# Packaging Design Method of Modern Cultural and Creative Products Based on Rough Set Theory

Authors: XiaoTing Xu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Nowadays, the popularity of cultural and creative industry in China is rising, and cultural and creative products are loved by young people with high cultural added value. Through the field investigation, it is found that the tie-dyeing products in the market are still facing the problems of insufficient market awareness, the same tie-dyeing products, serious homogenization, and the aging of inheritors. Therefore, after the questionnaire survey, based on the needs of the audience, we proposed a packaging design method for modern cultural and creative products based on a rough set. As one of the mathematical tools to deal with uncertain knowledge, a rough set theory can solve the uncertainty caused by knowledge granularity in cognitive diagnosis. Without prior knowledge, we can get the corresponding decision-making or classification rules of the specific problem and classify the research objects. This study aimed to apply a rough set theory to the packaging design of modern cultural and creative products and overcome some problems existing in the packaging design methods of cultural and creative products. Since the application of rough set in the packaging design of cultural and creative products is a new topic, whether it is effective in the packaging design of cultural and creative products, how effective it is, and what problems it can deal with in the whole procedure of the design are worth discussing.


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## Body

## 1. Introduction

With the development of social economy, people’s consumption patterns are constantly changing, and product design has changed from functionalism to emotionalism. Consumers pay more and more attention to the closeness of their emotional relationship when purchasing goods. Perceptual engineering is a technology that systematically excavates people’s perception of products and transforms them into design elements, which can transform fuzzy perceptual needs and images into morphological elements of detail design. Based on the theoretical framework and principles of perceptual engineering, this study will apply a rough set theory to establish the relationship between modeling design elements and perceptual images, which is very important for product creation. Type design has important guiding significance [1–3].In 1998, the British government first proposed that “enterprises that obtain development power from personal creativity, skills, and talents, as well as activities that can create potential wealth and employment opportunities with the development of intellectual property rights, can be called creative economy.” Therefore, the concept of creative economy was formally put forward. In today’s economic globalization, the creative industry has gradually become a pillar industry in various countries, and cultural export has become the top priority. The industrial model supported by cultural creativity has become a fast-growing industry, and this new model has become a new engine of cultural and economic development in Europe, the United States, and other developed countries [4–6]. Our country’s economy is in a critical period of transformation and upgrading. The development of the industrial model with creativity as the support can not only adjust the industrial structure and promote industrial upgrading but also promote “made in China” to “created in China,” so that Chinese history and culture can be spread all over the world through cultural derivatives. Whether the creative economy becomes the key factor of economic growth is an important condition to judge whether a country enters the creative economy. Although the cultural and creative economy industry in our country has grown rapidly over the years, there is still a long distance from developed countries, which shows that there is still a huge room for progress. Nowadays, the economic development of the world has entered the new normal. Economic growth can no longer rely on the investment of material factors, but more needs the promotion of human capital and technology [7–10]. The development of creative economy can not only promote industrial innovation and industrial upgrading but also liberate the social innovation potential to a greater extent. Promoting the development of cultural soft power has always been one of the important strategies for our country to accelerate the construction of a cultural power. Under the background of the rapid development of creative economy, museums, as an important gathering place of cultural resources, should make use of their own advantages to integrate with the economic cultural industry to find a new direction for the development of modern culture and the design and development mode of cultural and creative products [11,12].With the development of economy, people pay more and more attention to their spiritual satisfaction. The analysis and development of the industries in culture and creativity are not mature enough, and there are many problems in all links. Although the museum has rich collection resources, it still cannot get rid of the shortcomings of the same content and old form of cultural and creative products designed and produced, resulting in the development pace that cannot keep up with the diversified needs of consumers, but with the support of the government to develop the “Internet plus” policy, the combination of cultural and creative industries and new technologies will bring more possibilities and innovations to the design form and development mode of the products [13–15]. For the target consumer groups, the development of cultural and creative products based on cultural relics in the collection can drive people’s enthusiasm for traditional culture and better promote the consumption of cultural products; on the other hand, for museums, the innovative R&D and sales of cultural and creative products can greatly increase the income of museums, maintain their own sustainable development, and promote traditional culture in a more people-friendly way, to form a virtuous circle. Through the use of cultural and creative products, people imperceptibly feel the charm of traditional culture, which is not only conducive to the improvement of national quality but also further promotes the improvement of national cultural soft power. Taking the Beijing Palace Museum as the research object, this study will deeply study how the traditional cultural and creative industry such as museum cultural and creative industry revitalizes under the influence of the Internet, changes the development mode, increases the design expression form, improves the user experience, and finally promotes the sustainable development of cultural and creative industry. Because the research in this field began earlier in foreign countries, the research results will be more mature than in China. However, due to the different forms at home and abroad, foreign research guidance cannot be mechanically applied to the development of China’s cultural and creative industry [16–18].


## 2. Related Work

### 2.1. Concept, Characteristics, and Classification of Cultural and Creative Products

Cultural and creative products are creative activities in which designers reinterpret and refine culture with wisdom and integrate the extracted cultural symbols with designers’ creativity to obtain new products, so that they have both traditional cultural characteristics and modern aesthetic characteristics. Through the interpretation of cultural and creative products, we can find the characteristics. The most important characteristic of the products’ design in cultural and creative is its cultural and artistic characteristics. It can fully display its local culture, including regional and national characteristics. From a commercial point of view, as a product, consumers value the characteristics of practicality, economy, and commemoration. These characteristics of cultural and creative products can be seen that the transformation of modern people’s consumption concept and aesthetics drives the transformation of new product styles [19–23].Cultural and creative products can be divided into the following categories in terms of design discipline types. It includes design products in various professional directions, such as packaging design, industrial design, visual design, film and television production, advertising design, original animation design, and original games, and cultural and creative products can be developed through the combination of design and culture [24].


### 2.2. An Overview of Rough Set Theory

With the popularization and development of science and technology, people have more and more ways to obtain information and accumulate a large amount of data. When people’s ability to obtain valuable information from these data is limited, a situation of “data surplus” will be formed. How can we get useful knowledge and analysis of the data efficiently is still an urgent task, so knowledge discovery technology was born in this situation. In the application of knowledge discovery technology, people find that many data have uncertainty. There are some existing methods, such as evidence theory, fuzzy theory, and probability statistics, which were used to deal with the tasks with uncertainty. When using these methods to deal with uncertain problems, it is necessary to provide a priori information, such as fuzzy membership function and probability distribution, which is often not easy to obtain, but it is not necessary to provide this information when using a rough set theory to analyze data. As a mathematical tool, the rough set can be used in many different situations such as problem with fuzzy and uncertain knowledge proposed by Polish scholar Pawlak Z. Its main idea is to derive the decision-making or classification rules of problems through knowledge reduction in the premise of maintaining the classification ability. This method uses known information or knowledge to approximately describe imprecise or uncertain concepts, or to deal with uncertain phenomena and problems according to the observed and measured results. It can simplify data and obtain the minimum expression of knowledge on the premise of retaining key information, identify and evaluate the dependence between data, reveal the pattern with simple concept, and obtain easily verifiable rule knowledge from empirical data. A rough set theory has been widely concerned by many scholars because it is a very effective method to deal with uncertain problems. This method can form good complementarity with evidence theory, fuzzy theory, and probability statistics. Here are some concepts in a rough set theory.


#### 2.2.1. Knowledge and Classification

In information system, knowledge can be used to describe the characteristics of things in the real and abstract world, which belongs to the category of epistemology. Using knowledge to describe things differently can classify things.LetU≠∅ be a finite set of objects of interest, which is called universe. Any subset X⊆U is called a concept or category in U. For the sake of normalization, we believe that empty set is also a concept. Any concept family in U is called abstract knowledge about U, which is called knowledge for short. The rough set is mainly interested in that knowledge that can form division on U.Definition 1.
ℓ=X1,…,Xn;Xi⊆U,Xj≠∅,Xi∩Xj=∅,fori≠j,i,j=1,2,…,n,∪i=1nXi=U, so ℓ defines a partition.Theorem 1.
A partition of setU determines an equivalent relationship between the elements of U.It can be seen from the above that knowledge is related to division, and division is related to equivalence relationship. Next, we will further introduce the relationship, the definition of equivalence relationship, and how division corresponds to equivalence relationship.Definition 2.
The set of any order pair determines a binary relationshipR. Any order pair x,y in R can be recorded as x,y∈R or xRy. Any order pair x,y not in R can be recorded as x,y∉R.Definition 3.
LetR be a binary relation defined on set U. If there is xRx for x∈U, then the binary relation R is reflexive.Definition 4.
LetR be a binary relation defined on set U. If for each x,y⊂U, there is yRx whenever xRy, then the relation R on set U is said to be symmetric.Definition 5.
LetR be a binary relation defined on the set U. If for each x,y,z∈U, there is xRz whenever xRy,yRz, then the relation R is transitive on U.Definition 6.
LetR be a relation defined on set U. If R is reflexive, symmetric, and transitive, R is called an equivalence relation.Definition 7.
LetR be the equivalence relation on set U, denoted by xR=y|y∈U,xRy, which is called the R equivalent class formed by element x.Definition 8.
For the equivalence relationR on set U, its equivalence class set xR|x∈U is called the quotient set of U on R and is recorded as U/R.Theorem 1.
The equivalence relationR on set u determines a partition of u, which is the quotient set U/R. From the above definition theorem, if R is an equivalence relation on u, U/R represents the set composed of all equivalence classes of R, and xR represents the R equivalent class containing the element x∈U.A knowledge base is a relational systemK=U,ℛ, where U is a nonempty finite set, called a universe, and ℛ is a family of equivalent relations on U.If∅≠P⊆ℛ, then ∩P (the intersection of all equivalence relations in P) is also an equivalence relation, which is called the indiscernibility relation on P, which is recorded as indP and has xindP=∩R∈PXR. In this way, U/indP represents the knowledge related to the equivalence relation family P, which is called the P basic knowledge about U in K, and the equivalence class of ind (P) is called the basic concept or basic category of knowledge P. U/indP is replaced by U/R below. In fact, the basic category of P is the basic characteristic of the domain of knowledge P, that is, the basic module of knowledge.


