Oral Sessions Agenda Chemical Engineering I/ Fundamental and Applied Sciences I Koubai

14:45~16:15

Thursday, November 7

Session Chair: Prof. Yousef Saleh Al-Zeghayer

ICEAS-1633 Support Effects on Ethane Oxidation Catalyzed by MoVNb Catalyst Yousef Saleh Al-Zeghayer

King Saud University

Sulaiman Ibrahim Al-Mayman

King Abdulaziz City for Science and Technology

Abdulrhman Saleh Al-Awadi

King Saud University

Moustafa Aly Soliman

The British University in Egypt

ICEAS-1788 The preparation of Cu(In,Al)Se2 thin films using selenization of sputtering Cu-In-Al metal precursors for solar energy application Kong-Wei Cheng

Chang Gung University

Kei Hinaro

Chang Gung University

Yi Chiu

Chang Gung University

ICEAS-1693 Slip effect Study of 4:1 Contraction Flow with Rounded Corner Geometry for Newtonian Fluid Nawalax Thongjub

Chulalongkorn University

Bumroong Puangkird

King Mongkut’s Institute of Technology Ladkrabang

Vimolrat Ngamaramvaranggul

Chulalongkorn University

ICEAS-1764 The effect of slip boundary on the unsteady blood flow in 3D tubes Nathnarong Khajohnsaksumeth Curtin University Benchawan Wiwatanapataphee

Mahidol University

Yong Hong Wu

Curtin University

291

ICEAS-1779 Numerical Approximations of Average Run Length Sophana Somran

King Mongkut’s University of Technology North Bangkok

Saowanit Sukparungsee

King Mongkut’s University of Technology North Bangkok

Yupaporn Areepong

King Mongkut’s University of Technology North Bangkok

ICEAS-1985

Fuzzy rating score on the Likert scale Atchanut Rattanalertnusorn

Kasetsart University

Ampai Thongteeraparp

Kasetsart University

Winai Bodhisuwan

Kasetsart University

292

ICEAS-1985 Fuzzy Rating Score on the Likert Scale Atchanut Rattanalertnusorn Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand [email protected] Ampai Thongteeraparp Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand [email protected] Winai Bodhisuwan* Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand [email protected] The corresponding author: Winai Bodhisuwan Abstract This study presents a method for constructing new fuzzy rating scores on five-points Likert scale based on fuzzy set theory. New fuzzy rating scores are fuzzy linguistic variables: numerical rating scores associated with degree of membership or fuzzy numbers. This study designed five new fuzzy rating scores for each statement item, that is, around 1 ( 1 for strongly disagree), around 2 ( 2 for disagree), around 3 ( 3 for neither nor or neutral), around 4 ( 4 for agree) and around 5 ( 5 for strongly agree). For data collection, a new survey form is also designed based on five fuzzy rating scores. Each respondent can be easily assigned degree of membership to the agreement level in the new survey form. However, since the most of respondents assigned a partial degree of membership, thus we present a new decision tree based on probability as tool for helping recorder to manage the rest of degree of membership. Furthermore, when the respondent choose a fuzzy rating score in the survey form, we then transform fuzzy rating score into a real number. Thus, the defuzzification approach for transforming fuzzy rating score into crisp number is presented, namely the weighted mean method. An illustrated example is also provided. Finally, the useful conclusions is given. Keyword: Likert Scale, Fuzzy Rating Scores, Fuzzy Number, Triangular Fuzzy Number, Membership Function 1. Introduction A process of human making decision is complex and uncertain. Attitude is an important concept that is often used to understand and predict people's reaction to an object or change and how behaviour can be influenced [1]. The concept of attitude was founded and played major roles in many fields including psychology, social science and education. Some researchers were studied to measure attitude by construction a particular scale, which is used as an instrument for measuring subjective variables: attitudes, feelings, personal opinions, or word usage. The Likert scale is one of the popular rating scales used for measuring attitude. The original Likert scale was developed as a technique for measuring attitude in psychology by Likert [2] in 1932. The respondent is asked to indicate a degree of agreement and 318

