European Journal of Operational Research

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1 European Journal of Operational Research 196 (2009) Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: wwwelseviercom/locate/ejor Decision Support A problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy Rui-Yang Chen * Department of Management Sciences, Aletheia University, 32 Chen-Li Street, Tamsui, Taipei 25103, Taiwan, ROC article info abstract Article history: Received 6 May 2007 Accepted 7 March 2008 Available online 13 March 2008 Keywords: Intuitionistic fuzzy Product design Problem solving Customer complaint problem is a product design used to understand customer requirements Furthermore, product design corresponding to customer requirement does not feel adequately solved for a cause of problem The cause of the problem affecting product design is solved to prevent customer complaint from reoccurring However, the problems by customer may have observation uncertainty and fuzzy Fuzzy concept considers not only the degree of membership to an accept set, but also the degree of non-membership to a rejection set Therefore, we present a new approach for problem solving using decision tree induction based on intuitionistic fuzzy sets in this paper Under this approach, we first develop the problem formulation for the symptoms and causes of the problem based on intuitionistic fuzzy sets Next, we identify the cause of the problem using intuitionistic fuzzy decision tree by the problem formulation We then provide the approach to find the optimal cause of the problem for the consideration of product design A numerical example is used to illustrate the approach applied for product design Ó 2008 Elsevier BV All rights reserved 1 Introduction A product design is a procedure that specifies the means by which the product will provide the desired function For product function, the design procedure often leads to the introduction of products that do not meet customer requirement During the design procedure, the designer should transform customer requirement into the required product The design procedure represents the transformation of customer requirement to a specification from which the product can be adapted During the transformation, designers highlight certain aspects associated with this specific customer requirement such as complaint problem The design is seen to be related with the domain of problem-solving Unfortunately, product design corresponding to customer requirement does not feel adequately solved for a cause of problem As indicated, customers want a suitable product to meet intended needs A suitable product is one that executes its intended functions without problem as expected when required Problem-solving deployment is a systematic method for receiving the voice of customers into a product design through identifying the cause of the problem in order to solve customer complaint Customer complaint problem is a product design used to understand customer requirements The cause of the problem affecting product design specification is solved to prevent customer complaint reoccurring Customer complaint problem belongs to a set of customer * Tel: address: a168jacky@msahinetnet from requirements Park and Kim [1] and Trappey et al [2] have shown some approach for analyzing the relationship between customer requirements and product design specification Kim et al [3] used a fuzzy approach to find the relationships between customer requirements and product design specification However, problem-solving approach was not properly considered for product design in these approaches By analyzing the relationships between product design specification and customer requirements, while considering customer complaint problem, problem-solving approach is responsible for identifying the cause of the problem We apply intuitionistic fuzzy theory and decision tree induction in order to optimize the problem for considering customer complaint of product design specification in this paper The problems by customer may have observation uncertainty and fuzzy The problem should be understandable to customers It is often difficult to communicate about the problem owing to its vague nature of problem solving For the product design, owing to the typical vagueness of these observations, it is difficult to identify them using engineering knowledge This means that customers state their problems to be refined by developers for clarification until understanding is attained The problem is that product design gaps may appear by customers working in this largely observations only manner These observations arise as fuzzy representation and are not properly identified Fuzzy sets were introduced by Zadeh [4] and provide bases for fuzzy representation The main meaning of fuzzy sets is the fuzzy membership function In fuzzy set theory, a fuzzy subset of the universe of discourse U is described by a membership function U(x):U? [0, 1], in which x 2 U /$ - see front matter Ó 2008 Elsevier BV All rights reserved doi:101016/jejor

