1. 1 Application of a Fuzzy MCDM Model to the Evaluation and Selection of Smart Phones Advisor:Prof. Chu, Ta-Chung Student: Chen, Chih-kai

2. 2 OUTLINE INTRODUCTION LITERATURE REVIEW FUZZY SET THEORY MODEL ESTABLISHMENT NUMERICAL EXAMPLE CONCLUSIONS

3. 3 Background and Motivation Why We Apply FMCDM Research Objectives Research Framework INTRODUCTION

4. 4 Background and Motivation According to Gartner, International Research and Consulting: 1. In the third quarter of 2010, worldwide mobile phone sales volume of 417 million represented the growth of 35% over the same period in 2009. 2. In addition, smart phone sales volume is more substantial in the third quarter of 2009 which grew 96%. 3. The proportion of mobile phone sales volume has slightly increased to 19.3%.

5. 5 The prices of the mobile phones continue to lower and the market tends to be saturated, the manufacturers cannot get as high gross margin as they did in the past. Therefore, manufacturers have begun to research and produce smart phones. The stereotype about the smart phones: 1.These devices are just for the businessmen. 2.It’s expensive. 3.Interfaces are too incomprehensible.

6. 6 Why We Apply FMCDM Evaluating smart phone many criteria (or factors) need to be considered. Different decision-makers also have different thoughts about the weight of each criterion. evaluating smart phone QuantitativeQualitative HardwarePrice Brand Awareness of Smart Phone Operating Systems Number of Applications Security

7. 7 Research Objectives The objectives of this study are listed as follows: 1. Smart phone selection related to literature is investigated. 2. Criteria for selecting smart phones are analyzed. 3. A fuzzy MCDM approach is established. 4. A total relative area for ranking fuzzy numbers is suggested. 5. A numerical example is used to demonstrate the computational process of the proposed model.

8. 88 Research Framework Chapter 1 Introduction Chapter 2 Literature Review Chapter 3 Fuzzy Set Theory Chapter 4 Model Establishment Chapter 5 Numerical Example Chapter 6 Conclusion

9. 9 LITERATURE REVIEW Definition of Mobile Phone What is a System of Smart Phone The overview of the system development of the smart phone Criteria Assessment Related literatures on smart phones Related Works on FMCDM Fuzzy Number Ranking Criteria Assessment

10. 10 Definition of Mobile Phone Feature Phones Smart Phones

11. 11 Feature Phones Feature phone has its own mobile phone manufacturer’s operating system (OS), which has a basic audio and video call beside the additional features (e.g. taking photos, sending text message, listening to music, etc.) but it is not allowed to install or remove software (e.g. remove preset program or install GPS software). However, if the phone supports JAVA and BREW, it is able to install applications. The software being developed through the two systems is not user-friendly.

12. 12 Smart Phones Su (2009) Smart phone is a phone equipped with function of phone and PDA. Yang (2009) Smart phones are developed because industrial technology progresses and consumers require integrating multiple requirements into one device. Hsu (2004) In addition to the original function of voice communications, a mobile phone should also be equipped with an open operating system, and sufficient processing power, allowing users to choose application freely and expand multiple or limitless functions.

13. 13 According to the above-mentioned definitions of smart phones, this study defined “Smart Phone” as follows: 1.Opening source operating system platform. 2. Strong support on the third party's applications, and is allowed to install or remove software freely. 3. A strong hardware performance and faster processing power.

14. 14 What is a System of Smart Phone Alter (2002) Operating System (OS)  “The system that controls the execution of all other programs, communication with peripheral devices and use of memory and resources.” Malykhina (2007) OS  “the heart of the smart phone, it determines a phone's features, performance, security, and application installation.” 14

15. 15 The overview development of the smart phone According to Gartner's statistics, the leading market of smart phone operating system:

16. 16 Related literatures on smart phones Yang (2009), “ The Development Trend Analysis of Smart Phone Industry”, he designs an expert question- naire and interviews with 7 experts.  operating interface  entertainment platform  mobile business  specification of software and hardware.

17. 17 Lin and Ye (2009), “ Operating System Battle in the Ecosystem of Smart phone Industry”, they adopt concept of Food Web to explain ecosystem of various smart phone OS. They found out:  device maker  third-party application developer are two key sources.