#### 2.2.2. Imprecise Category, Approximation, and Rough Set

Definition 9.
Let⊆U, R be an equivalent relation on U. When X can be expressed as the union of some basic categories of R, X is said to be r definable; otherwise, X is called R, which is not definable. R definable set is also called R exact set, and R undefined set is also called R imprecise set or R rough set.
Rough sets can be defined approximately. We use two exact sets, namely upper approximation and lower approximation of rough sets.Definition 10.
Given the knowledge baseK=U,ℛ, for each subset X⊆U and an equivalence relation R∈indK, two subsets are defined as follows: R¯X=∪Y∈U/R|Y⊆X and R¯X=∪Y∈U/R|Y∩X+∅ are R lower approximation set and R upper approximation set of X, respectively. BNRX−R¯X−R¯X is set, which is called the R boundary domain of X.
POSRX=R¯X is called the R positive field of X; NEGRX=U−R¯X is called the R negative field of X.


#### 2.2.3. Knowledge Reduction

For a rough set, knowledge is represented as an information tableS=U,A,V,f. The information table is an information system, that is, knowledge base K=U,R. The knowledge base contains a large amount of information, usually the original records of many instances in fact; when building a knowledge base with original instance records, due to certain subjectivity in the selection of object attributes (knowledge), each attribute is obviously not equally important in the knowledge base, and some may be redundant. On the basis of ensuring the stability of information table classification ability, we call the removal of unimportant redundant attributes as knowledge reduction.Before discussing knowledge reduction, the following definitions are made.Definition 11.
LetK=U,ℛ be a knowledge base, where ℛ is a family of equivalence relations. If R∈ℛ, if indℛ=indℛ−R, the relationship ℛ is called unnecessary (redundant) in ℛ; otherwise, ℛ is called necessary in ℛ.
If the unnecessary relationℛ is removed from the knowledge base, the classification ability of the knowledge base will not be changed, because the indistinguishable relation indℛ in the knowledge base K=U,ℛ will not be changed after removal: on the contrary, if a necessary attribute is removed from the knowledge base, the classification ability of the knowledge base will be changed; that is, the indistinguishable relation in the knowledge base will be changed.


#### 2.2.4. Relative Knowledge Reduction

In the general process of knowledge reduction, the goal is to remove that redundant knowledge in the studied system. In this process, only one classification is considered; that is, only the relationship familyℛ is used as the classification. However, in practical application, it is often necessary to consider the classification ability of one classification (knowledge a) in the knowledge base relative to another classification (knowledge b); that is, in terms of knowledge b, which knowledge in knowledge a is redundant, the process of removing redundant knowledge relative to knowledge b in knowledge a is called relative reduction.


### 2.3. Product Image Modeling Design

It is a method to develop conceptual design based on the principle of human cognitive visual perception, taking modeling factors as the object and quantifying irrational perceptual images. Because the elimination of product color factors is helpful to the cognitive research of modeling image, the color attribute is not considered in the research.


## 2.1. Concept, Characteristics, and Classification of Cultural and Creative Products

Cultural and creative products are creative activities in which designers reinterpret and refine culture with wisdom and integrate the extracted cultural symbols with designers’ creativity to obtain new products, so that they have both traditional cultural characteristics and modern aesthetic characteristics. Through the interpretation of cultural and creative products, we can find the characteristics. The most important characteristic of the products’ design in cultural and creative is its cultural and artistic characteristics. It can fully display its local culture, including regional and national characteristics. From a commercial point of view, as a product, consumers value the characteristics of practicality, economy, and commemoration. These characteristics of cultural and creative products can be seen that the transformation of modern people’s consumption concept and aesthetics drives the transformation of new product styles [19–23].Cultural and creative products can be divided into the following categories in terms of design discipline types. It includes design products in various professional directions, such as packaging design, industrial design, visual design, film and television production, advertising design, original animation design, and original games, and cultural and creative products can be developed through the combination of design and culture [24].


## 2.2. An Overview of Rough Set Theory

With the popularization and development of science and technology, people have more and more ways to obtain information and accumulate a large amount of data. When people’s ability to obtain valuable information from these data is limited, a situation of “data surplus” will be formed. How can we get useful knowledge and analysis of the data efficiently is still an urgent task, so knowledge discovery technology was born in this situation. In the application of knowledge discovery technology, people find that many data have uncertainty. There are some existing methods, such as evidence theory, fuzzy theory, and probability statistics, which were used to deal with the tasks with uncertainty. When using these methods to deal with uncertain problems, it is necessary to provide a priori information, such as fuzzy membership function and probability distribution, which is often not easy to obtain, but it is not necessary to provide this information when using a rough set theory to analyze data. As a mathematical tool, the rough set can be used in many different situations such as problem with fuzzy and uncertain knowledge proposed by Polish scholar Pawlak Z. Its main idea is to derive the decision-making or classification rules of problems through knowledge reduction in the premise of maintaining the classification ability. This method uses known information or knowledge to approximately describe imprecise or uncertain concepts, or to deal with uncertain phenomena and problems according to the observed and measured results. It can simplify data and obtain the minimum expression of knowledge on the premise of retaining key information, identify and evaluate the dependence between data, reveal the pattern with simple concept, and obtain easily verifiable rule knowledge from empirical data. A rough set theory has been widely concerned by many scholars because it is a very effective method to deal with uncertain problems. This method can form good complementarity with evidence theory, fuzzy theory, and probability statistics. Here are some concepts in a rough set theory.


### 2.2.1. Knowledge and Classification

In information system, knowledge can be used to describe the characteristics of things in the real and abstract world, which belongs to the category of epistemology. Using knowledge to describe things differently can classify things.LetU≠∅ be a finite set of objects of interest, which is called universe. Any subset X⊆U is called a concept or category in U. For the sake of normalization, we believe that empty set is also a concept. Any concept family in U is called abstract knowledge about U, which is called knowledge for short. The rough set is mainly interested in that knowledge that can form division on U.Definition 1.
ℓ=X1,…,Xn;Xi⊆U,Xj≠∅,Xi∩Xj=∅,fori≠j,i,j=1,2,…,n,∪i=1nXi=U, so ℓ defines a partition.Theorem 1.
A partition of setU determines an equivalent relationship between the elements of U.It can be seen from the above that knowledge is related to division, and division is related to equivalence relationship. Next, we will further introduce the relationship, the definition of equivalence relationship, and how division corresponds to equivalence relationship.Definition 2.
The set of any order pair determines a binary relationshipR. Any order pair x,y in R can be recorded as x,y∈R or xRy. Any order pair x,y not in R can be recorded as x,y∉R.Definition 3.
LetR be a binary relation defined on set U. If there is xRx for x∈U, then the binary relation R is reflexive.Definition 4.
LetR be a binary relation defined on set U. If for each x,y⊂U, there is yRx whenever xRy, then the relation R on set U is said to be symmetric.Definition 5.
LetR be a binary relation defined on the set U. If for each x,y,z∈U, there is xRz whenever xRy,yRz, then the relation R is transitive on U.Definition 6.
LetR be a relation defined on set U. If R is reflexive, symmetric, and transitive, R is called an equivalence relation.Definition 7.
LetR be the equivalence relation on set U, denoted by xR=y|y∈U,xRy, which is called the R equivalent class formed by element x.Definition 8.
For the equivalence relationR on set U, its equivalence class set xR|x∈U is called the quotient set of U on R and is recorded as U/R.Theorem 1.
The equivalence relationR on set u determines a partition of u, which is the quotient set U/R. From the above definition theorem, if R is an equivalence relation on u, U/R represents the set composed of all equivalence classes of R, and xR represents the R equivalent class containing the element x∈U.A knowledge base is a relational systemK=U,ℛ, where U is a nonempty finite set, called a universe, and ℛ is a family of equivalent relations on U.If∅≠P⊆ℛ, then ∩P (the intersection of all equivalence relations in P) is also an equivalence relation, which is called the indiscernibility relation on P, which is recorded as indP and has xindP=∩R∈PXR. In this way, U/indP represents the knowledge related to the equivalence relation family P, which is called the P basic knowledge about U in K, and the equivalence class of ind (P) is called the basic concept or basic category of knowledge P. U/indP is replaced by U/R below. In fact, the basic category of P is the basic characteristic of the domain of knowledge P, that is, the basic module of knowledge.


