許多學者已經利用統計方法進行服務品質的評估研究，然而面對包含語意變數的問題時，統計方法應用在此類服務品質的評估時有其困難。因此，我們引進模糊評價系統作為處理此類問題的方法。在生產批量方面，許多文獻均將彈性與生產批量模式中的三個變數：單位時間的平均需求、相對準備時間、單位生產成本，視為固定單一數值以求取最佳解。然而，在實際的生產計畫期間，這些變數會因為未來的不確定性及需求的變動而有些少許的波動。因此，應用模糊評價系統以求解此類問題比較能夠和實際情況相吻合。
本論文有三個相關連的目標：第一，建立模糊評價系統以處理服務品質評估的問題。第二，使用新的模糊區間方法以建立模糊總成本函數，並進而求取彈性與生產批量模式的最佳解。第三，比較使用模糊評價系統與普通未模糊化方法計算結果的差異。本論文包含五章：第一章簡介本論文的研究動機及架構。第二章建構可應用在服務品質評估的模糊評價系統。第三章則提出另一種模糊評價系統，同樣可應用在評估服務品質。在第四章中，考慮變數的不確定性，因此，使用新的模糊區間方法以建立模糊總成本函數，並求取模式的最佳解。在本章中，將參數經由統計方法轉換為區間，再由這些區間導出總成本函數的區間，並進而形成三角模糊數，最後則利用帶符號距離法及重心法分別求出模糊觀點下的最佳解。此方法有別於以往將函數內參數模糊化的方式。最後一章則為結論，主要是針對各章的內容加以比較並總結一些重要的觀點及提出未來的研究方向。

There are a lot of literatures investigating the problem of the evaluation of service quality by applying the statistical method. However, because of the problems that consist of linguistic variables, the statistical method becomes no more efficient for evaluating service quality; the fuzzy evaluation system is therefore introduced to deal with these problems. Many literatures considered the average demand of per unit time, relative duration of setup, and unit cost of production as fixed values in flexibility and product variety in lot-sizing model. However, in reality, these variables involve uncertainty due to the nature of future production processes and fluctuations in demand. Therefore, it is a good alternative way to apply the fuzzy evaluation system to consider the problems.
This dissertation has three folds of objectives that are correlated: Firstly, it establishes fuzzy evaluation system to handle the assessment of service quality. Secondly, this study formulates a fuzzy total cost function by using a new interval fuzzification method for solving the product lot-sizing problem. And thirdly, it compares the results of fuzzification method among the crisp and the statistical method. This dissertation comprises of five chapters. In chapter 1, an introduction about the study is given. Chapter 2 presents the fuzzy evaluation system applying on assessment service quality. While in chapter 3, another fuzzy evaluation system applying on evaluating service quality is proposed. It proposes the two-stage evaluation structure which differs from that of chapter 2. In chapter 4, a new fuzzification method for solving the product lot-sizing problems is given. Furthermore, an interval fuzzification method which totally differs from the parameter fuzzification method is introduced. In the last chapter, some comparisons among the differences of fuzzification methods given in chapters 2–4 are made and some essential conclusions are also given.

CONTENTS
LIST OF TABLES........................................	III
LIST OF FIGURES...............................................	IV
CHAPTER 1. INTRODUCTION..........................................	1
1.1	Motivation...................................	1
1.2	Fuzzy Set Theory................................................	2
1.3	Dissertation Overview..............................................	3
CHAPTER 2. FUZZY EVALUATION OF SERVICE QUALITY........	5
2.1	Literature Review............................	5
2.2	Preliminaries................................	7
2.3	Methodology..................................	16
2.4	Numerical Example............................	22
2.5	Summary......................................	25
CHAPTER 3. A MEASURE OF SERVICE QUALITY OF HOTEL......	27
3.1	Evaluation Model.............................	28
3.1.1	 Evaluation Factors of Service Quality of Hotel.................................................	28
3.1.2	 Fuzzy Evaluation Procedure...................28
3.2	Numerical Example............................	36
3.3	Discussion and Summary.......................	39
CHAPTER 4. FUZZY FLEXIBILITY AND PRODUCT VARIETY IN 
	LOT-SIZING...................................	45
4.1	Introduction.................................	45
4.2	Fuzzy Flexibility and Product Variety in Lot-sizing................................................	47
4.2.1	Crisp Case...................................	47
4.2.2	Fuzzy Problem and Optimal Solution without Fuzzification of Crisp Total Cost Function............	49
4.2.2.1	Defuzzification of Fuzzy Total Cost by Using Signed Distance.......................................	51
4.2.2.2	Defuzzification of Fuzzy Total Cost by Using Centroid...............................................56
4.3	Numerical Examples...........................	58
4.4	Discussion...................................	64
4.4.1	The Comparisons between Optimal Solutions by Using Signed Distance for Defuzzification with That of Defuzzification by Using Centroid.....................	64
4.4.2	The Problem (in Eqs. (4.8)–(4.9)) of Crisp Case Is a Special Case of Theorems 4.1, 4.2 and Theorems 4.3, 4.4....................................................65
4.4.3	Fuzzification of Fixed Cost..................	66
4.5	Summary......................................	66
4.5.1	The First Step of Fuzzification..............	66
4.5.2	The Second Step of Fuzzification.............	67
4.5.3	The Defuzzification in Third Step of Fuzzification.........................................	68
CHAPTER 5. CONCLUSIONS AND FUTURE WORK................	70
5.1 Conclusions.......................................	70
5.1.1	The Fuzzification Problems of Chapters 2 and 3.....................................................	70
5.1.2	The Fuzzification Problems of Chapter 4...... 74
5.2 Future Work.......................................	78
REFERENCES............................................	80
APPENDIX..............................................	85

