and enhance perceptual information related to its target availability.The AIM (Availability Interaction Matrix) distinguishes itself from other matrices by its intention to remove superfluous elements, instead of adding extra positive perceptual information for certain actions.
Compared with existing availability design tools, AIM presents unique applicability during the user requirements collection phase and offers several notable advantages.The function of the Availability Interaction Matrix primarily manifests in two aspects: Firstly, it assists in the preliminary evaluation of designs, aiding the judgement of design content and breaking down and analyzing issues arising in product availability assessment.This approach ensures a more scientific and objective evaluation result.It precisely identifies availability conflicts in the product and optimizes identified availability scenarios.The matrix can construct different AIMs for various design concepts, select the optimal solution, and form the basis for subsequent priority research.
Secondly, AIM can serve as an attention guidance tool.It describes the availability attributes for each functional component, transforming abstract availability attributes into specific actions.The strength of AIM lies in the establishment of action interaction points and the visualization of the relationship with product components.Existing interactions are recognized.In other interaction matrices, the matrix represents the relationship between the product's technical functions and the user's task requirements.In this study, AIM is adapted to model the relationship between product components and user behavior.Furthermore, the AIM matrix can be applied to different elements of a component, multiple components of a product, or an environment comprising multiple products.

AIM-based design framework
This study does not use affordances directly as a purposeful action support analysis tool but combines perception with affordances as a conceptual tool providing an ecological perspective (as shown in Figure 7).The AIM aims to provide designers with a hierarchically organized nested affordance system to address the nesting issue of affordance perceptual information supported by the system.
An important distinction from traditional design matrices is that AIM captures only harmful relationships.Traditional design structure matrices aim to ensure the visibility of expected behaviors, reinforcing a certain behavior for the user, but this does not eliminate the possibility of other behaviors and may even lead to complex decoupling.AIM focuses on removing redundant elements within the product rather than increasing positive perceptual information of the behavior.This can avoid conflicting elements that may arise when reinforcing affordance perceptual information with unintentional actions, reducing complex decoupling and design difficulties within the product.
Therefore, the AIM matrix evaluation method reserves exploration space for users by "subtracting" and only judging conflicts to eliminate elements unrelated or conflicting with the target action.This reduces the difficulty of information acquisition, making specific affordance information easier for users to explore and discover.This reverse design method helps create coupling between user behavior and the product, mobilizes the user's subjective initiative, and achieves more efficient information pick-up.This also explains why affordance design is often associated with "minimalist design."The "absence" brought about by this "simplified" design approach is precisely the "need" for users' direct perceptual exploration.

Case study
Based on the Affordance Interaction Matrix (AIM), a connection is established between user behavior and accessible kitchen furniture components, leading to specific product component optimization design proposals.

AIM method steps
This study chooses accessible kitchen furniture as a simple example, using AIM to redesign the product.The steps of AIM optimization and redesign are summarized as follows: (1) Requirement analysis and target affordance identification: Analyze user requirements, identify product components and functions, and determine target affordances.For numbered lists.
(2) AHP determines the weights for target affordance: Based on the actual situation, determine the hierarchy structure, conduct corresponding pairwise comparisons, and calculate the weights.
(3) Construct the AIM matrix: Identify the relationship and potential conflicts between product components and target affordances.For numbered lists (4) Expert review: Confirm the nested relationship of affordances and conflicts with components.
(5) Optimize affordance perceptual information: Ensure harmonious coexistence between affordances and components and avoid interaction conflicts.
(6) Redesign and prototype development: Develop preliminary prototypes based on optimized information and conduct evaluations and user tests.
(7) Iterative optimization and final evaluation: Iteratively optimize the product according to the evaluation results to meet accessibility requirements and practicality.