2 R-Y Chen / European Journal of Operational Research 196 (2009) represents the degree to which belongs to the set A Accordingly, fuzzy representation is becoming increasingly popular in dealing with problems of uncertainty In a real problem to a fuzzy concept, fuzzy degree of the problem corresponding to the sum of the membership degree and non-membership degree in a universe may be less than one Fuzzy concept considers not only the degree of membership to a accept set, but also the degree of non-membership to a rejection set Intuitionistic fuzzy set, introduced by Atanassov [5], is the solution of non-membership degree in a universe In our opinion, the problem to be solved in the product design based on problem solving is to incorporate classification for the cause of the problem Classification is a data mining method which classifies a set of attributes into different classes according to a classification method Decision tree induction has been widely used in identifying knowledge from a collection of data for classification The popular classification method is the decision tree induction Decision tree classifies cases by sorting them with the tree from the root to the leaf nodes [6,7] Such a decision tree induction is then used to identify the cause of the problem There are well-known decision tree inductions such as CART [8], C45 [9] and QUEST [10] In the classification field, some fuzzy decision tree methods are required to deal with such fuzzy data A major contribution of the fuzzy decision tree is its capability of representing vague and unclassified data Fuzzy decision tree was introduced by Yuan s method [11] in this paper This existing induction method is improper to deal with the degree of membership for fuzzy data We are indeed interested in intuitionistic fuzzy decision tree for both the membership and non-membership of fuzzy data To build a problem solving approach, we present a new approach for problem solving using decision tree induction based on intuitionistic fuzzy sets in this paper The main purpose of this paper is to amend Yuan s fuzzy decision tree based on intuitionstic fuzzy set for problem-solving approach The rest of the paper is organized as follows: In Section 2, the intuitionstic fuzzy and fuzzy decision tree related to this study is presented In Section 3, a problem-solving approach is presented First, we develop the problem formulation for the symptoms of the problem based on intuitionistic fuzzy sets Next, we identify the cause of the problem using intuitionistic fuzzy decision tree by the problem formulation In the last two sections, numerical examples are discussed to illustrate the case of considering problem of customer complaint for product design and concluding summary is provided 2 Related work 21 Intuitionistic fuzzy set From several generalizations of fuzzy set theory for various objectives, the method introduced by Atanassov [5] in defining intuitionistic fuzzy sets (IF set) is adapted and is useful Gau and Buehrer [12] defined vague sets Bustince and Burillo [13] showed that the vague set is the same as IF set On the other hand, fuzzy set theory has been widely developed and various generalizations have applied One of them is the concept of intuitionistic fuzzy (IF) sets They consider not only the degree of membership to a accept set, but also the degree of rejection such that the sum of both values is less than 1 IFS theory has been applied in different areas such as logic programming and decision-making problems In this paper we study Atanassov s method using the notion of IFS theory We give here some basic definitions, which are used in the paper Definition 1 Let a set E be fixed An intuitionistic fuzzy set or IF set A in E is an object having the form A ¼fhX; l A ðxþ; m A ðxþi j X 2 Eg; ð1þ where the functions l A : E? [0,1] and m A : E? [0,1] define the degree of membership and degree of non-membership, respectively, of the element X 2 E to the set A, which is a subset of E, and every X 2 E, 06 l A (X)+m A (X) 6 1 Definition 2 The value of p A ¼ 1 ðl A ðxþþm A ðxþþ; is called the degree of non-determinacy (or uncertainty) of the element X 2 E to the intuitionistic fuzzy set A The amount p A =1 (l A (X)+m A (X)) is called the uncertainty, which may cater to either membership value or non-membership value or both 22 Fuzzy decision tree Decision trees classify data by sorting them down the tree from the root to leaf nodes On the other hand, fuzzy decision tree allows data to follow down simultaneously multiply branches of a node with different satisfaction degrees ranged on [01] A fuzzy decision tree is a generalization of the crisp case Fuzzy sets used for building the tree are imposed on the algorithm One of main objectives of fuzzy decision tree induction is to generate a tree with high accuracy of classification for unknown cases Experimental results [14] show, at least, that the selection of expanded attributes is an important factor The fuzzy decision tree construction method is designed for classification problem with attributes and classes represented in fuzzy linguistic terms [10] it is predefined with fuzzy linguistic in which the attribute values of training data are fuzzy Accordingly, fuzzy representation is becoming increasingly popular in dealing with problems of uncertainty, noise, and inexact data It has been successfully applied to problems in many industrial areas The fuzzy set theory has been used for handling fuzzy decision problem-solving problems [15] 3 A problem-solving approach 31 Problem formulation In addition to customer requirement emphasized by the customer complaint feedback, we also highlighted the need to consider the cause of the customer complaint problem in the product design Since all the requirement requests human s perception, they are vague by their nature The cause of the problem is also presented in fuzzy terms in order to consider the fuzzy concept in the product design In this paper, the problem-solving model is formulated to consider the degree of uncertainty (p A ) of the cause in the product design Normally, some data produced by problem cause identification are difficult to express, and they are vague and unclassified We can use the intuitionistic fuzzy set and the decision tree method to deal with these problems Intuitionistic fuzzy set theory deals with the vagueness Decision trees classify the data important index by sorting these data with a tree from the root to the leaf An intuitionistic fuzzy decision tree combines the intuitionistic fuzzy set with the decision tree A major contribution of the intuitionistic fuzzy decision theory is its capability of representing vague and uncertainty data For example, a designer s consideration about how to identify for the cause of the problem is usually vague and there is no crisp boundary for it The problem formulation could be represented as follows in Fig 1: A problem item (p i ) is described by a collection of the symptom (K j ) The symptom gets one of the mutually exclusive values V j ={V j1,,v jk } from the engineer s past experiences of product ð2þ

3 268 R-Y Chen / European Journal of Operational Research 196 (2009) d i1 d i2 d im Pi design, and each symptom is classified into only one of the mutually exclusive classes D i ={D i1,,d im } from the cause of the problem Nomenclature P {p i }, problem item i K i {k i1,,k ij }, symptoms of the problem, where j is the jth symptom of the problem item i V j {v j1,,v jn }, values of the symptom, where n is the nth value of the symptom item j D i {d i1,,d im }, causes of the problem, where m is the mth cause of the problem item i From the above formulation, the data of these nomenclatures can be represented as intuitionistic fuzzy set From the above statements, one heuristic key point of the formulation for identifying the cause of the problem in the intuitionistic fuzzy decision tree could be found In the formulation, it has two key points One point is how to decide the symptom to identify the class of cause (see Definition 3), and the other point is how to select the necessary symptoms (see Definition 4) Definition 3 Let R denote an identified degree; it identifies a symptom to the class of cause R is defined by Rðk 1j ¼ v jn ; d 1m Þ: ð3þ Definition 4 Compare the maximum values of R with one another on the different symptoms based on the same cause If the value is bigger, then its selection priority is higher k i1 k i 2 Cause Problem of product Symptom Values of symptom k ij Fig 1 The concept of the problem formulation v v v j1 j 2 jk although the vagueness of the symptom noise can be avoided by numerical measurement such as IF noise P60 decibels THEN cause identification is