### 2.2.2. Imprecise Category, Approximation, and Rough Set

Definition 9.
Let⊆U, R be an equivalent relation on U. When X can be expressed as the union of some basic categories of R, X is said to be r definable; otherwise, X is called R, which is not definable. R definable set is also called R exact set, and R undefined set is also called R imprecise set or R rough set.
Rough sets can be defined approximately. We use two exact sets, namely upper approximation and lower approximation of rough sets.Definition 10.
Given the knowledge baseK=U,ℛ, for each subset X⊆U and an equivalence relation R∈indK, two subsets are defined as follows: R¯X=∪Y∈U/R|Y⊆X and R¯X=∪Y∈U/R|Y∩X+∅ are R lower approximation set and R upper approximation set of X, respectively. BNRX−R¯X−R¯X is set, which is called the R boundary domain of X.
POSRX=R¯X is called the R positive field of X; NEGRX=U−R¯X is called the R negative field of X.


### 2.2.3. Knowledge Reduction

For a rough set, knowledge is represented as an information tableS=U,A,V,f. The information table is an information system, that is, knowledge base K=U,R. The knowledge base contains a large amount of information, usually the original records of many instances in fact; when building a knowledge base with original instance records, due to certain subjectivity in the selection of object attributes (knowledge), each attribute is obviously not equally important in the knowledge base, and some may be redundant. On the basis of ensuring the stability of information table classification ability, we call the removal of unimportant redundant attributes as knowledge reduction.Before discussing knowledge reduction, the following definitions are made.Definition 11.
LetK=U,ℛ be a knowledge base, where ℛ is a family of equivalence relations. If R∈ℛ, if indℛ=indℛ−R, the relationship ℛ is called unnecessary (redundant) in ℛ; otherwise, ℛ is called necessary in ℛ.
If the unnecessary relationℛ is removed from the knowledge base, the classification ability of the knowledge base will not be changed, because the indistinguishable relation indℛ in the knowledge base K=U,ℛ will not be changed after removal: on the contrary, if a necessary attribute is removed from the knowledge base, the classification ability of the knowledge base will be changed; that is, the indistinguishable relation in the knowledge base will be changed.


### 2.2.4. Relative Knowledge Reduction

In the general process of knowledge reduction, the goal is to remove that redundant knowledge in the studied system. In this process, only one classification is considered; that is, only the relationship familyℛ is used as the classification. However, in practical application, it is often necessary to consider the classification ability of one classification (knowledge a) in the knowledge base relative to another classification (knowledge b); that is, in terms of knowledge b, which knowledge in knowledge a is redundant, the process of removing redundant knowledge relative to knowledge b in knowledge a is called relative reduction.


## 2.2.1. Knowledge and Classification

In information system, knowledge can be used to describe the characteristics of things in the real and abstract world, which belongs to the category of epistemology. Using knowledge to describe things differently can classify things.LetU≠∅ be a finite set of objects of interest, which is called universe. Any subset X⊆U is called a concept or category in U. For the sake of normalization, we believe that empty set is also a concept. Any concept family in U is called abstract knowledge about U, which is called knowledge for short. The rough set is mainly interested in that knowledge that can form division on U.Definition 1.
ℓ=X1,…,Xn;Xi⊆U,Xj≠∅,Xi∩Xj=∅,fori≠j,i,j=1,2,…,n,∪i=1nXi=U, so ℓ defines a partition.Theorem 1.
A partition of setU determines an equivalent relationship between the elements of U.It can be seen from the above that knowledge is related to division, and division is related to equivalence relationship. Next, we will further introduce the relationship, the definition of equivalence relationship, and how division corresponds to equivalence relationship.Definition 2.
The set of any order pair determines a binary relationshipR. Any order pair x,y in R can be recorded as x,y∈R or xRy. Any order pair x,y not in R can be recorded as x,y∉R.Definition 3.
LetR be a binary relation defined on set U. If there is xRx for x∈U, then the binary relation R is reflexive.Definition 4.
LetR be a binary relation defined on set U. If for each x,y⊂U, there is yRx whenever xRy, then the relation R on set U is said to be symmetric.Definition 5.
LetR be a binary relation defined on the set U. If for each x,y,z∈U, there is xRz whenever xRy,yRz, then the relation R is transitive on U.Definition 6.
LetR be a relation defined on set U. If R is reflexive, symmetric, and transitive, R is called an equivalence relation.Definition 7.
LetR be the equivalence relation on set U, denoted by xR=y|y∈U,xRy, which is called the R equivalent class formed by element x.Definition 8.
For the equivalence relationR on set U, its equivalence class set xR|x∈U is called the quotient set of U on R and is recorded as U/R.Theorem 1.
The equivalence relationR on set u determines a partition of u, which is the quotient set U/R. From the above definition theorem, if R is an equivalence relation on u, U/R represents the set composed of all equivalence classes of R, and xR represents the R equivalent class containing the element x∈U.A knowledge base is a relational systemK=U,ℛ, where U is a nonempty finite set, called a universe, and ℛ is a family of equivalent relations on U.If∅≠P⊆ℛ, then ∩P (the intersection of all equivalence relations in P) is also an equivalence relation, which is called the indiscernibility relation on P, which is recorded as indP and has xindP=∩R∈PXR. In this way, U/indP represents the knowledge related to the equivalence relation family P, which is called the P basic knowledge about U in K, and the equivalence class of ind (P) is called the basic concept or basic category of knowledge P. U/indP is replaced by U/R below. In fact, the basic category of P is the basic characteristic of the domain of knowledge P, that is, the basic module of knowledge.


## 2.2.2. Imprecise Category, Approximation, and Rough Set

Definition 9.
Let⊆U, R be an equivalent relation on U. When X can be expressed as the union of some basic categories of R, X is said to be r definable; otherwise, X is called R, which is not definable. R definable set is also called R exact set, and R undefined set is also called R imprecise set or R rough set.
Rough sets can be defined approximately. We use two exact sets, namely upper approximation and lower approximation of rough sets.Definition 10.
Given the knowledge baseK=U,ℛ, for each subset X⊆U and an equivalence relation R∈indK, two subsets are defined as follows: R¯X=∪Y∈U/R|Y⊆X and R¯X=∪Y∈U/R|Y∩X+∅ are R lower approximation set and R upper approximation set of X, respectively. BNRX−R¯X−R¯X is set, which is called the R boundary domain of X.
POSRX=R¯X is called the R positive field of X; NEGRX=U−R¯X is called the R negative field of X.


## 2.2.3. Knowledge Reduction

For a rough set, knowledge is represented as an information tableS=U,A,V,f. The information table is an information system, that is, knowledge base K=U,R. The knowledge base contains a large amount of information, usually the original records of many instances in fact; when building a knowledge base with original instance records, due to certain subjectivity in the selection of object attributes (knowledge), each attribute is obviously not equally important in the knowledge base, and some may be redundant. On the basis of ensuring the stability of information table classification ability, we call the removal of unimportant redundant attributes as knowledge reduction.Before discussing knowledge reduction, the following definitions are made.Definition 11.
LetK=U,ℛ be a knowledge base, where ℛ is a family of equivalence relations. If R∈ℛ, if indℛ=indℛ−R, the relationship ℛ is called unnecessary (redundant) in ℛ; otherwise, ℛ is called necessary in ℛ.
If the unnecessary relationℛ is removed from the knowledge base, the classification ability of the knowledge base will not be changed, because the indistinguishable relation indℛ in the knowledge base K=U,ℛ will not be changed after removal: on the contrary, if a necessary attribute is removed from the knowledge base, the classification ability of the knowledge base will be changed; that is, the indistinguishable relation in the knowledge base will be changed.


## 2.2.4. Relative Knowledge Reduction

In the general process of knowledge reduction, the goal is to remove that redundant knowledge in the studied system. In this process, only one classification is considered; that is, only the relationship familyℛ is used as the classification. However, in practical application, it is often necessary to consider the classification ability of one classification (knowledge a) in the knowledge base relative to another classification (knowledge b); that is, in terms of knowledge b, which knowledge in knowledge a is redundant, the process of removing redundant knowledge relative to knowledge b in knowledge a is called relative reduction.