Obtaining target affordances and product components
Based on user requirements, including factors such as different ages, physical conditions, and usage scenarios, target affordances are determined.At the same time, existing kitchen furniture is broken down to identify various product components and functions.In Maier's ASM, requirements are translated into different types of function (Maier et al., 2007).In this study, requirements are converted into different actions (behavioral functions), focusing on how users utilize subconscious perception of behavioral functions (affordances) within the product rather than the initially intended functions in the design.
Taking accessible cabinets as an example, 12 participants each from independent elderly, walker-assisted elderly, and wheelchair-bound elderly were invited, totaling 36 participants aged between 60-80.Participants need to have a certain level of education and logical thinking ability, as well as at least 10 years of kitchen usage experience.First, the design team identifies users' primary needs in the kitchen through observation.Then, target actions are determined through questionnaires and focus interviews.To avoid ambiguous results due to abstract requirement descriptions, each requirement in the questionnaire is converted into a specific action.For example, cabinet questions include the following: What is the correct operating procedure to open upper cabinets?The available answers are: push, pull, turn, press, grab, and release (S.W. Hsiao et al., 2012).
Through group discussions of industrial designers and product design professionals and students, 14 target affordances that accessible kitchen furniture should provide were determined from 121 valid questionnaires, Refer to Table 1 below for more information.Components are broken down according to washing and preparation, cooking, and storage areas, obtaining product component information (as shown in Figure 8).

AHP determines the weights of user actions
Utilizing the AHP method to construct the AIM matrix, determine the weights of user goal affordance (behavior).
Step 1: Establish a hierarchical structure diagram.By filtering, decomposing, and combining user requirements collected through questionnaire surveys, focus group interviews, and other methods, a hierarchical structure diagram is established (as shown in Table 2).The first layer represents the overall user goals, the second layer breaks down the overall user goals into three categories found in wall cabinet areas, countertops, and lower cabinet areas, and the third layer represents the specific user goal actions for each category.
Step 2: Construct the judgment matrix.Using the elements in the previous layer as the comparison basis, a pairwise comparison of elements is performed based on the nine importance levels and their values suggested by Saaty (Saaty, 2004).The ratio Bij is determined by the importance of element i compared to element j, with nine typical values being 1/9, 1/7, 1/5, 1/3, 1, 3, 5, 7, 9, and their reciprocals.The comparison results form the judgment matrix A=(a ij ) n×n , where a ji = 1/s ij .The characteristic equation corresponding to judgment matrix A is: Step 3: Solve for the eigenvector and perform consistency testing.Solve for the maximum eigenvalueλand corresponding eigenvector W, then normalize as weights.This result requires consistency testing, which can be determined by calculating CR: In formula (2): CRis the consistency ratio; CI is the consistency index; I is the average random consistency index.In formula (3): λ is the maximum eigenvalue of the characteristic equation; nis the order of judgment matrix A.
Using the mathematical software MATLAB to obtain the eigenvector and normalize it, the final calculation result is W = [0.320,0.557, 0.123], λ = 3.018, RI = 0.580, CI ¼ 0:009, CR ¼ 0:018 < 0:1.This indicates that the judgment matrix passes the consistency test, and the result has a high degree of reliability.Similarly, the weights of the third-layer target actions can be calculated, and the results are included in the AIM matrix.The comprehensive results are shown in Figure 7.

Constructing the AIM
Based on the information obtained from Section 5.2, a matrix based on affordances and product components is constructed (as shown in Figure 9).To determine the nested relationship between target affordances and potential interaction conflicts between product features and user actions, the process of constructing the Affordance Interaction Matrix is as follows: (1) Inputting target ffordances: Similar to the Quality Function Deployment (QFD) method (Hauser J.R. & Clausing, 2008), we first list the affordances that the product should provide on the left wall of the matrix.When inputting, we add the weight results of AHP to ensure that the user's highest priority needs can be gradually met during subsequent modifications of product features.This helps to present affordance perception information in a clear and hierarchical manner.The left-side structure of the matrix is used to capture the nested relationships between target affordances.
(2) Input primary components of user-product interaction: At the top of the matrix, we input the main components with which users interact with the product and divide them into three areas according to kitchen functions: storage area (A), cleaning and preparation area (B), and cooking area (C).The top of the matrix represents the component relationship matrix, describing the relationship between product components.When modifying a component, it may affect other related components.For example, modifying the hanging cabinet body may affect the design of the lift basket.

Matrix interaction assessment
Consult experts in relevant fields to confirm the nested relationship between affordances and conflict relationships with components.

Perception conflict assessment
For each alternative component, analyze its potential negative impact on the realization of target affordances one by one.Negative impact assessment is divided into two aspects: first, perception -judging whether the product attributes hinder the intuitive cognition of an affordance, thereby increasing the burden of information acquisition; second, physical-judging whether the objective physical structure of the product conflicts with the realization of affordances.In the case study (as shown in Figure 4), we identified 17 perceptual interaction conflicts and 12 physical interaction conflicts among the 12 target affordances.
It is worth noting that since the perception of affordances may vary among designers, different designers may produce different AIMs.To ensure the accuracy of the matrix, it is recommended to submit it to experts with different backgrounds for review.These experts can examine the interactions in the AIM and reach consensus on the accuracy of most captured interaction conflicts.