Dislocated tray, but how about when the noise is 59 decibels? Obviously the crisp boundary is not always desirable Although there may be no vagueness between two causes Disc is scraped and Dislocated tray for this symptom, the classification when it is interpreted as the desire to identify can still be vague This symptom alone is the identified cause, so the classification ambiguity may also occur It is hard to select one We define the classification accuracy for each value of the symptom, which is identified to a class of causes If it could not be identified clearly, it shows that there is a degree of classification ambiguity This probability of the degree is desired to be lower for the identification clearly According to the smaller classification ambiguity of the symptom, we select this symptom From the intuitionistic fuzzy decision tree point of view, we use the classification accuracy of the p A in order to gain the smaller classification accuracy If the smaller classification accuracy of p A is lower than the threshold value of the classification accuracy, the symptom will be identified corresponding to the cause An intuitionistic fuzzy decision tree is a generalization of the membership degree and non-membership degree in a universe The fuzzy classification method can be well adapted and amended by Yuan s fuzzy decision tree methodology [11] in this paper We only use the concept of the classification accuracy and classification ambiguity from this methodology The proposed classification accuracy can be applied to the membership and non-membership fuzzy sets For the intuitionistic fuzzy decision tree, we denote the following symbols based on the membership and the non-membership fuzzy sets They are represented as follows: First, we denote the following symbols based on the membership fuzzy set A fuzzy set K named symptom in a universe of discourse U(x) is characterized by a membership function U K which takes values in the interval [0,1] Forx 2 U, U K (x) = 1 means that x is definitely a member of K and U K (x) = 0 means that x is definitely not a member of K In the same manner, D named cause in a universe of U(x) is defined by the membership of a fuzzy subset U D which takes values in the interval [1,0] In our problem, all values of causes and symptoms are defined as fuzzy sets on the same universe Definition 5 The measure of a fuzzy set K is defined bymðkþ ¼ P x2u U KðxÞ, which is the measure of the size K The measure of an intersection fuzzy set K \ D is defined by MAXfRðk 11 ¼ v 1n ; d 1m Þ; Rðk 12 ¼ v 2n ; d 1m Þ; Rðk 1j ¼ v jn ; d 1m Þg: ð4þ MðK \ DÞ ¼ X minðu K ðxþ; U D ðxþþ: x2u ð5þ From the above description, there are two questions which need to be solved: 1 How a problem with fuzzy symptoms can be identified to its causes, especially when the causes may also be intuitionistic fuzzy set? This is equal to the classification accuracy of p A discussed in Section 32 later 2 How good is the optimal identification of the causes? This is equal to the classification ambiguity discussed in Section 32 later The abovementioned problem-identifying procedure can be shown as follows in Section Problem identifying Human s feeling of symptom-identified cause is vague and there is no crisp boundary between them For CD-ROM example, Definition 6 Given the fuzzy data, the accuracy probability of the classification (S) can be defined as P x2u SðK; DÞ ¼MðK \ DÞ=MðKÞ ¼ minðu KðxÞ; U D ðxþþ P x2u ðu : ð6þ KðxÞÞ The fuzzy subset S(K, D) measures the degree with the accuracy probability of the classification to which K is a subset of D The definition is similar to Eq (3) It is transferred to the problem formulation of this paper Sðk 1j ¼ v 1jk ; d 1m Þ¼Mðk 1j ¼ v 1jk \ d 1m Þ=Mðk 1j Þ: It measures the classification probability of the mapping values of the symptoms which belong to the cause of the problem, and it replaces the traditional entropy of the decision tree with the classification accuracy For CD-ROM example, we have S(noise = High, Disc is scraped), which can be interpreted as IF noise is high decibels ð7þ

