A Study on Multiattribute Aggregation Approaches to Product Recommendation

In today’s increasingly competitive market, consumers usually have to face a huge number of products with different designs but having the same use. Therefore, an important problem for manufacturers is to attract consumers by special designs of the products. This paper aims at the improvement of a consumer-oriented approach in recommending products, and proposing a recommendation system for Japanese traditional crafts based on target-oriented fuzzy method and ontological engineering. Specifically, a target-oriented fuzzy method is used for measuring the fitness of a selected attribute to a certain object. Two aggregation models for dealing with a multiattribute evaluation and ranking are introduced; four ranking methods are also examined for getting a recommendation list. To test the aggregation models and the ranking methods, a recommendation system was developed and a comparison test was conducted.


Introduction
Nowadays, the design and sense of a product is increasingly important in marketing, since consumers put more attention to their sensibilities or to feelings of the products, not only to the quality of the products.In today's increasingly competitive market, consumers usually have to face a huge number of products with different designs but having the same use [1].Therefore, it is an important problem for manufacturers to attract consumers by special designs of the products.Because consumers accept a tacit understanding that the quality of product is appropriate (consumers cannot know the quality before they buy the product), they usually focus on their subjective feelings of the products when they select the products, so the design is now becoming as important as the quality of a product [2].Thus it is necessary to further develop a consumer-oriented approach in recommending products; such approach focuses on the satisfactions of the consumers' requirements.This issue has received increasing attention in the research of consumer-oriented design and Kansei Engineering since the 1970s.Kansei Engineering, which was invented by Nagamachi at Hiroshima University in the 1970s which was and defined as "translating technology of a consumer's feeling and image for a product into design elements" [3], has been proved to be an efficient and successful approach in many fields [4,5], such as automotive, home electronics, office machines, cosmetics, food and drink, packaging, building products, and other sectors [6].The word Kansei expresses the subjective feelings of a product by people's immanent phenomenological perception using all senses, viewing, hearing, touching, smelling, and other ways [5].In Kansei-related researches, the most common method of the collection of data is the semantic differential (SD) method, which uses a set of adjectives and asks evaluators to express their feeling to an object with those words [5,[7][8][9][10], and for the personalization in Kansei-engineering, the fuzzy-theory-based methods have been improved as an efficient solution, which have been used in many fields, such as medicine, industry [11,12].
Many studies of Kansei Engineering or other consumeroriented decision-making technologies have been used in many decision-support fields [2], even in commercial products and traditional crafts.These issues are studied in order to be helpful for marketing or recommendation purposes [13], particularly in e-commerce [14].

Advances in Fuzzy Systems
When consumers express their requirements for purchasing products, they usually have a multiattribute expression; this means that an aggregation model of those attributes becomes an important part in matching consumer's requirements.We can suppose that the requirement of the consumer is a whole entity, and we can use the Kansei words selected by consumers to describe the entity, so it would become an ontological issue.(Ontology is understood here as a word borrowed from philosophy to describe matching words and concepts in computer science; more precisely, it is sometimes called ontological engineering.On the other hand, Kansei engineering has also connections to another part of philosophy called phenomenology, meaning perceiving the world as a whole, by all senses.)The consumers' requirements would be then interpreted as consumers' ontological profile.
In this paper, we will focus on the evaluation of Japanese traditional crafts, and on the personalization of consumers' requirements by an ontological profile described by consumers; some aggregation models of the multiattribute aspects and some ranking methods will be also discussed, including the comparison of them.
In order to propose an efficient fuzzy target-based Kansei evaluation and multiattribute aggregation models, as it is common in researches on Kansei Engineering, an experimental study is conducted first by means of the SD method [15] or its modifications [7][8][9][10].In such procedure, about 60 volunteers are gathered to evaluate 30 traditional crafts, and a Kansei Database about the crafts is obtained.This database is the starting point of this paper, in which a fuzzy targetbased personalization method for a single Kansei word will be proposed, and the satisfaction of the single Kansei word selected by consumer will be measured.Next, according to consumers' requirements profiles, two aggregation models and four ranking methods on multiattribute aspects will be defined, and a recommendation ranking list will be given to consumers.Finally, a recommendation system as an ecommerce system will be developed, and a comparison about the efficiency of different aggregation models and ranking methods will be conducted.