## 2.3. Product Image Modeling Design

It is a method to develop conceptual design based on the principle of human cognitive visual perception, taking modeling factors as the object and quantifying irrational perceptual images. Because the elimination of product color factors is helpful to the cognitive research of modeling image, the color attribute is not considered in the research.


## 3. Packaging Design Method Based on the Rough Set for Modern Cultural and Creative Products

### 3.1. Construction of Knowledge Expression System

We can use the relational table to represent the knowledge expression system. The rows of the relational table correspond to the object to be studied, and the columns correspond to the attributes of the object. The information of the object is expressed by specifying various attribute values of the object. A decision table can be defined as follows: letS=U,A,V,f be a knowledge expression system; A=C∪D, C∩D=φ, and C is called conditional attribute set; D is called decision attribute set, and the knowledge expression system with conditional attributes and decision attributes is called decision table.


#### 3.1.1. Condition Properties

Glasses are generally composed of more than 10 components such as frame, lens, and nose bridge. By means of morphological analysis, the shape of glasses is divided into five main design items, namely frame style, frame thickness, lens shape, nose bridge, and foot swish, and then, each design item is divided into several design elements. For example, the frame style is divided into four unexpected elements; see Table1 for the design elements of glasses. Each design item of glasses is taken as a conditional attribute.Table 1
Classification of design elements.
Design projectDesign elements1234C1: frame styleFull frameHalf frameFramelessotherC2: frame thicknessThin frameThick frameotherC3: glasses nose beamSingle beam frameDouble beam frame


#### 3.1.2. Decision Attributes

After research and analysis, the perceptual vocabulary of glasses is determined as four perceptual vocabulary gates: beautiful, fashionable, unique, and elegant. Here, only “beautiful” is taken as an example. The questionnaire was designed using a 7-order Likert scale. 50 subjects were selected for the survey. After sorting out the survey results, the perceptual evaluation matrix can be obtained, as shown in Table2.Table 2
Kansei evaluation’s matrix of glasses.
OrderC1C2C3C4Graceful112415.66211114.32………………821414.19Perceptual evaluation data are not suitable for the rough set since the data in it are continuous. Therefore, we need to discretize it in order to use the rough set theory. According to the characteristics of evaluation data distribution, the discretization method is as follows: the evaluation grade of interval [1,4.5] is 1; the evaluation grade of interval [4.5,5.5] is 2; and the rating grade of interval [5.5, 7.0] is 3, and the discretized perceptual evaluation grade is taken as the decision attribute.


#### 3.1.3. Decision Table

The pictures of 18 typical glasses are taken as the research object, the top item of modeling is taken as the condition attribute C, and the discrete perceptual evaluation level is taken as the decision attribute D. Table3 contains the information about the decision.Table 3
Decision table.
UC1C2C3C4D112413211111………………821411


### 3.2. Attribute Reduction

For attribute reduction, we need to delete the irrelevant features while maintaining the information in the data as much as possible. Definitions13 and 14 are the basic definitions used in attribute reduction of decision table.Definition 13.
Given the database, which is denoted asK=U,ℛ, for each subset X⊆U and an equivalence relationship ℛ∈indK, we have two different sets, which are as follows:(1)R−X=UY∈U/R|Y∈X,R−X=UY∈U/R|Y∩X≠φ.
Here,ℛ is the lower approximation set and ℛ is the upper approximation set of X and posRX=R_X is the positive field of X.Definition 14.
LetP and Q be a family of equivalent relations, R∈P. If posindpindQ=posindP−RindQ, R is called Q unnecessary in P. Otherwise, R is Q necessary in P, and all of the necessary primitive relations in P is called the kernel of Q and is denoted as coreQP.
In Table3, the attribute behavior in Table 3 is the attribute of the sense of importance, which is as follows:(2)U/indC1=1,2,3,4,5,6,7,9,10,13,15,17,8,12,16,18,14,11,U/indC2=2,3,6,7,8,9,10,11,13,16,17,18,1,4,5,12,15,14,U/indC3=2,3,9,5,17,1,4,7,8,10,11,14,16,18,6,12,13,15U/indC4=1,2,4,6,7,8,10,11,12,14,15,16,18,3,5,9,13,17,U/indC5=2,3,4,5,6,7,8,9,11,16,17,1,10,13,15,18,12,14,U/indD=2,5,8,14,16,18,4,7,10,11,15,17,1,3,6,9,12,13.
C=C1,C2,C3,C4,C5 is set, and then, we have the following:(3)U/indC=2,3,9,17,7,10,6,13,5,4,1,15,8,16,18,12,14.
According to Definition13, we have the following:(4)posCD=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18.
Then:(5)U/indC−C1=2,3,9,17,7,8,11,16,10,18,6,13,5,4,posC−C1D=1,2,3,4,5,6,9,12,13,14,15,17≠posCD.
According to Definition14, C1 is necessary for D in C and C4 is unnecessary for D in C. Similarly, C2,C3,C5 are necessary for D in C, so core=C1,C2,C3,C5; that is, the “beautiful” perceptual image of glasses is mainly determined by C1 (frame style), C2 (frame thickness), C3 (lens shape), and C5 (glasses legs and feet), while C4 (glasses nose bridge) is an unnecessary attribute and can be omitted.


### 3.3. Calculation of Importance of Attributes

Attributes in the knowledge base are not equally important. Attributes with high importance should be considered. See Definitions15 and 16 for the calculation of important attributes.Definition 15.
LetK=U,R be a knowledge base, and P,Q⊆R. When k=γPQ=posPQ/U, we say knowledge Q is k0≤k≤1 and depends on knowledge P, denoted as P⇒kQ.Definition 16.
SupposeS=U,A,V,f is an expression system of knowledge, A=C∪D, C∩D=φ, and the importance of attribute subset C′⊆C about D is σCDC′=γCD−γC−C′D.
According to Definition15, the dependence degree of decision set D on attribute set C is k=γCD=posCD/U=1.
Based on Definition16, the weights of attribute C1 are αCDC1=γCD−γC−C1D=1−posC−C1D/U=1−0.67=0.33. Similarly, it can be obtained that αCDC2=0.22, αCDC3=0.44, αCDC4=0, and αCDC5=0.11. Therefore, the order of importance of each design item of glasses to the “beautiful” of perceptual image is as follows: C3 (lens shape) > C1 (frame style) > C2 (frame thickness) > C5 (glasses feet) > C4 (glasses nose bridge). It can be seen that the lens shape should be considered in the image shape design of glasses.


### 3.4. The Formulation of Decision Rules

Rosetta software is used in the extraction of decision rules. This software is tabular logic data analysis software based on the rough set framework. By the rough set theory, we can execute some data analysis tasks such as data mining and knowledge discovery, can reduce attributes, generatei-then decision rules, and verify and analyze the obtained rules.18 groups of data are randomly divided into 14 groups of training data and 4 groups of prediction data. We use the genetic algorithm to reduce the attributes of 14 groups of training data, and the decision rules of the system are obtained on this basis. Because there are many rules, according to Definition6, the minimum accuracy value and coverage are set to be 0.75 and 0.05, respectively. After filtering the rules, there are 14 rules. See Table 4 for decision-making rules. These rules are applied to the classification of hot test data to obtain the systematic prediction results. This result is written into the actual data for comparison. The prediction result is shown in Figure 1. The overall accuracy of the prediction is 75%. Because only 18 groups of data are trained and tested, the accuracy is low, but with the increase in the amount of data, the prediction accuracy will be improved.Table 4
Partial glass dataset.
SampleRiNaMgAiSiKCaBaFeType11.5210113.644.491.171.780.068.7500121.5176113.983.61.3672.730.487.8300131.5161713.533.551.5472.990.397.7800141.5176613.213.691.2972.610.578.2200151.5174213.273.621.2473.080.558.0700161.5159612.793.611.6272.970.648.0700.26171.5174313.303.601.1473.090.588.1700181.5175613.153.6110.573.420.578.2400191.5191814.043.581.3772.080.568.30001…………………………………………………………Figure 1
Index of packing for transportation.