4 R-Y Chen / European Journal of Operational Research 196 (2009) THEN classification accuracy identified the cause Disc is scraped is S Next, we denote the following symbols based on the non-membership fuzzy set: With the fuzzy set, m(x) is the family of all non-membership fuzzy subsets defined on X, and the cardinality measure of a fuzzy subset x is given finite data of m(x) A is defined by the non-membership of a fuzzy subset v A which takes values in the interval [1, 0] in a universe of m(x) Forx 2 v, v A (x) = 1 means that x is definitely a member of A, and v A (x) = 0 means that x is definitely not a member of A, A is a crisp set The amount p A =1 (l A (X)+m A (X)) is called the degree of uncertainty, which may cater to either membership value or non-membership value or both On the other hand, this degree probability of the p A is desired to be lower for the identification uncertainty The proposed classification ambiguity is represented as follows Definition 7 Given a set of fuzzy data, the classification ambiguity of the symptom values could be defined as GðS j;z Þ¼ Xn ðs Z S Zþ1 Þ ln z; Z¼1 where Z is the running index for possible causes with respect to the symptom j,lnzis the weight applied on the gap between S Z and S Z+1 Notice that ln1 = 0 The idea being that higher gap between earlier normalized classification accuracy results in lower classification ambiguity S Z represents the accuracy probability of classification in different classes by normalization of the Z attribute value S Z is the normalized classification accuracy for classifying symptom j with value to cause by scaling the maximum classification accuracy of 1 with respect to all possible causes Let S Z be the ordered S in descending order with biggest S being the first A value 0 is padded after the smallest classification accuracy From the definition, we know G(S j,z ) P 0 If G(S j,z ) = 0, which indicates no ambiguity since only value of the symptom is identified for the cause If G(S j,z )=lnz, which indicates that all values of the symptom are possibly identified for the cause, representing the greatest ambiguity Definition 8 Given a set of fuzzy data, classification ambiguity of the symptom could be defined as GðSÞ ¼ Xj j¼1 GðS j Þ=j: The computed analysis procedure of the problem identifying for IF decision tree is represented as follows: Step 1: Calculate the classification accuracy (S) ofl A associated with each symptom value identifying all causes in the same symptom for all symptoms Step 2: Repeat step1 for the classification accuracy (S) ofp A Step 3: Calculate the classification ambiguity (G) associated with each symptom value identifying the cause in the same symptom Step 4: Calculate the classification ambiguity of a symptom for all symptoms Step 5: Select the smaller classification ambiguity for all symptoms Step 6: Identify the optimal cause of the symptom from that mentioned in step5 according to the smaller classification accuracy (S) ofp A The computed analysis procedure is shown in Fig 2 ð8þ ð9þ Step3 Calculate the classification ambiguity (G) for symptom values Step5 Selecting the smaller classification ambiguity of the symptom Compare the minimum of the classification accuracy of the π A from the selected symptoms 4 Numerical examples Step1 & Step2 Calculate the classification accuracy (S) of the ua and π A Select symptom? Min (probability of classifying j ambiguity) G ( S ) = G ( Sj ) / j threshold threshold value value Step6 Identified the cause of the symptom Step4 Calculate the classification ambiguity (G) for symptom classification accuracy < threshold value? No identified Fig 2 The computed analysis of problem identifying for IF decision tree procedure In order to demonstrate the validation of the proposed approach, let us illustrate the approach to solve the following numerical examples in Fig 3 Feedback of the customer complaint problem of the product design is applied to identify the cause of the problem The illustration example of problem identifying is shown as follows: Step 1 Decide a problem: CD-ROM does not work Step 2 Analyze the causes from the same problem and each cause is defined as a fuzzy set on the universe of U Step 3 Analyze the symptoms from the same problem and each symptom is defined as a fuzzy set on the universe of U Step 4 Each symptom has three values that indicate correlation degree identified in the problem, such as High (H), Medium (M), and Low (L) Step 5 The cause of the problem is identified through the values of the symptoms of the problem It should be mentioned that the sum of the membership (l A ), non-membership (m A ) and Decision Fuzzy Complaint problem feedback of product design Step3 Symptom of problem is vague and cause do not easy identify Yes Step4 According to symptom of problem for CD-ROM product, these have fuzzy membership and non-membership values of the symptom j=1 No Step1 Problem: CD-ROM does not work Step2 Cause of problem for product: 1 Disc be scraped 2 Tray move 3 Not set Jump Step5 Identify cause of the problem through the values of the symptoms of the problem Fig 3 Illustration of the identified cause of the problem