Fuzzy Target-Oriented Decision Making
We will introduce a method in this paper, which can measure consumer's personal preference on products in order to find which product can meet his/her tastes best.First of all, we need to identify the attributes of products and show a measurement method of the attributes to get a common understanding of the products by an average customer; and then, for a certain attribute selected by an individual consumer, including the attribute's level or target, we need to find a way to describe how a product meets consumer's personal preference on these selections; in other words, we need to measure a specific, individual consumer's preference.

Measurement of the Attributes of the Products.
We will describe in this paper a consumer-oriented evaluation problem with Kansei data and Context data for traditional crafts (for detail, see [16][17][18]).Let us denote by  the collection of  Then we use semantic differential method to make a questionnaire to collect both Kansei data and Context data.We use -point method to make the questionnaire.Specifically, to the left-side word of the paired Kansei attribute, we attach point 1, and to the other side of the paired Kansei attribute, we attach point ; in this case,  = 7.Let us denote the -point scale by where V  means the level of attribute.If  = 7, then there will be 7 levels to describe the paired attribute, and then V  =  and  = {1, 2, 3, 4, 5, 6, 7}.
The questionnaire is given to the evaluators to express their emotional assessments; we denote  as the set of evaluators, where || = .Specifically, for a certain object   ∈ , evaluator   gives his/her marks on every Kansei attribute and Context attribute; thus we denote   (  ) as the mark of evaluator   to attribute  of   , and attribute  can be Kansei attributes or Context attributes.Here   (  ) ∈ .Then we can denote   (V ℎ ) as the distribution of the evaluators, which is given by ℎ , a fuzzy target-based personalization method was proposed in Nakamori [19].Here we will use this idea and make some modifications.Firstly, we can know the probable general feelings of   evaluated by all evaluators and the distribution of the evaluators' feelings.We denote avg  (  ) as the average value of evaluators feelings about object 's attribute , and we denote sdiv  (  ) as the standard deviation of these feelings.The corresponding formula is as follows: According to avg  (  ) and sdiv  (  ), we can make a triangle-type membership function expressed as {avg  (  ) −  ⋅ sdiv  (  ), avg  (  ), avg  (  ) +  ⋅ sdiv  (  )}, to describe the distribution of the data, where  is a positive number.(In this study, we set the positive number  = 3, which can make the shape of the triangle-type membership function to be reasonable; specifically, the shape should be matched with the scale of the levels.)We denote this triangle-type membership function as ℎ  (  , ), where  ∈ [V 1 , V  ].We can define a function  V  () to measure the fitness value in different level; V  can be considered as consumer's target of   , and the formula is as follows: (5) avg − c * sdiv avg + c * sdiv When the consumer set the target V  , we can use  V  () and the triangle-type membership function ℎ  (  , ) to calculate the fitness value, and the formula is given by An example is shown in Figure 1, where the fitness value is the height of the point in the figure.
For each attribute (generally, we use a Kansei attribute   as an example, where  = 1, . . ., ), a different evaluator may have different feelings on the same object.This means that some evaluators may mark the attribute   in the    area, but others may mark it in the    area.Therefore, when we calculate the fitness value of an attribute for a certain object, we should separate the paired attribute into two single parts, which we call left part (   area) and right part (   area).We denote SC   as the significance coefficient of   when it is in the left part; relatively, SC   means the significance coefficient when   is in the right part.The formula is given as follows: These two coefficients interpret the significance of the two sides; in other words, they can measure the distribution of the evaluation data obtained from evaluators.The function   (  , V  ) should be adjusted as follows: Here V  is the target of the selected Kansei attribute .ℎ   (  , ) and ℎ   (  , ) are the triangle-type membership functions, and the average value and the standard deviation contained in these two triangle-type membership functions are modified.Specifically, we only use one side of the evaluation data of a paired attribute to calculate them.If consumer's target is set in the left part of the paired attribute, we can use (8) to calculate the fitness value; correspondingly, if the target is set in the right part of the paired attribute, then we can use ( 9) to do so.