Nested affordance relationship evaluation
To determine whether there is a link between target affordances, we need to judge whether modifying one target action will affect another action.This involves assessing the impact of product feature adjustments on the user action sequence.For example, in the process of pulling down a basket, the subsequent action is to pick up the item, and the previous action may affect the following action.Similarly, each expert can examine the links in the AIM and reach consensus on the accuracy of most captured nested relationships.

Using the AIM for redesign
Through comprehensive analysis, we find that this matrix is driven by room data, using floor data to select components that need improvement, and determining affordance optimization goals through right-wall data.According to the matrix evaluation results, we can identify the number of product conflicts and recognize the product appearance features that need optimization.
Next, based on the matrix analysis and expert review results, we reorganize and optimize the affordance nesting and perceptual information to ensure harmonious coexistence between various affordances and components and avoid potential interaction conflicts.Iterate and modify the problematic interaction relationships until satisfactory results are obtained.
Based on the optimized affordance perceptual information, redesign the product components.In the process of redesigning product components, multiple design aspects need to be considered for effective information transmission, such as using sensory elements such as touch, color, size, shape, position, material, texture, gloss, sound, temperature, and weight.Figure 10 shows the final design effect of the improved solutions for 10 product components, and the specific improvement effects are shown in Figure 11.

Discussion
This paper proposes a nested affordance-based design tool aimed at supporting the overall design of target actions through systematic information.We analyzed the impact of nested affordances on product design and proposed the Affordance Interaction Matrix.This matrix can simplify the complex affordance information within the product, helping designers to more clearly identify the causes of triggering unconscious user behavior, optimize product appearance features, and achieve a reasonable arrangement of perceptual information within the product.This tool has significant advantages in design detection and solution comparison at the conceptual design stage, helping designers to clarify intuitive interaction design basis and make quick and generally effective decisions.
However, although AIM provides some suggested steps in product system design, due to the inherent phenomenological characteristics of affordances, it still relies on the designer's abilities, experience, and aesthetic preferences to shape the product.This method carries the risk of exaggerating the subjective judgment of designers.
To address this issue, future work will explore quantitative design evaluation criteria in the fields of ergonomics, HCI, and cognitive science.We plan to combine experimental research to quantify matrix judgment and impact levels to determine the standards of physical dimensions, shapes, colors, etc., that affect human intuitive perception, thus providing a clearer basis for adjusting product features.

Conclusions
This paper introduces a nested affordance-based design method, providing designers with a reasoning framework that helps them systematically shape products that are naturally coherent, concise, and clearly perceptible through rational choices.Although we provided practical design examples, due to space constraints, we could not demonstrate the affordance evaluation results before and after modification.In future research, as an extension of this study, we plan to conduct validation experiments to compare the evaluation results before and after improvement, assessing whether the design helps to complete interactive tasks more efficiently and effortlessly.
This method aims to serve as the foundation for more advanced methods that may be developed in the future.The focus is on utilizing the unique attributes of affordances to develop new methods and embracing nested affordances as a conceptual tool.This provides a reasoning framework and general principles for achieving the overall design of target systems, applicable to the development of general-purpose human behavior technologies, and serving as an extension of the "direct perception" research agenda.Through quantitative research, we hope to provide new insights into the direct perception mechanisms, standards, and conditions of product interactions, and reveal through reverse reasoning how animals interact with their natural environment and how possibilities for supporting human behavior can be realized.This will help us gain a deeper understanding of the fundamental principles of intuitive interaction design, thereby optimizing the human-computer interaction experience.

Figure
Figure 1.Nested affordance and perceptual mediation.

Figure 3 .
Figure 3. Two kinds of calculator.Which affords a stronger pressing?

Figure 5
Figure 5. Optimization of nested affordance perceptual information in products.

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Figure 7. Design framework based on nested affordance.

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Figure 8. Preliminary design plan of accessible kitchen furniture.

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Figure 9. Affordance interaction matrix of accessible kitchen furniture.

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Figure 10.Improved accessible kitchen furniture design solutions.