### 3.5. Construction of Evaluation Index Set of Packaging Design

Most of the data collected from the real world are not suitable for direct application to knowledge learning algorithms. The main reasons are as follows: first, the scale of original data is often very large, and there is some interference information, which is inaccurate, inconsistent, and incomplete; second, the attribute types of the original dataset are often very complex, including not only discrete attribute space but also continuous attribute space. If such a dataset is not processed and directly used in the later algorithm, the corresponding efficiency and accuracy will not be obtained. In addition, most classification algorithms can only deal with the dataset of discrete value attributes. Continuous attribute discretization belongs to a part of data preprocessing. According to different attribute value ranges, the attributes of the original dataset can be divided into three types: digital attributes (such as page number, 1, 2, 3, and 4), noun attributes (such as color, red, yellow, and blue), and continuous attributes (such as weight and distance). Both digital attributes and noun attributes belong to discrete attributes. After repeated experimental comparison, it is found that the classification results, whether accuracy or efficiency, are significantly improved by discretizing continuous attributes into discrete attributes and then learning classification.To sum up, the overall objectives of the discretization algorithm should be as follows:(1)
To generate high-quality discretization schemes to help experts understand the data more easily (the quality of discretization schemes can be measured by car criteria, which will be mentioned later).(2)
The generated discrete scheme should improve the accuracy and efficiency of the learning algorithm (for a decision tree algorithm, the efficiency is determined by the number of rules and training time).(3)
The process of discretization should be as fast as possible. Continuous attribute discretization is to convert the value space of continuous value attributes into a limited number of cells, use some different symbols or numbers to represent the divided interval, give each interval a discrete value, and use this discrete value to represent all attribute values in the small interval. Attribute discretization can be carried out artificially; that is, through the expert’s advice experience establishes a more reasonable division method. For example, when evaluating attribute scores, the results after discretization are as follows: 0–59 points are unqualified, 60–69 points are qualified, 70–79 points are medium, 80–89 points are good, and 90–100 points are excellent. It can also be discretized through machine learning, and sample learning makes the discretization results more objective and reasonable. The essence of the discretization process is to give some partition points to divide the attribute space.


#### 3.5.1. Classification of Packaging

According to the functional differences undertaken, packaging is divided into transportation packaging and sales packaging. Transportation packaging mainly meets the functional requirements of shock and mildew resistance. The analysis of its index system is shown in Figure1.It can be seen from the above that the functional requirements of transportation packaging are simple and easy to quantify, which will not be discussed in this study.Sales packaging first reflects the unity of perceptual and rational needs. Consumers will pay attention to the appearance and brand when purchasing goods, but they will pay more attention to its function and operation. The packaging design should meet various needs. While reflecting the aesthetic value, it should ensure that the packaging is easy to operate and the product description and logo design are easy to understand.Second, the functions of sales packaging are diverse, including use function, aesthetic function, and symbolic function, which need to be considered in the design.Third, the sales packaging time is adapted to the new materials and new processes representing the development level of productivity, and modern materials are widely used, which constitute the factors to promote the development of packaging technology.Finally, sales packaging plays the role of “silent salesman” and needs to design diversified works from the aspects of economy, environment, practicality, beauty, and so on.In conclusion, the structure of sales packaging is complex and contains many uncertain factors, so its evaluation is difficult. The discussion in this article refers to the sales packaging if there is no explanation.


#### 3.5.2. Functional Analysis of Packaging

Generally speaking, products have three basic functions: use function, symbolic function, and aesthetic function. The use function of packaging is characterized by the protection of goods and the convenience of being operated; the symbolic function of packaging means that packaging has the symbolic significance of marking product identity and reflecting product characteristics, including the characteristics of added value and brand integration; and the aesthetic function of packaging includes psychological characteristics and visual communication characteristics. It is worth mentioning that the symbolic function and aesthetic function of packaging are interactive in some places. For example, visual communication features not only reflect the aesthetic function but also reflect the basis of symbolic function.(1)
Anti-vibration, moisture-proof, and anti-damage are the most basic protection functions of packaging.(2)
The convenience of being operated is manifested in the convenience of action. The specification, size, shape, weight, packaging process, packaging materials, packaging structure, and opening method of packaging are directly related to the operation. Considering the impact of packaging on the environment, the convenience also includes the convenience of recycling and waste disposal.(3)
In modern society, almost all products are inseparable from packaging, and almost all packaging places a certain kind of symbol, and the symbolic function of products can also produce value. For example, the value of famous brands known to the public is much higher than that of similar products, and its added value is obvious. The estimation and measurement of packaging added value should have a set of scientific, reasonable, and operable methods, and the market positioning of products should be clear, to estimate the symbolic functions that products and packaging can bring consumers. The generation and recognition of added value are also related to the artistic level of conception and design, advertising effect, social awareness, participation in major social events, public response to products, etc. However, the packaging needs to be appropriate. Excessive packaging may not only harm the interests of consumers but also become a joke to buy money and return beads.(4)
The characteristics of brand integration make the design have the effect of inheritance and visual consistency. On the packaging of brand goods, symbolic special colors or attractive advertising words are used to enhance the display effect and quality of the identification effect, such as green arrow, Coca Cola, Chivas, and other packaging designs, is the overall identification concept. The serial design of the brand makes local adjustments in color combination, picture composition, and capacity design, respectively. Such design is conducive to establishing consumers’ identification and memory points and promoting the continuous sales of goods.(5)
In the market economy, promotion constitutes the psychological function of packaging, which is also the most direct and interesting factor in the visual characteristics of packaging. If the use function is the value of packaging as a material, the promotion function is the embodiment of the vitality of packaging, because its self-salesman image is loved and accepted.(6)
The visual communication characteristics of packaging design mainly embody directness, implication, and competitiveness. Directness means that packaging, as an external addition, accurately and quickly transmits the product content to consumers with its direct visual language. Due to the limitations of various conditions, it is not necessary and impossible to show all the information when designing packaging. It is more to directly attract consumers’ attention and interest through color and modeling.Allergenicity refers to associating consumers, stimulating their recognition and closeness to product value (including added value), and finally producing the desire to buy. Some modern philosophers and psychologists believe that people’s understanding and understanding of external objective things are always interactive with their own subjective psychology formed through practice. The moral of packaging is the result of the joint action of subjective and objective elements (see Figure2).Figure 2
Emotional reactions.The semantics of packaging visual design elements (namely modeling, color, and text) can convey meanings and associations, such as the size and shape of containers, which directly reflect the nature of objects in containers. They are high-grade perfume or general detergent. Mineral water packaging usually reflects the purity of water quality with blue as the main tonal. Color is the fastest information symbol that stimulates people’s vision; in other words, it is the easiest to be captured. According to the research, people’s attention to color accounts for about 80% of the total attention. Therefore, according to the main color of packaging, consumers can associate the characteristics and performance of commodities. For example, red means enthusiasm and enthusiasm, which is mostly used in cosmetics and food; blue is quiet and cool. It can be used for cold drinks, refrigerators, etc.; purple is noble, elegant, and mysterious. It is mostly used for high-end clothing, precious jewelry, gifts, etc.; yellow is pleasant and lively. It is used as the main color of household goods, which will make people feel warm. If you violate these practices, it may make people uncomfortable. For example, if some foods are made into cold color, it will be very disgusting. The use of image color is not necessarily invariable. In short, the use of packaging color should be in line with the commodity content as the basic starting point. Visual elements are closely related to consumers’ economic and cultural levels. Consumers with different economic abilities and educational levels have different perspectives on beauty appreciation. When designing packaging, we must also consider the color, texture, and other elements related to consumers’ living environment.Competitiveness: the competitiveness of packaging design is mainly reflected in the strength and identification of visual elements, the memory of visual image, and so on. Among them, the strength of visual elements refers to the competitiveness of color and modeling, the recognition degree of visual elements refers to the recognition degree of various elements on the packaging, and the memory degree of visual image is the degree that consumers can clearly remember, which involves the uniqueness, allegory, and association of various graphics and colors on the packaging.


#### 3.5.3. Construction of Packaging Design Index System

At present, the research on packaging design has been sufficient, but the research on design evaluation is slightly weak; in particular, the research on the construction of index system is obviously insufficient, which is very unreasonable and abnormal. According to the basic principle of establishing index set, this study analyzes the specific functions of packaging from the three functions of general products and then tries to establish a set of perfect packaging design evaluation index system. According to the principles of packaging design and the basic functions of packaging, we gradually deepen the design to the detailed features. See Figure3 for the specific contents.Figure 3
Data distribution of the 2th attribute.


## 3.1. Construction of Knowledge Expression System

We can use the relational table to represent the knowledge expression system. The rows of the relational table correspond to the object to be studied, and the columns correspond to the attributes of the object. The information of the object is expressed by specifying various attribute values of the object. A decision table can be defined as follows: letS=U,A,V,f be a knowledge expression system; A=C∪D, C∩D=φ, and C is called conditional attribute set; D is called decision attribute set, and the knowledge expression system with conditional attributes and decision attributes is called decision table.