18. Information Week (2007), “Survey of Emphasized Functions of Smart phones towards 325 Experts in Related Field”. The results demonstrated that security and easy integration with PC obtain the first and second place respectively. Gizmodo (2008), “Smart phone OS Comparison Chart”. 17 functions are listed in a table and the presence and absence of each function are compared. 18

19. Many works investigated smart phone operating system as the research object, however, these works cannot offer consumers a method to evaluate and select smart phones. Most importantly, when consumers choose to buy smart phones, they will usually consider both hardware and operating system. This thesis proposes a fuzzy multiple criteria decision making approach to comprehensively consider criteria in hardware and operating system in order to help consumers evaluate and select smart phones. 19

20. Related literature on fuzzy MCDM In 1970, Bellman and Zadeh introduced fuzzy set theory to multi-criteria decision making, which involved fuzzy decision analysis concepts and models for solving the problem of uncertainty in decision-making. Since then, the fuzzy multiple criteria decision making has resulted in many researches. Fuzzy numbers can be used to better describe suitability of alternatives versus qualitative criteria under fuzzy multiple criteria decision making environment. 20

21. 21 Fuzzy MCDM is mainly divided into two categories: 1.fuzzy multiple-objective decision-making: It is mainly used in the "planning; design aspects ". 2.fuzzy multiple criteria (attributes) decision-making: It is mainly used in the "assessment; selection aspects".

22. 22 Chang et al. (2009) applied the fuzzy multi-criteria decision making method in enterprise organization to establish the key influential factors for the success of knowledge management. Chou (2007) used fuzzy multiple criteria decision making method to resolve the selection problem of transshipment container port in marine transportation industry.

23. 23 Fuzzy Number Ranking In fuzzy multiple criteria decision making, the final evaluation values are usually still fuzzy numbers. A ranking method is needed to transform these final fuzzy evaluation values into crisp values for decision making. At present, there are many defuzzification methods which have been investigated for ranking fuzzy numbers. 23

24. 24 Some methods are briefly introduced as follows: Liou and Wang (1992) introduced a total integral value generated by the left and right integral values of a fuzzy number for ranking fuzzy numbers; Chen and Hwang (1992) proposed ranking fuzzy numbers by preference relations, the average of fuzzy number and degree, fuzzy rating, and linguistic terms; Abbasbandy and Hajjari (2009) presented a new approach for ranking trapezoidal fuzzy numbers based on left and right spreads at some α-levels of trapezoidal fuzzy numbers; Farhadinia (2009) proposed a new approach to rank fuzzy numbers based on the concept of lexicographical ordering in order to provide decision makers algorithm in a simple and efficient way. 24

25. 25 In this research, we suggest total relative area to rank the final fuzzy numbers, and it is developed based on the concept of Chen’s (1985) maximizing set and minimizing set which is one of the most frequently used methods for the problems under fuzzy MCDM environment. 25

26. 26 Criteria Assessment Evaluation criteriaNatureLiterature source Qualitative brand awareness of smart phone C1C1 BenefitThis Study brand awareness of OS C2C2 BenefitJ.D. Power(2010) Designs C3C3 BenefitJ.D. Power(2010) Security C4C4 BenefitJakajima (2008) Operability C5C5 BenefitJakajima (2008) Entertainment C6C6 BenefitSu (2009) Execution efficiency C7C7 BenefitGizmodo (2009)

27. 27 Quantitative Screen size C8C8 BenefitThis Study Camera resolution C9C9 BenefitThis Study Number of applications C 10 BenefitLin and Ye (2009) Price of applications C 11 CostDistimo (2010) Price C 12 CostThis Study Weight C 13 CostThis Study

28. 28 FUZZY SET THEORY Fuzzy Sets Fuzzy Numbers α-cut Arithmetic Operations on Fuzzy Numbers Linguistic Values

29. 29 Fuzzy Set The fuzzy set A can be expressed as: (3.1) where U is the universe of discourse, x is an element in U, A is a fuzzy set in U, is the membership function of A at x. The larger, the stronger the grade of membership for x in A.

30. 30 Fuzzy Numbers A real fuzzy number A is described as any fuzzy subset of the real line R with membership function which possesses the following properties (Dubois and Prade, 1978): (a) is a continuous mapping from R to [0,1]; (b) (c) is strictly increasing on [a,b]; (d) (e) is strictly decreasing on [c,d]; (f) where, A can be denoted as.

31. 31 The membership function of the fuzzy number A can also be expressed as: (3.2) where and are left and right membership functions of A,respectively.

32. 32 α-cut The α-cuts of fuzzy number A can be defined as: (3.3) where is a non-empty bounded closed interval contained in R and can be denoted by, where and are its lower and upper bounds, respectively.