5 270 R-Y Chen / European Journal of Operational Research 196 (2009) uncertainty (p A ) values of all linguistic terms for a values of the symptom may equal to 1 An example of a small training data set with fuzzy membership and non-membership values is briefly shown in Table 1 See Appendix A for the 9 instances of this example The value of membership and non-membership fuzzy associated with any item is between 0 and 1, which could be from the complaint records of customer For example, if 5 out of ten complaints records identify the cause Disc be scraped, we may assign 05 as the fuzzy membership degree to the No 1 (l A )oftable 1 If 3 out of ten complaints records do not identify the cause Disc be scraped, we may assign 03 as the fuzzy membership degree to the No 1 (m A ) of Table 1 According to this example, we know that the uncertainty value of p A is 02 from Eq (2) This example has three symptoms: K ¼fTray not move; Occur noise; Drive could not be detectedg; and each symptom has three values of the symptom:ðv j1 Þ Tray not move {high (H), medium (M), low (L)} ðv j2 Þ Occur noise {high (H), medium (M), low (L)} ðv j3 Þ Drive could not be detected {high (H), medium (M), low (L)} The classification can identify the cause of the problem, such as ðd im Þcauses ¼fNot set Jump; Disc be scraped; Dislocated trayg: The analysis of problem identifying for intuitionistic fuzzy decision tree is represented as follows using the data of the Table 1: Step 1 Calculate the classification accuracy (S) of the l A An example of 9 instances of the CD-ROM problem with fuzzy values l A from complaint records of customer The 9 instances appear as shown in Table 1 The S of the l A is shown in Table 2 For example l A : SðOccur noise ¼ H; Not set JumpÞ ¼MðOccur noise ¼ H \ Not set JumpÞ=MðOccur noise ¼ HÞ 0:6 þ 0:5 þ 0:6 þ 0:3 þ 0:5 þ 0:4 þ 0:5 þ 0:3 þ 0:2 ¼ 0:7 þ 0:5 þ 0:6 þ 0:3 þ 0:5 þ 0:4 þ 0:5 þ 0:3 þ 0:2 ¼ 0:98: Step 2 Repeat step 1 for the classification accuracy (S) of the p A An example of 9 instances of the CD-ROM problem with fuzzy values p A from complaint records of customer The 9 instances that appear are shown as Table 1 The S of p A is shown in Table 2 For example p A : SðOccur noise ¼ H; Not set JumpÞ ¼ MðOccur noise ¼ H \ Not set JumpÞ=MðOccur noise ¼ HÞ 0:1 þ 0:1 þ 0:1 þ 0:1 þ 0 þ 0:1 þ 0:1 þ 0:1 þ 0:3 ¼ 0:1 þ 0:2 þ 0:1 þ 0:2 þ 0:1 þ 0:2 þ 0:1 þ 0:4 þ 0:4 ¼ 0:56: Step 3 Calculate classification ambiguity of the values of the same symptom for l A S(Occur noise = H, Not set Jump) = 098 S(Occur noise = H, Disc be scraped) = 078 S(Occur noise = H, Dislocated tray) = 035 The classification accuracy after normalization S Z = (1, 079, 036) G(Occur noise = H) = (1 079)ln1 + ( )ln2 + (036 0)ln3 = 0697 G(Occur noise = M) = 0928, G(Occur noise = L) = 0624 The G of the values of the same symptom for l A is shown as Table 2 Step 4 Calculate classification ambiguity of a symptom for l A G(Occur noise) = ( )/3 = 0749 The G of the symptom for l A is shown in Table 2 Step 5 Select the smaller classification ambiguity for l A Using the same abovementioned step 3 and step 4 procedure, we can obtain G(Tray not move) = 0575, G(Drive could not be detected) = 0560 MIN(G(Tray not move), G(Occur noise), G(Drive could not be detected)) = MIN(0575,0749,0560) = 0560 Accordingly, the symptom term Drive could not be detected becomes the dominant symptom for cause identification Step 6 Identifying the optimal cause of the symptom from that mentioned in step 5 according to the smaller classification accuracy (S) ofp A Table 1 The value of membership and non-membership fuzzy data CD-ROM Tray not move Occur noise Drive could not be detected Causes H M L H M L H M L Not set jump Disc is scraped Dislocated tray No 1 (l A ) No 1 (m A ) No 1 (p A ) Table 2 identifying the cause of the problem Symptom Tray not move Occur noise Drive could not be detected H M L H M L H M L (l A ) classification ambiguity (G) (l A ) classification ambiguity (G)-minimum (l A ) classification ambiguity (G)-average (l A ) classification ambiguity (G)-average minimum 0560 Causes p A (S) (p A ) not set jump (S) (p A ) disc be scraped (S) (p A ) dislocated tray (S) l A (S) (l A ) not set jump (S) (l A ) disc be scraped (S) (l A ) dislocated tray (S)