disagreement with a series of statements. For example, each statement item has five response categories ranging from strongly disagree (SD), disagree (D), neither agree nor disagree (NN), agree (A) to strongly agree (SA). Each statement item can be assigned a numerical rating score match with the agreement level. For example, assigned number 1 for SD, 2 for D, 3 for NN, 4 for A and 5 for SA or others. In conventional Likert scale, when the respondent chosen the agreement level on the statement item, we collected the rating score associated with agreement level. For instants, the respondent chose agree (A) in any statement item means that the rating score is number four (4) on that statement item, but we do not know how much the respondent agree. In addition, when the two respondents given the same agreement level on the same statement item, we can not implied to the same degree of agreement (or disagreement). The problem is occurred because the degree of agreement (or degree of disagreement) on Likert scale is subjective to the respondents. On the other hand, the degree of agreement (or disagreement) is vagueness or fuzziness. To overcome above problem, a modified Likert scale based on fuzzy set theory is introduced by Li [3, 4]. He described the conventional Likert scale has several weakness and developed a new Likert scale based on fuzzy set theory. Based on his approach, the respondents can be assigned a degree of membership associated with the agreement level (or disagreement level) in the data collection process. This study we present a new method for constructing rating scores associated with fuzzy numbers on five-points Likert scale, namely fuzzy rating scores as shown in Section 2. A new survey form adapted from Li’s concept as shown in Section 3. The measurement of fuzzy rating scores is presented in Section 4, A demonstrated example is given in Section 5. Finally, the conclusions is provided in Section 6. 2. Methodology For Constructing Fuzzy Rating Scores Before we go to the construction method of fuzzy rating scores, the briefly concept of classical set theory and fuzzy set theory are presented as the following: In classical set theory, let U is an universe of discourse and S is a subset of U. If x is said to being in set S means that x has the fully membership in set S. Similarly, if x is said to not being in set S means that x has the null membership in set S. Note that the degree of membership can be fully or null membership. The partial membership is not permitted in classical set (or conventional set). In fuzzy set theory, a degree of membership can be more flexible than classical set because x can be has null membership, fully or partial membership in set S. The degree of membership is characterized by the membership function, S (x) , where 0  S (x)  1 . If S (x)  0 , then x is said to not being in set S. If S (x)  1, then x is said to fully membership in the set S. If

0  S (x)  1 , then x is said to partial membership in the set S. Thus, we can called set S to be fuzzy set (or fuzzy subset), denoted by S . This study we put a tilde symbol over the set or the number to refer to the fuzzy set or fuzzy number. Generally fuzzy number is fuzzy set (or fuzzy subset) which is normal and convex [5 ,6 ,7, 8]. In this moment, there are various types of membership function such as triangular, trapezoidal, sigmoid, normal membership function and etc. The most commonly used membership function is triangular membership function because it is simply implement to fuzzy number and easy to transform into real number. 319

The construction method of fuzzy rating scores can be presented as the following: Step 1. Define the linguistic variables. For example, on five-points Likert scale, the linguistic variables are agreement levels for the respondents, that is, strongly disagree ( R 1 ), disagree ( R 2 ), neither agree nor disagree ( R 3 ), agree ( R 4 ) and strongly agree ( R 5 ). Since linguistic variables are vagueness, thus the fuzzy rating variables are R1 , R 2 , R 3 , R 4 and R 5 , respectively . Step 2. Giving numerical rating scores associated with fuzzy rating variables in Step1. That is, setting fuzzy rating scores are 1, 2,3, 4,5 corresponding to fuzzy rating variables R1 , R 2 , R 3 , R 4 and R 5 , respectively. Step 3. Implementing membership function match with fuzzy rating scores. For convenience, triangular membership function is suitable because it is easy to implement and transform in to crisp number. Thus, letting R j is triangular fuzzy rating score for the jth agreement level (1 for SD, 2 for D, 3 for NN, 4 for A and 5 for SA), which is denoted by R j  (c j , j , rj ),  j  1, 2,3, 4,5 and its membership function can be expressed as

 x  (c j  j )  j   (c j  rj )  x  R j (x)   rj   0 ,   where c j , j , rj are the mode point (or middle respectively, and

j

, cj 

j

 x  cj

, c j  x  c j  rj otherwise, point), the left and right spread of R j ,

, rj  0, j . When the two spreads are equal, R j is called symmetric

triangular fuzzy number. By contrast, the two spreads are unequal, R j is called asymmetric triangular fuzzy number . The characteristics of triangular fuzzy rating score R as shown in Fig. 1.

Fig. 2 The characteristics of triangular fuzzy number R . Step 4. Setting the values (c j , j , rj ) of R j . This study thought about they are simply implementation and computation more than finding a proper membership functions. Thus, if fuzzy rating score ( R j ) as the symmetric triangular fuzzy number. Then the spectrum of 320

fuzzy rating scores can be shown in Fig. 2.