33. 33 Arithmetic Operations on Fuzzy Numbers Given fuzzy numbers A and B,, the α-cuts of A and B are and respectively. By interval arithmetic, some main operations of A and B can be expressed as follows (Kaufmann and Gupta, 1991):  (3.4)  (3.5)  (3.6)  (3.7)  (3.8)

34. 34 Linguistic Variable According to Zadeh (1975), the concept of linguistic variable is very useful in dealing with situations which are complex to be reasonably described by conventional quantitative expressions. A 1 =(0,0,0.2)=Unimportant A 2 =(0.1,0.3,0.5)= Between Unimportant and Important A 3 =(0.3,0.5,0.7)=Important A 4 =(0.5,0.7,0.9)=Very important A 5 =(0.8,1,1)=Absolutely important Figure 3.1. Linguistic Values and Fuzzy Numbers for Degree of Importance

35. 35 MODEL DEVELOPMENT Average Importance Weights Aggregate Ratings of Alternatives versus Qualitative Criteria Normalize Values of Alternatives versus Quantitative Criteria Aggregate the Ratings and Weights Rank Fuzzy Numbers

36. 36 Model Development decision makers, candidate of smart phones, selected criteria, In model development process, criteria are categorized into three groups:  Benefit qualitative criteria:  Benefit quantitative criteria:  Cost quantitative criteria:

37. 37 Average Importance Weights

38. 38 Aggregate Ratings of Alternatives versus Qualitative Criteria

39. 39 Normalize Values of Alternatives versus Quantitative Criteria is the value of an alternative versus a benefit quantitative criterion and cost quantitative criterion. denotes the normalized value of (4.3) For calculation convenience, assume

40. 40

41. 41

42. 42 When applying Eq. (4.8) to Eq.(4.4), three equations are developed:

43. 43 To simplify equation, assume:

44. 44 By applying the above equations, Eqs. (4.9)-(4.11) can be arranged as Eqs. (4.12)-(4.14) as follows:

45. 45 Applying Eqs.(4.12)-(4.14) to Eq.(4.4) to produce Eq.(4.15): Assume:

46. 46 By applying the above equations, Eqs. (4.15) can be arranged as Eqs. (4.16) and (4.17) as follows: The left and right membership function of T i can be obtained as shown in Eq. (4.18) and (4.19) as follows:

47. 47 Rank Fuzzy Numbers In this research, we applied total relative area to rank the final fuzzy numbers, and it is developed based on the concept of Chen’s (1985) maximizing set and minimizing set.

48. 48 Using Chen’s maximizing set and minimizing set on the given sets of examples, we can see three rankings for the same alternatives. To resolve the inconsistency problem above, modification was made to Chen’s ranking method.

49. 49 Definition 1 The maximizing set M is a fuzzy subset with f M as (4.20) The minimizing set N is a fuzzy subset with f N as (4.22) Where usually k is set to 1.

50. 50 Figure 4.1. Total Relative Area

51. 51 By applying the new method, we can see that the rankings have changed and are now consistent.

52. Compare the Chen’s (2010) maximizing area and minimizing area and the total relative area method by changing values of A 2. Using Chen’s maximizing area and minimizing area on the given sets of examples, we can see three rankings for the same alternatives as shown in Table 4.6. Table 4.6 Maximizing area and minimizing area ranking outcomes The Chen’s (2010) method have the inconsistency problem. 52 ExampleA1A1 A2A2 A3A3 A4A4 Ranking 1(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(8, 9, 10)A1=A2A1=A2 2(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(6, 7, 8)A1>A2A1>A2 3(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(10, 11, 12)A1<A2A1<A2

53. By applying the total relative area method, we can see that the rankings have changed and are now consistent as shown in Table 4.8. 53 ExampleA1A1 A2A2 A3A3 A4A4 Ranking 1(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(8, 9, 10) A1>A2A1>A2 2(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(6, 7, 8) A1>A2A1>A2 3(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(10, 11, 12) A1>A2A1>A2 Table 4.8 Total relative area ranking outcomes

54. Using Liou and Wang method on the given sets of examples, we can see three rankings for the same alternatives as shown in Table 4.10. According to Table 4.10, the rankings are consistent; therefore, the feasibility of this model can be demonstrated. 54 ExampleA1A1 A2A2 A3A3 A4A4 Ranking 1(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(8, 9, 10) A1>A2A1>A2 2(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(6, 7, 8) A1>A2A1>A2 3(3, 5, 7)(41/20, 5, 55/8)(2, 3, 5)(10, 11, 12) A1>A2A1>A2 Table 4.10 The Liou and Wang method ranking outcomes

55. 55 is developed as follows: (4.29)

56. 56 is developed as follows: (4.30)

57. 57 is developed as follows: (4.33)

58. 58 is developed as follows: (4.34)

59. 59 By equations(4.29) ， the area, denoted as: (4.31) = equations(4.29)

60. 60 By equations(4.30) ， the area, denoted as: (4.32) = equations(4.30)

61. 61 By equations(4.33) ， the area, denoted as: (4.35) = equations(4.33)

62. 62 By equations(4.34) ， the area, denoted as: (4.36) =equations(4.34)

63. 63 By equations (4.31),(4.32),(4.35)and(4.36), the total area, denoted as: (4.37)

64. 64