Aggregation Models Based on Ontological Structure
Consumer can select some attributes of the product and set the importance coefficients of these attributes to describe his/her requirements in this recommendation system.Therefore, we have to face a situation that the consumer's preference profile includes several attributes of the products; in other words, we face a multiattribute requirement, and we need to integrate the multiattribute selection to obtain a scalar measure of consumer's preference.
As we have discussed above, there are two kinds of attributes to describe a product: Kansei attributes and Context attributes.Kansei attributes are usually expressed by the adjective words; they are usually used to describe the sensibilities of a consumer about an object.These sensibilities usually have a vague nature for a human to describe; for example, "a little" or "very much" can express the degree of a Kansei word.Correspondingly, Context attributes usually express the product's purpose of use or characteristic of users.They usually include some short phrases, and they are different from Kansei attributes.A Context attribute usually has an explicit meaning for a consumer.For example, for a Context attribute "for seniors", we cannot set a degree to describe this attribute as our requirement, and it just means that we want a product for seniors.According to these characteristics of Context attributes, we can use an ontological structure to describe them: specifically, we could use Context attributes as subrequirement entities (selected Context attribute), and we use Kansei attributes to describe these subrequirement entities.Then we could integrate these subrequirement entities as consumer's personal requirements.
When we use Kansei attributes to describe the subrequirement entity (selected Context attribute), the relationship between them should be taken into account.There are 4 possibilities when consumers face the relationship given as follows.
(1) They want to decide the relations according to their preferences freely.
(2) They want to use the same relations for different Kansei attributes, and do not want to adjust them.(3) They accept the relations calculated by the system, and do not want to adjust them.(4) They partly accept the relations calculated by the system, but can adjust the relations in a certain range.Within this range, the personal tastes and the rules of the correlations between attributes can all be considered.
In this study, we will focus on the fourth possibility, and we will discuss it in the following part.
The overview of this recommendation system is shown in Figure 2.There are 4 parts in this system: Interface, Specification module, Aggregation module, and Database.The consumer can select attributes and set their levels and importance coefficients in the interface to describe his/her requirement; the specification module can measure the satisfactions of the selected attributes; the aggregation module can aggregate the selected attributes and make a recommendation list to consumer.
As we have discussed above, we will use some results of ontological engineering; specifically, we will split consumer's requirement into several subrequirement entities, and for each entity we will use Kansei attributes to describe it.Here we will propose two models for the aggregation of the subrequirement entity.