6 R-Y Chen / European Journal of Operational Research 196 (2009) According to the abovementioned symptom with the smaller classification ambiguity in step 5, we compare the lowest classification accuracy (S) ofp A for this symptom The answer is the cause Disc be scraped (classification accuracy = 018) through the symptom is Drive could not be detected of the problem If the classification accuracy is lower than the classification accuracy threshold value (=02), this cause for the problem classification will be identified The abovementioned data are shown in Table 2 According to the analysis procedure in this example, the result of the whole of S and G indexes is presented in Table 2 From Table 2, the numerical results indicate that classification accuracy (S) ofp A of the three symptoms is strictly concave as shown in Fig 4 Consequently, we are sure that this symptom Drive could not be detected with the smallest uncertainty p A obtained here is indeed the optimal solution Accordingly, the optimal identified cause is Disc is scraped If this cause is physically tested for correctness to fix the problem, the number of trials is one If the first cause fails to fix the problem, the value of next dominant symptom will be used to identify a plausible cause based on the same manner until a correct cause is identified For the proposed IF decision tree and fuzzy decision tree, we evaluated the performance under different experiments by varying 6 instances in terms of number of trials The trials mean how many times the problem is identified to locate correct causes The number of trials is smaller, and then the accuracy degree to locate correct causes is higher For each experiment, both intuitionistic fuzzy decision tree and fuzzy decision tree are evaluated for comparisons The way of their computed analysis is the same, but only the difference is fuzzy set Intuitionistic fuzzy decision tree uses both fuzzy non-membership set and fuzzy membership set Fuzzy decision tree uses only fuzzy membership set The accuracy of identification of the cause of the problem was influenced by different identification methods as shown in Table 3 The result from the number of trials is represented by performance evaluation The intuitionistic fuzzy decision tree method proposed out-performed the other method, because difference in the average number of trials of the accuracy of identification is greater than 0 The average numbers of trials mean an average trial of 6 instances Drive could not be detected Occur noise Tray notmove Fig 4 Graphical representation of classification accuracy (p A ) Submit problem process Product design End user Customer complaint problem is a product design used to understand customer from requirements The cause of the problem affecting product design is solved to prevent customer complaint reoccurring We provide the approach to find the optimal cause of the problem for the consideration of product design While considering customer complaint problem, problem-solving approach is responsible for identifying the cause of the problem However, the problems by customer may have observation uncertainty and fuzziness Accordingly, fuzzy representation is becoming increasingly popular in dealing with problems of uncertainty data It has been successfully applied to problems in many industrial areas The problem solving for the consideration of product design is represented in Fig 5 The problem solving of the product design is that the downstream customers bring up the problems of product These problems are via the interface of the product problem feedback tracing system and it will be via two ways One way, if the product problem is a new problem, it will be identified automatically to the cause through problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy sets, and stores into the knowledge database These can avoid happening again and to be the guild line reference to the product design consideration The other way, we can get the cause from the knowledge database to respond to the product design instantly and to solve problems 5 Conclusion Problem screening Consider the cause 1 Problem-cause 1 First way identified Select? Respond process Problem-cause 2 no identified 2 Second way Database Problem-identifying for IF decision tree Search identified result from database Fig 5 Problem solving for consideration of product design Identify process In this paper, we develop a problem solving approach that can be used to examine the integration of customer complaint problem into the desired design The approach deployed an approach for problem solving in an intuitionistic fuzzy concept and using decision tree induction based on intuitionistic fuzzy set Furthermore, we have identified the cause of the problem for problem-solving approach This approach not only improves the existing methods of the fuzzy decision tree but also solves the problem of the intuitionistic fuzzy concept to product design application Therefore, we present a new approach for problem solving using decision tree induction based on intuitionistic fuzzy sets in this paper In a real Table 3 Empirical results to demonstrate the performance Consideration of problem-solving The fuzzy decision The intuitionistic fuzzy Difference in # of trials to in Product design tree method (X) decision tree method (Y) locate correct causes CD-ROM # of trials of the accuracy of identify # of trials of the accuracy of identify X Y Instance Instance Instance Instance Instance Instance Total Average of the 6 instances