Fig. 2 The spectrum of fuzzy rating scores. As in Fig. 2, let R 1 , R 2 , R 3 , R 4 and R 5 are triangular fuzzy numbers, denoted by R1  (1, 0,1) , R 2  (2,1,1) , R 3  (3,1,1) , R 4  (4,1,1) and R 5  (5,1, 0) , respectively. The next section will be show a new survey form for the respondents in the process of data collection.

3. A New Survey Form on the Five-Points Likert Scale A new survey form is designed for the respondents to assigned the agreement level and degree of membership corresponding to the statement item. A new survey form based on the five-points Likert scale is shown in Table 1. In survey form, instruction for the respondents must be included, such as Instruction for the respondents: 1. Please choose only one agreement level . 2. Please assign a degree of membership between 0 and 1 to the chose level. 3. SD=strongly disagree, D=disagree, NN=neither agree nor disagree, A=agree and SA=strongly agree. Table 1: A new survey form on the five-points Likert scale. Statement Item Agreement level SD D NN A SA (1) (2) (3) (4) (5) 1. Item1 0.7 0.8 . . . n. Item n Overall Item The respondents is asked for choosing one of the agreement level and assigning a degree of membership between 0 and 1 to the chosen level. For example, the respondent Mr. X chose strongly disagree (SD) on statement Item1 and assigned a degree of membership is 0.7 means that the rest of degree of membership is 1-0.7=0.3 can be assigned to the others: disagree, neither nor, agree and strongly agree. Similarly, the respondent Mr. Y chose agree (A) on the same statement Item1 and assigned the degree of membership is 0.8 means that that the rest of membership degree is 0.2 can be assigned to the others: strongly disagree, disagree, neither nor and strongly agree. The problem will be occurred because how can we assigned the rest 321

of degree of membership to the others level. To overcome this problem, we designed a new decision tree based on probability as a tool for helping assigned the rest of membership degree. The designed decision tree based on probability is shown in Fig. 3

Fig. 3 The designed decision tree based on probability. As in Fig. 3, if the respondent chose strongly disagree (SD) and assigned a degree of membership is 0.7, then the rest of membership degree is 0.3 will be assigned to disagree (D) with probability is 1. In the other case, if the respondent chose disagree (SD) and assigned a degree of membership is 0.7, then the rest of membership degree is 0.3 will be assigned to disagree (D) and agree (A) with the same probability (p=0.5). That is, a half of the rest of degree of membership (0.15) is assigned to disagree and agree, respectively. Similarly, in the other cases. 4. Measuring Fuzzy Rating Scores In the context of the survey question, these fuzzy rating scores can not directly use for interpreting. They need to be defuzzified back to crisp values [4]. There are existence various defuzzification methods to scalar (real number) in fuzzy logic theory [5]. This study we modified the weighted mean method for transforming fuzzy rating score into crisp value as j u R j R j (u) S ,  R j (u) j

where u R j is the agreement level subject to fuzzy rating score R j and  R j (u) is a degree of membership of R j . An illustrated example will be presented in Section 5. 5. An Illustrated Example This example is designed for measuring fuzzy rating scores on the five-points Likert scale. Suppose we have only one statement item is “Do you agree with Thai government’s policy to prohibited using Liquefied Petroleum Gas (LPG) for a new car ? ”. The five response categories and its corresponding numerical rating scores are assigned as follows: 1 for strongly disagree (SD), 2 for disagree (D), 3 for neither agree nor disagree (NN), 4 for agree (A) and 5 for strongly agree (SA). For data collection, the partial survey form is designed as shown in Table 2. Suppose we have three respondents (Mr. A, B and C). They are asked to 322

choose the agreement level and assign a degree of membership for this statement item. Three respondents chose and assigned degree of membership as shown in Table 3. Table 2: A partial survey form on Thai government’s policy to prohibited using Liquefied Petroleum Gas (LPG) for a new car. Instruction to respondents: 1. Please choose only one agreement level. 2. Please assign a degree of membership degree between 0 and 1 to the chose level. 3. SD=strongly disagree, D=disagree, NN=neither agree nor disagree, A=agree and SA=strongly agree. Statement Item

Agreement level SD D NN A SA (1) (2) (3) (4) (5)