Consumer Target-Based Aggregation Model.
Given that  =   ∪   as the requirements set of consumer, where   means the Context requirements and   means the Kansei requirements, then   = { 1 , . . .,   },   = { 1 , . . .,   }.We have calculated how the object meets the selected attributes  ∈  separately, and then we will use a method to aggregate them to see how the object meets the consumer's preference.Here we use an ontological structure to describe consumer's preference.Specifically, we concentrate on the Context attributes, and we use the selected Kansei attributes to describe them.We use the selected Kansei attribute set   to describe a selected Context attribute   .This is some kind of enlarged Context attribute, or we can say it is a enlarged concept, and then we denote it as   ∈   , where   = {  ,   }, and   is the set of enlarged Context attributes.
When we use Kansei attributes to describe the Context attribute, we should know how important a Kansei attribute to a Context attribute is.We denote (  ,   ) as the importance coefficient between   and   , and we can use the correlation coefficient of attributes average values (see (3)) to describe a possible strength of their relationships.Generally, we define CC  as the correlation coefficient between Kansei attribute  and Context attribute , and we then assume the following.
If 0.8 ≤ CC  ≤ 1, then there is a completely positive correlation.If 0.2 ≤ CC  < 0.8, then there is a certain degree of positive correlation.If −0.2 ≤ CC  < 0.2, then there is no correlation.If −1 ≤ CC  < −0.2, then there is a negative correlation.
From these definitions, we can map the correlation coefficient to the importance coefficient.Specifically, when the correlation effect between a Kansei attribute and a Context attribute is significant, this means that the Kansei attribute is important to describe the Context attribute.Correspondingly, if the correlation effect between the Kansei attribute and the Context attribute is not significant, or it appears to be a negative correlation effect, then the Kansei attribute is not suitable to describe the Context attribute.We assume that the Kansei attribute is not suitable to describe the Context attribute when their correlation coefficient is smaller than 0.2, and we then set the importance coefficient of the Kansei attribute to the Context attribute as 0. If their correlation coefficient is bigger than 0.2, then we assume that there is linear relationship between the importance coefficient and the correlation coefficient: the linear relationship is described by the segment AB in Figure 3.The composite line CDB indicates a reasonable upper limit to the importance coefficients set by a consumer; hence we define it as the upper recommended transformation line for an adjustment range, defined to meet consumer's personal requirements, by which consumer can adjust the importance coefficient in a certain degree.This range is defined in a sense objectively by taking into account the correlation coefficients obtained from the database.The lower limit of the range is expressed by the composite line CAB: specifically, if the correlation coefficient is bigger than 0.2, then we assume that line segment AB defines a reasonable lower limit for importance coefficients set by the consumer.To sum up, if the correlation coefficient is smaller than −0.2, then we set the importance coefficient as 0; if the correlation coefficient is bigger than 0.8, then we set the upper limit of the importance coefficient as 1; if the correlation coefficient is in the range (−0.2-0.8), then we assume that there are limits to the importance coefficients set by the consumer, expressed by linear relationships between the correlation coefficient and the importance coefficient.The vertical lines in the shadowed area in Figure 3 indicated the range of possible importance coefficients that can be selected by the consumer; as reasonable starting points, we can suggest to the consumer the middle values of these ranges, denoted on Figure 3 by a broken line.
Thus, consumers can set their preferred importance of a Kansei attribute to a certain Context attribute, which we denoted as (  ,   ).We define   (  ,   ) and   (  ,   ) as the recommended lower transformation function and the upper transformation function (see Figure 3), respectively, and we define   (  ,   ) as the middle value function which we recommend to a consumer as starting values, in detail, as follows: According to (  ,   ) and ( 10), we can define (  ,   ) as in (11).The equation can make the adjusted importance coefficient in the shadow part of Figure 3 as For the enlarged Context attribute   , the fitness of the object   can be calculated by Here V   and V   are the targets of the selected Context attribute and Kansei attribute.As it is shown in Figure 4, each selected Context attribute can be treated as a subrequirement entity, and for each subentity, we use all selected Kansei attributes to describe it according to the importance coefficients and correlation coefficients.
Then we should aggregate all   ∈   to see how the object meets consumer's preference.For each selected Context attribute, the consumer can also set the importance coefficients which describe the importance of the Context attribute to his/her preference.We denote it by (  ).
If we assume that all selected Context attributes have a fuzzy logical relation "", then it means all Context attributes have no difference of importance, and then the aggregation model is as follows: If we assume that the fuzzy logical relation "AND" rules all Context attributes, then it means that the consumer wants every selected Context attribute to meet his/her requirements, and then the aggregation model is as follows: For the selected Context words, there might be some very small fitness value to an object, which will make the final score indiscernible, so we will introduce two other ranking methods to solve this problem.These two methods follow the essential criteria and compensable criteria.The compensable criteria means that a large value of criteria will compensate a small one, and it is some kind of weighted average approach; the essential criteria means that all criteria should have reasonably large values, and it is some kind of reference point method (RPM) which was proposed by Wierzbicki et al. [20].First, we should compute the statistical mean to see the average fitness of all objects for a given selected Context attribute: where (  ,   ) is computed as in (12) and || is the number of the objects.Then we can define the compensable criteria and the essential criteria as follows: ess (  ) = min where (  ,   ) is also computed as in (12) and the coefficient  > 0 in (17) indicates a compromise between interpreting the relations between the selected Context attributes as a fuzzy logical "AND" operation and interpreting them as compensable criteria.

An Indirect Aggregation Model Using the Idea of a
Prototype System PrOnto.The prototype system PrOnto was developed in the Requested Research Project of Poland in the National Institute of Telecommunications, entitled "Teleinformatic Services and Networks of Next Generation-Technical, Applied and Market Aspects".The system PrOnto is based on radically personalized ontological profiles of users, and it takes into account the interaction with different users (see [20]).If we use the idea of PrOnto system that a certain userdefined concept usually has a set of keywords to describe it, and a user can adjust the importance coefficients of these keywords, then we can assume that, for a certain Context attribute, treated as a concept, there is also a set of Kansei attributes, treated as a set of keywords, that can describe it commonly (we can call it a description set).And when we want to measure the satisfaction of a Context attribute, we can measure it by the related Kansei attributes, and personalize it by consumer's wishes.Specifically, we can make a set of Kansei attributes, which have higher correlations to that Context attribute, and instead of specifying the Context attribute by fuzzy method, we can use the fitness values of the set of Kansei attributes to describe the Context attribute indirectly; there is at least an advantage that we can distinguish different Context words in detail, because instead of using evaluation data only, there are many other Kansei attributes that can show their differences.If we want to take a typical selected Kansei attribute into account for the subrequirement entity (a selected Context attribute), then we can reset the correlation coefficient between this pair of Kansei attribute and Context attribute.Figure 5 shows a small part of Figure 4, which expresses the interior of a subrequirement entity.As shown in Figure 5, a subrequirement entity can be described by a set of Kansei attributes with higher correlation to this entity.Obviously, the consumer can also reset the correlation coefficient in a certain range (see Figure 3).The algorithm is similar to the method we have mentioned above the difference is that how to calculate the fitness of the enlarged Context attribute   .We just use the Kansei attributes to describe the enlarged Context attribute in this model, and we will not take the fitness of selected Context attribute   into account; the reason is that all Kansei attributes have special relationships with a certain Context attribute, and we can just use the Kansei attributes which have significant relations with that Context attribute to distinguish Context attributes.We denote    as the Kansei attributes set, which have significant relations with   , and as mentioned above,   is the selected Kansei attributes set.Then (  ,   ) is given by The first part on the right side of the equation is the satisfaction of the selected Context attributes calculated by the description set; the second part on the right side of the equation is the satisfaction of the additional selected Kansei attributes, which are not included in the description set.