7 272 R-Y Chen / European Journal of Operational Research 196 (2009) problem to a fuzzy concept, fuzzy degree of the problem corresponding to the sum of the membership degree and non-membership degree in a universe may be less than one Under this approach, we first develop the problem formulation for the symptoms of the problem based on intuitionistic fuzzy sets Appendix A The value of membership and non-membership fuzzy data CD-ROM Tray not move Occur noise Drive could not be detected Causes H M L H M L H M L Not set Jump Disc is scraped Dislocated tray No 1 (l A ) No 1 (m A ) No 1 (p A ) No 2 (l A ) No 2 (m A ) No 2 (p A ) No 3 (l A ) No 3 (m A ) No 3 (p A ) No 4 (l A ) No 4 (m A ) No 4 (p A ) No 5 (l A ) No 5 (m A ) No 5 (p A ) No 6 (l A ) No 6 (m A ) No 6 (p A ) No 7 (l A ) No 7 (m A ) No 7 (p A ) No 8 (l A ) No 8 (m A ) No 8 (p A ) No 9 (l A ) No 9 (m A ) No 9 (p A ) The purpose of this paper is to consider the cause of the problem for product design in order to accumulate problems and experience throughout the problem-solving procedure: 1 Quickly identify the cause of the problem and resolve it 2 Accumulate problem-solving experience to make Out-of-control action plans so that future problems can be properly and quickly avoided 3 Store to knowledge database from solving experience in order to consider in the product design Accumulate problem-solving experience and consideration to product design so that mechanisms such as design guidelines can be developed to prevent problem reoccurrences in the future The contributions of this paper include: (1) Propose a problemsolving approach using decision tree induction based on intuitionistic fuzzy sets (2) Propose an automatic identifying cause of the problem for consideration to product design from problem-solving oriented viewing Some suggestions for future research are as follows: In this study, the intuitionistic fuzzy decision tree method is applied to identify the cause automatically for the membership degree and non-membership fuzzy symptoms of the problem However, in the future, one can use other mathematical methods to perform the task, for example, using the fuzzy AHP method based on intuitionistic fuzzy sets References [1] T Park, K-J Kim, Determination of an optimal set design requirements using house of quality, Journal of Operations Management 16 (1998) [2] CV Trappey, AJC Trappey, S-J Hwang, A computerized quality function deployment approach for retail services, Computers and Industrial Engineering 30 (4) (1996) [3] K-J Kim, H Moskowitz, A Dhingra, G Evans, Fuzzy multicriteria models for quality function deployment, European Journal of Operational Research 121 (2000) [4] LA Zadeh, Fuzzy sets, Information and Control 8 (3) (1965) [5] K Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) [6] A Berson, K Smith, K Thearing, Building Data Mining Applications for CRM, McGraw-Hill, New York, 2000 [7] J Kim, B Lee, M Shaw, H Chang, M Nelson, Application of decision-tree induction techniques to personalized advertisements on internet storefronts, International Journal of Electronic Commerce 5 (3) (2001) [8] L Beiman, J Friedman, R Olshen, C Stone, Classification and Regression Trees, Wadsworth International Group, California, 1984 [9] JR Quinlan, C45: Programs for Machine Learning, Morgan Kaufmann, Los Altos, CA, 1993 [10] WY Loh, YS Shih, Split selection methods for classification trees, Statistica Sinica 7 (8) (1997) [11] Y Yuan, MJ Shaw, Induction of fuzzy decision trees, Fuzzy Sets and Systems 69 (1995) [12] WL Gau, DJ Buehrer, Vague sets, IEEE Transactions on Systems Man and Cybernetics 23 (2) (1993) [13] H Bustince, P Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems 79 (1996) [14] W Buntine, T Niblett, A further comparison of splitting rules for decision-tree induction, Machine Learning 8 (1992) [15] SM Chen, A new approach to handling fuzzy decision making problems, IEEE Transactions on Systems Man and Cybernetics 18 (1988)