### 3.1.1. Condition Properties

Glasses are generally composed of more than 10 components such as frame, lens, and nose bridge. By means of morphological analysis, the shape of glasses is divided into five main design items, namely frame style, frame thickness, lens shape, nose bridge, and foot swish, and then, each design item is divided into several design elements. For example, the frame style is divided into four unexpected elements; see Table1 for the design elements of glasses. Each design item of glasses is taken as a conditional attribute.Table 1
Classification of design elements.
Design projectDesign elements1234C1: frame styleFull frameHalf frameFramelessotherC2: frame thicknessThin frameThick frameotherC3: glasses nose beamSingle beam frameDouble beam frame


### 3.1.2. Decision Attributes

After research and analysis, the perceptual vocabulary of glasses is determined as four perceptual vocabulary gates: beautiful, fashionable, unique, and elegant. Here, only “beautiful” is taken as an example. The questionnaire was designed using a 7-order Likert scale. 50 subjects were selected for the survey. After sorting out the survey results, the perceptual evaluation matrix can be obtained, as shown in Table2.Table 2
Kansei evaluation’s matrix of glasses.
OrderC1C2C3C4Graceful112415.66211114.32………………821414.19Perceptual evaluation data are not suitable for the rough set since the data in it are continuous. Therefore, we need to discretize it in order to use the rough set theory. According to the characteristics of evaluation data distribution, the discretization method is as follows: the evaluation grade of interval [1,4.5] is 1; the evaluation grade of interval [4.5,5.5] is 2; and the rating grade of interval [5.5, 7.0] is 3, and the discretized perceptual evaluation grade is taken as the decision attribute.


### 3.1.3. Decision Table

The pictures of 18 typical glasses are taken as the research object, the top item of modeling is taken as the condition attribute C, and the discrete perceptual evaluation level is taken as the decision attribute D. Table3 contains the information about the decision.Table 3
Decision table.
UC1C2C3C4D112413211111………………821411


## 3.1.1. Condition Properties

Glasses are generally composed of more than 10 components such as frame, lens, and nose bridge. By means of morphological analysis, the shape of glasses is divided into five main design items, namely frame style, frame thickness, lens shape, nose bridge, and foot swish, and then, each design item is divided into several design elements. For example, the frame style is divided into four unexpected elements; see Table1 for the design elements of glasses. Each design item of glasses is taken as a conditional attribute.Table 1
Classification of design elements.
Design projectDesign elements1234C1: frame styleFull frameHalf frameFramelessotherC2: frame thicknessThin frameThick frameotherC3: glasses nose beamSingle beam frameDouble beam frame


## 3.1.2. Decision Attributes

After research and analysis, the perceptual vocabulary of glasses is determined as four perceptual vocabulary gates: beautiful, fashionable, unique, and elegant. Here, only “beautiful” is taken as an example. The questionnaire was designed using a 7-order Likert scale. 50 subjects were selected for the survey. After sorting out the survey results, the perceptual evaluation matrix can be obtained, as shown in Table2.Table 2
Kansei evaluation’s matrix of glasses.
OrderC1C2C3C4Graceful112415.66211114.32………………821414.19Perceptual evaluation data are not suitable for the rough set since the data in it are continuous. Therefore, we need to discretize it in order to use the rough set theory. According to the characteristics of evaluation data distribution, the discretization method is as follows: the evaluation grade of interval [1,4.5] is 1; the evaluation grade of interval [4.5,5.5] is 2; and the rating grade of interval [5.5, 7.0] is 3, and the discretized perceptual evaluation grade is taken as the decision attribute.


## 3.1.3. Decision Table

The pictures of 18 typical glasses are taken as the research object, the top item of modeling is taken as the condition attribute C, and the discrete perceptual evaluation level is taken as the decision attribute D. Table3 contains the information about the decision.Table 3
Decision table.
UC1C2C3C4D112413211111………………821411


## 3.2. Attribute Reduction

For attribute reduction, we need to delete the irrelevant features while maintaining the information in the data as much as possible. Definitions13 and 14 are the basic definitions used in attribute reduction of decision table.Definition 13.
Given the database, which is denoted asK=U,ℛ, for each subset X⊆U and an equivalence relationship ℛ∈indK, we have two different sets, which are as follows:(1)R−X=UY∈U/R|Y∈X,R−X=UY∈U/R|Y∩X≠φ.
Here,ℛ is the lower approximation set and ℛ is the upper approximation set of X and posRX=R_X is the positive field of X.Definition 14.
LetP and Q be a family of equivalent relations, R∈P. If posindpindQ=posindP−RindQ, R is called Q unnecessary in P. Otherwise, R is Q necessary in P, and all of the necessary primitive relations in P is called the kernel of Q and is denoted as coreQP.
In Table3, the attribute behavior in Table 3 is the attribute of the sense of importance, which is as follows:(2)U/indC1=1,2,3,4,5,6,7,9,10,13,15,17,8,12,16,18,14,11,U/indC2=2,3,6,7,8,9,10,11,13,16,17,18,1,4,5,12,15,14,U/indC3=2,3,9,5,17,1,4,7,8,10,11,14,16,18,6,12,13,15U/indC4=1,2,4,6,7,8,10,11,12,14,15,16,18,3,5,9,13,17,U/indC5=2,3,4,5,6,7,8,9,11,16,17,1,10,13,15,18,12,14,U/indD=2,5,8,14,16,18,4,7,10,11,15,17,1,3,6,9,12,13.
C=C1,C2,C3,C4,C5 is set, and then, we have the following:(3)U/indC=2,3,9,17,7,10,6,13,5,4,1,15,8,16,18,12,14.
According to Definition13, we have the following:(4)posCD=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18.
Then:(5)U/indC−C1=2,3,9,17,7,8,11,16,10,18,6,13,5,4,posC−C1D=1,2,3,4,5,6,9,12,13,14,15,17≠posCD.
According to Definition14, C1 is necessary for D in C and C4 is unnecessary for D in C. Similarly, C2,C3,C5 are necessary for D in C, so core=C1,C2,C3,C5; that is, the “beautiful” perceptual image of glasses is mainly determined by C1 (frame style), C2 (frame thickness), C3 (lens shape), and C5 (glasses legs and feet), while C4 (glasses nose bridge) is an unnecessary attribute and can be omitted.


## 3.3. Calculation of Importance of Attributes

Attributes in the knowledge base are not equally important. Attributes with high importance should be considered. See Definitions15 and 16 for the calculation of important attributes.Definition 15.
LetK=U,R be a knowledge base, and P,Q⊆R. When k=γPQ=posPQ/U, we say knowledge Q is k0≤k≤1 and depends on knowledge P, denoted as P⇒kQ.Definition 16.
SupposeS=U,A,V,f is an expression system of knowledge, A=C∪D, C∩D=φ, and the importance of attribute subset C′⊆C about D is σCDC′=γCD−γC−C′D.
According to Definition15, the dependence degree of decision set D on attribute set C is k=γCD=posCD/U=1.
Based on Definition16, the weights of attribute C1 are αCDC1=γCD−γC−C1D=1−posC−C1D/U=1−0.67=0.33. Similarly, it can be obtained that αCDC2=0.22, αCDC3=0.44, αCDC4=0, and αCDC5=0.11. Therefore, the order of importance of each design item of glasses to the “beautiful” of perceptual image is as follows: C3 (lens shape) > C1 (frame style) > C2 (frame thickness) > C5 (glasses feet) > C4 (glasses nose bridge). It can be seen that the lens shape should be considered in the image shape design of glasses.


## 3.4. The Formulation of Decision Rules

Rosetta software is used in the extraction of decision rules. This software is tabular logic data analysis software based on the rough set framework. By the rough set theory, we can execute some data analysis tasks such as data mining and knowledge discovery, can reduce attributes, generatei-then decision rules, and verify and analyze the obtained rules.18 groups of data are randomly divided into 14 groups of training data and 4 groups of prediction data. We use the genetic algorithm to reduce the attributes of 14 groups of training data, and the decision rules of the system are obtained on this basis. Because there are many rules, according to Definition6, the minimum accuracy value and coverage are set to be 0.75 and 0.05, respectively. After filtering the rules, there are 14 rules. See Table 4 for decision-making rules. These rules are applied to the classification of hot test data to obtain the systematic prediction results. This result is written into the actual data for comparison. The prediction result is shown in Figure 1. The overall accuracy of the prediction is 75%. Because only 18 groups of data are trained and tested, the accuracy is low, but with the increase in the amount of data, the prediction accuracy will be improved.Table 4
Partial glass dataset.
SampleRiNaMgAiSiKCaBaFeType11.5210113.644.491.171.780.068.7500121.5176113.983.61.3672.730.487.8300131.5161713.533.551.5472.990.397.7800141.5176613.213.691.2972.610.578.2200151.5174213.273.621.2473.080.558.0700161.5159612.793.611.6272.970.648.0700.26171.5174313.303.601.1473.090.588.1700181.5175613.153.6110.573.420.578.2400191.5191814.043.581.3772.080.568.30001…………………………………………………………Figure 1
Index of packing for transportation.