Do you agree with Thai government’s policy to prohibited using Liquefied Petroleum Gas (LPG) for a new car? Table 3: An example of responded data form some respondents on Thai government’s policy to prohibited using LPG for a new car. Statement Item Agreement level Do you agree with Thai government’s SD D NN A SA policy to prohibited using Liquefied (1) (2) (3) (4) (5) Petroleum Gas (LPG) for a new car? Mr. A 1.0 Mr. B 0.3 Mr. C 0.8 As in Table 3, each respondent data can be recorded as a pair of values: that is, a selected agreement level and degree of membership. For example, Mr. A’s response data is (5, 1.0), Mr. B’s response data is (5, 0.3) and Mr. C’s response data is (5, 0.8). According to the new decision tree based on probability in Section 3, the rest of degree of membership in each respondent can be managed as follows: For Mr. A, the indirect agreement level is agree level (A) with probability is 1. That is, we also can be obtained the indirect agreement level is (4, 0). Similarly, we obtained the indirect agreement level is (4, 0.7) from Mr. B and (4, 0.2). from Mr. C, respectively. Now we modified the weighted mean method in Section 4 for transforming fuzzy response of Mr. A, Mr. B and Mr. C back to crisp values as S

u A  A (u)  u SA SA (u) A (u)  SA (u)

where u A  4 and u SA  5 . For Mr. A, A (u)  0 and SA (u)  1 . For Mr. B , A (u)  0.7 and SA (u)  0.3 . For Mr. C,

A (u)  0.2 and SA (u)  0.8 By substituting these values into above formulae, thus the defuzzified values of Mr. A, Mr. B and Mr. C can be obtained as follows: 4(0)  5(1) 4(0.7)  5(0.3) 4(0.2)  5(0.8) SA   5 , SB   4.3 and SC   4.8 0 1 0.7  0.3 0.2  0.8 323

The summarized result of fuzzy rating scores is shown in Table 4. Table 4: The summarized result of the fuzzy rating scores. Statement Item Agreement level Traditional Fuzzy Rating Rating Score Scores Do you agree with Thai SD D NN A SA government’s policy to (1) (2) (3) (4) (5) prohibited using Liquefied Petroleum Gas (LPG) for a new car? Respondent 1 (Mr. A) 0 1.0 5 5 Respondent 2 (Mr. B) 0.7 0.3 5 4.3 Respondent 3 (Mr. C) 0.2 0.8 5 4.8 Average 5 4.70 In Table 4, fuzzy rating score of Mr. A is 5 which is the same as the traditional rating score (5) . For Mr. B, fuzzy rating score is 4.3 while the traditional rating score is 5. The last one is Mr. C, fuzzy rating score is 4.8 while the traditional rating score is 5. It is clearly to see that fuzzy rating score can be measured agreement (or disagreement) level more precise than the traditional rating score. 6. Conclusions In the traditional five-points Likert scale, the rating scores match with the agreement level is assigned by numerical values: 1 for strongly disagree (SD), 2 for disagree (D), 3 for neither agree nor disagree (NN), 4 for agree (A) and 5 for strongly agree (SA). The respondent is asked to choice the agreement level match with the numerical rating score. When the respondent chose agreement level as strongly disagree (SD), a numerical rating score is 1. Actually, the agreement levels (SD, D, NN, A, SA) are subject to the respondents or vagueness (fuzziness). To overcome this problem, the concept of the fuzzy set theory can be applied to manipulate the agreement levels and the rating scores. This study present a new construction method of fuzzy rating scores on the five-points Likert scale. A new survey form is designed for the respondent choose agreement level and assign a degree of membership match with that level in the process of data collection. Furthermore, a new decision tree based on probability is designed as a tool for helping a recorder assigned the rest of degree of membership into the indirect agreement level. This study we found that fuzzy rating score can be measured rating score more precise than the traditional rating score. Also, the method for transforming fuzzy rating score back into real number is not complex. For the future work, a package program will be developed for computing fuzzy rating score on four-points Likert scale or the others. Acknowledgments Authors grateful thank to Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani, for financial support.

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References Fishbein M, Ajzen I, Belief, Attitude, Intention and Behaviour: An Introduction to Theory and Research. Addison-Wesley, London, 1975. Likert R, A Technique for the Measurement of Attitudes. Archives of Psychology, 1932, 140: 1-55. Li Q, A novel Likert scale based on fuzzy sets theory. Expert Systems with Applications, 2013, 40: 1609-1618. Li Q, A new Likert Scale Based on Fuzzy Sets Theory. Ph.D. dissertation, University of Connecticut, USA, 2010. Ross T J, Fuzzy Logic with Engineering Applications. John Wiley and Sons, Singapore, 2010. Zimmermann, H J, Using fuzzy sets in operational research. European Journal of Operational Research, 1983, 13: 201-216 Zadeh, L A, The concept of a linguistic variable and its application to approximate resoning, Information Sciences, 1975, 8: 199-249 Zadeh, L A, Fuzzy sets. Information and Control, 1965, 6: 338-353.

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