LIST OF TABLES
Table 2.1 Linguistic Terms Correspond to Triangular Fuzzy Numbers................................................18
Table 2.2 The Assessment Results of Relative Importance of All Evaluation Factors from m Customers...............	19
Table 2.3 The Assessment Results of Relative Importance of All Evaluation Factors from 1000 Customers............	23
Table 2.4 The Relative Weight of Each Evaluation Factor	..............................................24
Table 2.5 The Statistical Analysis of Rating the Score of Evaluation Factor.....................................	25
Table 2.6 The Aggregate Triangular Fuzzy Number of Evaluation Point and the Aggregate Evaluation Point in the Fuzzy Sense..........................................	26
Table 3.1 Evaluation Factors of Hotel’s Service Quality	............................................  30
Table 3.2 The Frequency of Assessment of Relative Importance of Evaluation Factors from 1000 Customers..	38
Table 3.3 The Mean and Variance of Evaluation Factors from 1000 Customers.......................................	39
Table 3.4 The Related Quantifier of Point of Evaluation Factors..............................................	40
Table 4.1(a) Illustration of Theorem 4.2 and Theorem 4.4 of Example 4.1..........................................	60
Table 4.2(a) Illustration of Theorem 4.2 and Theorem 4.4 of Example 4.2..........................................	61
Table 4.3(a) Illustration of Theorem 4.2 and Theorem 4.4 of Example 4.3...........................................	62
Table 4.1(b) The Relative Percentages for Table 4.1(a)	63
Table 4.2(b) The Relative Percentages for Table 4.2(a)	63
Table 4.3(b) The Relative Percentages for Table 4.3(a)	63
 
LIST OF FIGURES
Figure 2.1 Case 1....................................	15
Figure 2.2 Case 2....................................	15
Figure 2.3 Triangular Fuzzy Number L1, L2,...Ln......	16
Figure 2.4 Fuzzy Numbers of q........................	18
Figure 2.5 Fuzzy Numbers of VL, L, M, H, and VH......	18
Figure 3.1 Statistical Data according to yij is skew to the Right................................................	41
Figure 3.2 Statistical Data according to yij is skew to the Left.................................................	42
Figure 4.1 Change of L ...............................	56
Figure A1. Sets of L  and U ...........................	86