A Recommendation System for Japanese Traditional Crafts
We will show how the recommendation system works in this section, including a case study about Japanese traditional crafts.This system contains all aggregation models and ranking methods that we have discussed above.
For evaluation and comparison, we will use a group of samples called "Kutani ware" to test the aggregation models and ranking methods."Kutani ware" is a kind of craft produced by traditional method; it has almost 400 years' history, and it is now a very important industry in Japan, not only because of its economic value, but also because of its traditional national culture values.
The samples we used are groups of cups made by traditional methods, and for each sample, we use 6 pairs of Context words and 20 pairs of Kansei words to describe it.To evaluate them, we have 60 volunteers to participate in.They were given some kind of questionnaire with 26 pairs of attributes (including 6 pairs of Context words and 20 pairs of Kansei words) on it.For each attribute, there are 7 degrees to select for describing how you feel about the samples.The part of the questionnaire is shown in Figure 6.
We have programmed a recommendation system for personalized consumers' requirements, according to the data we got from the evaluation and personal requirements selected by consumers; this program can recommend a list of the cups' numbers for consumers, which can help them to select their favorite cups (see Figure 7).
As shown in Figure 7, the consumer should select some Context words and set his/her importance coefficients; the consumer also need to select some Kansei words and set their levels and importance coefficients, then the requirements can be described by these selected attributes.The requirements will be also printed in the requirements block.Next step is to set the aggregation model and ranking method.We Advances in Fuzzy Systems   have two aggregation models (Consumer target-based model and PrOnto-based model) and four ranking methods (ranking method based on logical relation "OR", ranking method based on logical relation "AND", essential criteria, and compensable criteria) for selection.At step 3, if we click "Compute" button, we will see the recommended list in the result block (as the pictures of cups in Figure 7).