## 3.5. Construction of Evaluation Index Set of Packaging Design

Most of the data collected from the real world are not suitable for direct application to knowledge learning algorithms. The main reasons are as follows: first, the scale of original data is often very large, and there is some interference information, which is inaccurate, inconsistent, and incomplete; second, the attribute types of the original dataset are often very complex, including not only discrete attribute space but also continuous attribute space. If such a dataset is not processed and directly used in the later algorithm, the corresponding efficiency and accuracy will not be obtained. In addition, most classification algorithms can only deal with the dataset of discrete value attributes. Continuous attribute discretization belongs to a part of data preprocessing. According to different attribute value ranges, the attributes of the original dataset can be divided into three types: digital attributes (such as page number, 1, 2, 3, and 4), noun attributes (such as color, red, yellow, and blue), and continuous attributes (such as weight and distance). Both digital attributes and noun attributes belong to discrete attributes. After repeated experimental comparison, it is found that the classification results, whether accuracy or efficiency, are significantly improved by discretizing continuous attributes into discrete attributes and then learning classification.To sum up, the overall objectives of the discretization algorithm should be as follows:(1)
To generate high-quality discretization schemes to help experts understand the data more easily (the quality of discretization schemes can be measured by car criteria, which will be mentioned later).(2)
The generated discrete scheme should improve the accuracy and efficiency of the learning algorithm (for a decision tree algorithm, the efficiency is determined by the number of rules and training time).(3)
The process of discretization should be as fast as possible. Continuous attribute discretization is to convert the value space of continuous value attributes into a limited number of cells, use some different symbols or numbers to represent the divided interval, give each interval a discrete value, and use this discrete value to represent all attribute values in the small interval. Attribute discretization can be carried out artificially; that is, through the expert’s advice experience establishes a more reasonable division method. For example, when evaluating attribute scores, the results after discretization are as follows: 0–59 points are unqualified, 60–69 points are qualified, 70–79 points are medium, 80–89 points are good, and 90–100 points are excellent. It can also be discretized through machine learning, and sample learning makes the discretization results more objective and reasonable. The essence of the discretization process is to give some partition points to divide the attribute space.


### 3.5.1. Classification of Packaging

According to the functional differences undertaken, packaging is divided into transportation packaging and sales packaging. Transportation packaging mainly meets the functional requirements of shock and mildew resistance. The analysis of its index system is shown in Figure1.It can be seen from the above that the functional requirements of transportation packaging are simple and easy to quantify, which will not be discussed in this study.Sales packaging first reflects the unity of perceptual and rational needs. Consumers will pay attention to the appearance and brand when purchasing goods, but they will pay more attention to its function and operation. The packaging design should meet various needs. While reflecting the aesthetic value, it should ensure that the packaging is easy to operate and the product description and logo design are easy to understand.Second, the functions of sales packaging are diverse, including use function, aesthetic function, and symbolic function, which need to be considered in the design.Third, the sales packaging time is adapted to the new materials and new processes representing the development level of productivity, and modern materials are widely used, which constitute the factors to promote the development of packaging technology.Finally, sales packaging plays the role of “silent salesman” and needs to design diversified works from the aspects of economy, environment, practicality, beauty, and so on.In conclusion, the structure of sales packaging is complex and contains many uncertain factors, so its evaluation is difficult. The discussion in this article refers to the sales packaging if there is no explanation.


### 3.5.2. Functional Analysis of Packaging

Generally speaking, products have three basic functions: use function, symbolic function, and aesthetic function. The use function of packaging is characterized by the protection of goods and the convenience of being operated; the symbolic function of packaging means that packaging has the symbolic significance of marking product identity and reflecting product characteristics, including the characteristics of added value and brand integration; and the aesthetic function of packaging includes psychological characteristics and visual communication characteristics. It is worth mentioning that the symbolic function and aesthetic function of packaging are interactive in some places. For example, visual communication features not only reflect the aesthetic function but also reflect the basis of symbolic function.(1)
Anti-vibration, moisture-proof, and anti-damage are the most basic protection functions of packaging.(2)
The convenience of being operated is manifested in the convenience of action. The specification, size, shape, weight, packaging process, packaging materials, packaging structure, and opening method of packaging are directly related to the operation. Considering the impact of packaging on the environment, the convenience also includes the convenience of recycling and waste disposal.(3)
In modern society, almost all products are inseparable from packaging, and almost all packaging places a certain kind of symbol, and the symbolic function of products can also produce value. For example, the value of famous brands known to the public is much higher than that of similar products, and its added value is obvious. The estimation and measurement of packaging added value should have a set of scientific, reasonable, and operable methods, and the market positioning of products should be clear, to estimate the symbolic functions that products and packaging can bring consumers. The generation and recognition of added value are also related to the artistic level of conception and design, advertising effect, social awareness, participation in major social events, public response to products, etc. However, the packaging needs to be appropriate. Excessive packaging may not only harm the interests of consumers but also become a joke to buy money and return beads.(4)
The characteristics of brand integration make the design have the effect of inheritance and visual consistency. On the packaging of brand goods, symbolic special colors or attractive advertising words are used to enhance the display effect and quality of the identification effect, such as green arrow, Coca Cola, Chivas, and other packaging designs, is the overall identification concept. The serial design of the brand makes local adjustments in color combination, picture composition, and capacity design, respectively. Such design is conducive to establishing consumers’ identification and memory points and promoting the continuous sales of goods.(5)
In the market economy, promotion constitutes the psychological function of packaging, which is also the most direct and interesting factor in the visual characteristics of packaging. If the use function is the value of packaging as a material, the promotion function is the embodiment of the vitality of packaging, because its self-salesman image is loved and accepted.(6)
The visual communication characteristics of packaging design mainly embody directness, implication, and competitiveness. Directness means that packaging, as an external addition, accurately and quickly transmits the product content to consumers with its direct visual language. Due to the limitations of various conditions, it is not necessary and impossible to show all the information when designing packaging. It is more to directly attract consumers’ attention and interest through color and modeling.Allergenicity refers to associating consumers, stimulating their recognition and closeness to product value (including added value), and finally producing the desire to buy. Some modern philosophers and psychologists believe that people’s understanding and understanding of external objective things are always interactive with their own subjective psychology formed through practice. The moral of packaging is the result of the joint action of subjective and objective elements (see Figure2).Figure 2
Emotional reactions.The semantics of packaging visual design elements (namely modeling, color, and text) can convey meanings and associations, such as the size and shape of containers, which directly reflect the nature of objects in containers. They are high-grade perfume or general detergent. Mineral water packaging usually reflects the purity of water quality with blue as the main tonal. Color is the fastest information symbol that stimulates people’s vision; in other words, it is the easiest to be captured. According to the research, people’s attention to color accounts for about 80% of the total attention. Therefore, according to the main color of packaging, consumers can associate the characteristics and performance of commodities. For example, red means enthusiasm and enthusiasm, which is mostly used in cosmetics and food; blue is quiet and cool. It can be used for cold drinks, refrigerators, etc.; purple is noble, elegant, and mysterious. It is mostly used for high-end clothing, precious jewelry, gifts, etc.; yellow is pleasant and lively. It is used as the main color of household goods, which will make people feel warm. If you violate these practices, it may make people uncomfortable. For example, if some foods are made into cold color, it will be very disgusting. The use of image color is not necessarily invariable. In short, the use of packaging color should be in line with the commodity content as the basic starting point. Visual elements are closely related to consumers’ economic and cultural levels. Consumers with different economic abilities and educational levels have different perspectives on beauty appreciation. When designing packaging, we must also consider the color, texture, and other elements related to consumers’ living environment.Competitiveness: the competitiveness of packaging design is mainly reflected in the strength and identification of visual elements, the memory of visual image, and so on. Among them, the strength of visual elements refers to the competitiveness of color and modeling, the recognition degree of visual elements refers to the recognition degree of various elements on the packaging, and the memory degree of visual image is the degree that consumers can clearly remember, which involves the uniqueness, allegory, and association of various graphics and colors on the packaging.


### 3.5.3. Construction of Packaging Design Index System

At present, the research on packaging design has been sufficient, but the research on design evaluation is slightly weak; in particular, the research on the construction of index system is obviously insufficient, which is very unreasonable and abnormal. According to the basic principle of establishing index set, this study analyzes the specific functions of packaging from the three functions of general products and then tries to establish a set of perfect packaging design evaluation index system. According to the principles of packaging design and the basic functions of packaging, we gradually deepen the design to the detailed features. See Figure3 for the specific contents.Figure 3
Data distribution of the 2th attribute.


## 3.5.1. Classification of Packaging

According to the functional differences undertaken, packaging is divided into transportation packaging and sales packaging. Transportation packaging mainly meets the functional requirements of shock and mildew resistance. The analysis of its index system is shown in Figure1.It can be seen from the above that the functional requirements of transportation packaging are simple and easy to quantify, which will not be discussed in this study.Sales packaging first reflects the unity of perceptual and rational needs. Consumers will pay attention to the appearance and brand when purchasing goods, but they will pay more attention to its function and operation. The packaging design should meet various needs. While reflecting the aesthetic value, it should ensure that the packaging is easy to operate and the product description and logo design are easy to understand.Second, the functions of sales packaging are diverse, including use function, aesthetic function, and symbolic function, which need to be considered in the design.Third, the sales packaging time is adapted to the new materials and new processes representing the development level of productivity, and modern materials are widely used, which constitute the factors to promote the development of packaging technology.Finally, sales packaging plays the role of “silent salesman” and needs to design diversified works from the aspects of economy, environment, practicality, beauty, and so on.In conclusion, the structure of sales packaging is complex and contains many uncertain factors, so its evaluation is difficult. The discussion in this article refers to the sales packaging if there is no explanation.