Evaluation and Comparison of Different Aggregation Models
In this section, we will make an evaluation of the recommendation system to test different aggregation models and ranking methods.In this evaluation, we had 25 volunteers, and let them select some of Context attributes and Kansei attributes as the descriptions of their requirements they also need to set the level and importance of the attributes they have selected, and then according to their selections, they should pick up one of the samples which they like best.We can use the recommendation system with these descriptions to test which models and which ranking methods are better.There are 30 coffee cups in this test.With the recommendation system and consumer's special description of the requirement, we could get a recommendation list of the coffee cups for each time's test.Comparing this list with consumer's favorite coffee cup, we can know the position of the favorite coffee cup in this list.For example, if the number of the consumer's favorite cup is 23, and this No. 23 cup is at the 3rd position of the list, then we mark it as 3 (see Table 2; we have gathered 49 items of data evaluated by 25 volunteers).According to the marks, we can know the satisfaction of the recommendation results roughly; for example, if one of the marks in Table 2 is 5, then the satisfaction would be (30 − 5)/30 = 0.83.
As shown in Table 2, for each time of evaluation, there are two different aggregation models and 4 different ranking  methods.At first, we compared the satisfactions of different aggregation models.Specifically, we have got the average marks of different aggregation models for each item of data, and then used the t-test to analyze the two series of data to find whether there is difference on their means; if so, we can compare their means to see which aggregation model is better (see Table 3).
As shown in Table 3, the mean values of the two aggregation models have a significant difference under the possibility of 90% ( value of -test is smaller than 0.1), and the PrOntobased aggregation model has a higher average satisfaction; it also has a lower variance, this means the PrOnto-based aggregation model is more efficient and stable.The reason might be that consumers usually concentrate on the main attributes of a product (in this case, the main attributes should be Context attributes).The main attributes (Context attributes) are described by a group of Kansei attributes (description group) in the PrOnto-based aggregation model, and some of the selected Kansei attributes involved in the description group will not be concerned again in the description group; correspondingly, the main attributes are calculated by targetbased fuzzy method in Consumer target-based aggregation model, and the selected Kansei attributes are calculated separately.Therefore, a duplicate calculation would happen when selected Kansei attributes have higher correlations to the main attributes.That would make the main attributes more easily affected by selected Kansei attributes in Consumer target-based aggregation model.The evaluation data of all attributes express the general understandings/feelings of the object, so there might be some deviations when we use them to calculate the satisfactions of consumers.In the PrOntobased aggregation model, the satisfaction of the Context attributes is calculated by description set (a set of Kansei attribute with higher correlation to that Context attribute) instead of using the evaluation data of the Context attribute, it means that we used several pieces of evaluation data to measure the satisfaction of the selected Context attribute, therefore, the deviations might be averaged.That may be the reason why PrOnto-based aggregation model is more stable.
The index of stability is necessary; if the model is not stable enough, then maybe, some time the system could get a higher satisfaction, and some time get a lower one.We use the variance to see which one is more stable, but we cannot use this value to see how stable the model is.According to the analysis above, we could say that the PrOntobased aggregation model is better.Then under this aggregation model, we will compare different ranking method.
As shown in Table 4, the two ranking methods with essential criteria (ESS) and compensable criteria (COM) have significant difference from the ranking method based on logical operation "AND" under the possibility of 95%.This means that we can compare the mean value (the satisfaction values are calculated by mean values) of the ranking method ESS and the ranking method based on logical operation "AND" (including the ranking method COM and the ranking method based on logical operation "AND") to see which one is better.We can see that the ranking methods of ESS, COM, and the ranking method based on logical operator "OR" have higher average satisfactions than the method based on logical operator "AND" (see Table 5), but from the analysis above, we can only say that ESS and COM are better than the ranking method based on logical operator "AND".According to the variance value of each ranking method (see Table 5), we find that ranking method ESS has a lower variance; this means that the ranking method ESS is more stable than others, so we can say that ranking method ESS is better than other methods with using the PrOnto-based aggregation model.

Conclusions
We have discussed and tested two multiattribute aggregation models and four ranking methods for the recommendation problem of Japanese traditional crafts in this paper; we have taken consumer personalized preferences about the attributes of the objects into account.We have also compared different aggregation models and ranking methods with using the recommendation system we have developed.According to the analysis of the comparison, we found that the PrOntobased aggregation model is more efficient and stable, and under using this aggregation model, the ranking method of ESS results in a better performance.We indicated also some problems, such as the matching problem between general understanding and personal understanding: the data we used in this paper are based on some kind of general understanding evaluated by a set of volunteers and recorded in the system database, so when consumers set their requirements, they might express some deviations between the database and the needs which consumers really want.

Figure 2 :
Figure 2: Overview of the recommendation system.

Figure 3 :
Figure 3: Conversion from correlation coefficient to importance coefficient.

Figure 7 :
Figure 7: The interface of the recommendation system.

Table 1 :
Kansei attributes and Context attributes list.
specific crafts (products), a finite set, and let us denote its cardinality by || = .There are two kinds of data in this paper: Kansei data and Context data.Kansei data is used to describe consumer's feelings regarding traditional crafts, they are defined by pairs of adjective characters; Context data is used for describing the application situations and they are defined by pairs of phrases (see Table1

𝐾} as the set of Context attributes, and we can also denote 𝑋 as the set of all attributes, where 𝐹 ⊂ 𝑋, 𝐶 ⊂ 𝑋.
).Let(1) { 1 ,  2 , . ..,   } be the set of selected Kansei attributes, (2) { 1 ,  2 , . ..,   } be the set of selected Context attributes.Attribute   consists of a pair of Kansei words: Suppose that the consumer target of   can be expressed as V  ℎ ∈ .To calculate how   of   meets the target V

Table 2 :
Comparison results of different aggregation models and ranking methods.

Table 3 :
Comparison of different aggregation models.