## 3.5.2. Functional Analysis of Packaging

Generally speaking, products have three basic functions: use function, symbolic function, and aesthetic function. The use function of packaging is characterized by the protection of goods and the convenience of being operated; the symbolic function of packaging means that packaging has the symbolic significance of marking product identity and reflecting product characteristics, including the characteristics of added value and brand integration; and the aesthetic function of packaging includes psychological characteristics and visual communication characteristics. It is worth mentioning that the symbolic function and aesthetic function of packaging are interactive in some places. For example, visual communication features not only reflect the aesthetic function but also reflect the basis of symbolic function.(1)
Anti-vibration, moisture-proof, and anti-damage are the most basic protection functions of packaging.(2)
The convenience of being operated is manifested in the convenience of action. The specification, size, shape, weight, packaging process, packaging materials, packaging structure, and opening method of packaging are directly related to the operation. Considering the impact of packaging on the environment, the convenience also includes the convenience of recycling and waste disposal.(3)
In modern society, almost all products are inseparable from packaging, and almost all packaging places a certain kind of symbol, and the symbolic function of products can also produce value. For example, the value of famous brands known to the public is much higher than that of similar products, and its added value is obvious. The estimation and measurement of packaging added value should have a set of scientific, reasonable, and operable methods, and the market positioning of products should be clear, to estimate the symbolic functions that products and packaging can bring consumers. The generation and recognition of added value are also related to the artistic level of conception and design, advertising effect, social awareness, participation in major social events, public response to products, etc. However, the packaging needs to be appropriate. Excessive packaging may not only harm the interests of consumers but also become a joke to buy money and return beads.(4)
The characteristics of brand integration make the design have the effect of inheritance and visual consistency. On the packaging of brand goods, symbolic special colors or attractive advertising words are used to enhance the display effect and quality of the identification effect, such as green arrow, Coca Cola, Chivas, and other packaging designs, is the overall identification concept. The serial design of the brand makes local adjustments in color combination, picture composition, and capacity design, respectively. Such design is conducive to establishing consumers’ identification and memory points and promoting the continuous sales of goods.(5)
In the market economy, promotion constitutes the psychological function of packaging, which is also the most direct and interesting factor in the visual characteristics of packaging. If the use function is the value of packaging as a material, the promotion function is the embodiment of the vitality of packaging, because its self-salesman image is loved and accepted.(6)
The visual communication characteristics of packaging design mainly embody directness, implication, and competitiveness. Directness means that packaging, as an external addition, accurately and quickly transmits the product content to consumers with its direct visual language. Due to the limitations of various conditions, it is not necessary and impossible to show all the information when designing packaging. It is more to directly attract consumers’ attention and interest through color and modeling.Allergenicity refers to associating consumers, stimulating their recognition and closeness to product value (including added value), and finally producing the desire to buy. Some modern philosophers and psychologists believe that people’s understanding and understanding of external objective things are always interactive with their own subjective psychology formed through practice. The moral of packaging is the result of the joint action of subjective and objective elements (see Figure2).Figure 2
Emotional reactions.The semantics of packaging visual design elements (namely modeling, color, and text) can convey meanings and associations, such as the size and shape of containers, which directly reflect the nature of objects in containers. They are high-grade perfume or general detergent. Mineral water packaging usually reflects the purity of water quality with blue as the main tonal. Color is the fastest information symbol that stimulates people’s vision; in other words, it is the easiest to be captured. According to the research, people’s attention to color accounts for about 80% of the total attention. Therefore, according to the main color of packaging, consumers can associate the characteristics and performance of commodities. For example, red means enthusiasm and enthusiasm, which is mostly used in cosmetics and food; blue is quiet and cool. It can be used for cold drinks, refrigerators, etc.; purple is noble, elegant, and mysterious. It is mostly used for high-end clothing, precious jewelry, gifts, etc.; yellow is pleasant and lively. It is used as the main color of household goods, which will make people feel warm. If you violate these practices, it may make people uncomfortable. For example, if some foods are made into cold color, it will be very disgusting. The use of image color is not necessarily invariable. In short, the use of packaging color should be in line with the commodity content as the basic starting point. Visual elements are closely related to consumers’ economic and cultural levels. Consumers with different economic abilities and educational levels have different perspectives on beauty appreciation. When designing packaging, we must also consider the color, texture, and other elements related to consumers’ living environment.Competitiveness: the competitiveness of packaging design is mainly reflected in the strength and identification of visual elements, the memory of visual image, and so on. Among them, the strength of visual elements refers to the competitiveness of color and modeling, the recognition degree of visual elements refers to the recognition degree of various elements on the packaging, and the memory degree of visual image is the degree that consumers can clearly remember, which involves the uniqueness, allegory, and association of various graphics and colors on the packaging.


## 3.5.3. Construction of Packaging Design Index System

At present, the research on packaging design has been sufficient, but the research on design evaluation is slightly weak; in particular, the research on the construction of index system is obviously insufficient, which is very unreasonable and abnormal. According to the basic principle of establishing index set, this study analyzes the specific functions of packaging from the three functions of general products and then tries to establish a set of perfect packaging design evaluation index system. According to the principles of packaging design and the basic functions of packaging, we gradually deepen the design to the detailed features. See Figure3 for the specific contents.Figure 3
Data distribution of the 2th attribute.


## 4. Experiment and Results

As mentioned above, three intervals are obtained after discretization by the CAIM algorithm, which is obviously over discretization. The improved algorithm is used for discretization. The intervals [0.20,1.00] and (1.007.00] and GlobalNCA = 1.3846 are obtained in the first cycle; interval discontinuity of 2.80 is obtained in the second cycle; and three intervals [0.20,1,00], (1.00,2,80), and (2.80,7,00], NCA = 2.2 (>1.3846), GlobalNCA = 2.2, and interval discontinuity of 6.00 are obtained in the third cycle; four intervals [0.20,1.00, (1.00280), (2.80,6.00), and (6.00,7.00], NCA = 2.53 (>2.2), GlobalNCA = 2.53, interval discontinuity of 4.95 are obtained in the fourth cycle; and NCA = 3 (>2.53), GlobalNCA = 3, and maximum NCA = 3 (no more than 3) are obtained in the fifth cycle, and the algorithm ends.For illustrating the effectiveness of this method, this method is used to process the samples in the commonly used UCI machine learning database, and the sample glass dataset is selected. The dataset contains 214 samples, 9 conditional attributes, and 6 classes. A partial glass dataset is shown in Table4.Taking the second attribute in the glass sample as an example, the distribution of the attribute data is illustrated in Figure3.Some data of glass dataset after discretization are shown in Table5.Table 5
Glass dataset’s discretization.
SampleRiNaMgAiSiKCaBaFeType143411121112334322111131333321111432422221115324232111161143321131733423211118324142211194333122111…………………………………………………………The discrete dataset samples are randomly divided into two groups, 70% of the data is used to train the model, while the remaining 30% is used as the test set. Rosetta rough set software is used to process and predict the classification accuracy counted by the algorithm. The rules with accuracy >0.75 and coverage >0.05 are selected. Table6 shows the comparison results of classification rules and classification test.Table 6
Classification accuracy of discretization schemes.
Method usedEntropy-based discretizationCAIM algorithmThis studyClassification ruleGenerate 78 articlesGenerate 32 articlesGenerate 37 articlesClassification accuracy46.9%61.2%69.7%From the results, the improved algorithm in this study produces more classification rules than the CAM algorithm. This is because the discrete interval generated by the CAIM algorithm is relatively simple, so there are fewer classification rules, but less than the number of classification rules generated by the entropy-based discretization algorithm, which can make the classification rules simple and have better universality. Moreover, the optimized discretization algorithm is obviously more accurate than the CAIM algorithm.


## 5. Conclusion

Taking glasses as an example, this paper studies the application of rough set theory in product perceptual image design. Firstly, the knowledge expression system is constructed, and then, the reduction in top purpose and the importance of each item in modeling design are calculated. On this basis, the relationship between perceptual image and design elements is extracted. The application of rough set theory in product perceptual image design helps designers design products that meet the perceptual needs of consumers, which is of great significance to improve the competitiveness of enterprises. Based on the results of this research, a virtual perceptual engineering system can be constructed for more in-depth research.



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*Source: 2140075-2022-05-10.xml*