REFERENCES 
[1]	Bandemer, H. and Gottwald, S. (1995). Fuzzy Sets, Fuzzy Logic, Fuzzy Methods, with Application. N.Y.: John Willy & Sons
[2]	Bellman, R. E. and Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Sciences, Vol. 17, No. 4, 141-164.
[3]	Chang, Y. H. and Yeh, C. H. (2002). A survey analysis of service quality for domestic airlines. European Journal of Operational Research, Vol. 139, 166-177.
[4]	Chen, S. H. (1985). Operations on fuzzy numbers with function principle. Tamkang Journal of Management Sciences, Vol. 6, No. 1, 13-26.
[5]	Chen, S. H. and Hsieh, C. H. (2000). Representation, ranking, distance, and similarity of L-R type fuzzy number and application. Australian Journal of Intelligent Information Processing Systems, Vol. 6, No. 4, 217-229.
[6]	Chen, S. J. and Huang, C. L. (1992). Fuzzy Multiple Attribute Decision Making Method and Application. A state-of-the-art Survey. N.Y.: Springer-Verlag.
[7]	Chien, C. and Tsai, H. H. (2000). Using fuzzy numbers to evaluate perceived service quality. Fuzzy Sets and Systems, 116(2), 289-300.
[8]	Churchill, G. A. and Jr. Peter, J. P. (1998). Marketing-Creating value for customers, Boston: McGraw-Hill.
[9]	Denis, H. and Gary, A. (1996). Service quality and business performance in the UK hotel industry. International Journal of Hospitality Management, Vol. 15, No. 3, 283-298.
[10]	Fick, G. R. and Ritchie, J. B. R. (1991). Measuring service quality in the travel and tourism industry. Journal of Travel Research, Fall, 2-9.
[11]	Gronroos, C. (1983). Strategic Management and Marketing in the Service Sector. Cambridge, Mass.: Marketing Science Institute.
[12]	Gronroos, C. (1990). Service Management and Marketing: Managing the moments of truth in service competition. Lexington, MA.: Lexington Books.
[13]	Hadley, G. and Whitin, T. (1963). Analysis of Inventory System, New Jersey: Prentice Hall, Englewood Cliffs.
[14]	Hsieh, C. H. (2002). Optimization of fuzzy production inventory models. Information Sciences, Vol. 146, 29-40.
[15]	Hsieh, S. and Chiang, C. C. (2002). Manufacturing-to-sale planning model for fuel oil production. The International Journal of Advanced Manufacturing Technology, Vol. 18, 303-311.
[16]	Huang, T. T. and Huang, W. T. (2005). Using signed distance and order statistics method for fuzzy evaluation of service quality. Journal of Information & Optimization Sciences, Accepted.
[17]	Huang, T. T. and Huang, W. T. (2005). Using statistical data and signed distance of fuzzy aggregate evaluation method on application of measuring service quality of hotel. International Journal of Information and Management Sciences, Vol. 16, No.3, 17-35.
[18]	Huang, T. T., Huang, A. D., and Li, H. T. (2002). An application of fuzzy theory on service quality of department store. In Proceedings of the Conference of Modern Administration Technology, TakMing College, Taipei City. (In Chinese).
[19]	Kahne, S. (1975). Aprocedure for optimizing development decisions. Automatica, Vol. 11, 261-269.
[20]	Kaufmann, A. and Gupta, M. M. (1991). Introduction to Fuzzy Arithmetic Theory and Applications, New York: Van Nostrand Reinhold.
[21]	Klir, G. J. and Yuan, Bo. (1995). Fuzzy Sets and Fuzzy Logic, New Jersey: Prentice Hall, Upper Saddle River.
[22]	Klir, G. J. St. Clair, Ute and Yuan, Bo. (1997). Fuzzy Set Theory-Foundations and Applications, New Jersey: Prentice Hall, Upper Saddle River.
[23]	Kotler, P. (1997). Marketing Management: Analysis, Planning, Implementation and Control. 6th ed. New Jersey: Prentice-Hall, Englewood Cliffs.
[24]	Lee, H. M. and Yao, J. S. (1998). Economic production quantity for fuzzy demand and fuzzy production quantity. European Journal of Operational Research, Vol. 109, 203-211.
[25]	Lehtinen, U. and Lehtinen, J. R. (1982). Service Quality: A Study of Quality Dimensions. Helsinki: Service Management Institute.
[26]	Lin, D. C. and Yao, J. S. (2000). Fuzzy economic production for production inventory. Fuzzy Sets and Systems, Vol. 111, 465-495.
[27]	Michael, J. W. and William, J. S. (2001). Marketing, 12th Ed. New York: McGrow-Hill.
[28]	Ouyang, L. Y. and Yao, J. S. (2002). A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand. Computers & Operations Research, Vol. 29, 471-487.
[29]	Parasuraman, A. Zeithaml, V. and Berry, L. (1985). A conceptual model of service quality and its implications for future research. Journal of Marketing, Vol. 49, 41-50.
[30]	Parasuraman, A. Zeithaml, V. and Berry, L. (1988). SERVQUAL: A multiple-item scale for measuring consumer perceptions of service quality. Journal of Retailing, Vol. 64, 12-40.
[31]	Parsons, J. A. (1966). Multiproduct lot size determination when certain restrictions are active. Journal of Industrial Engineering, Vol. 27, 360-365.
[32]	Pu, P. M. and Liu, Y. M. (1980). Fuzzy topology 1, neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematics Analysis and Applications, Vol. 76, 571-599.
[33]	Sasser, E. W. Olsen, P. R. and Wyckoff, D. D. (1978). Management of Service Operations. Boston: Allyn and Bacon.
[34]	Spence, A. M. and Porteus, E. L. (1987). Setup reduction and increased effective capacity. Management Science, Vol. 35, 1291-1301.
[35]	Tsaur, S. H. Chang, T. Y. and Yen, C. H. (2002). The evaluation of airline service quality by fuzzy MCDM. Tourism Management, Vol. 23, 107-115.
[36]	Wang, R. C. and Fang, H. H. (1997). Aggregate production planning with multiple objectives in a fuzzy environment. European Journal of Operational Research, Vol. 133, 521-536.
[37]	Wang, R. C. and Fang, H. H. (1997). Aggregate production planning with fuzzy variables. International Journal of Industrial Engineering, Vol. 8, 37-44.
[38]	Website. (2002). www.dgbas.gov.tw/dgbas03/bs3/report/doc/N910920.doc. Directorate General of Budget Accounting and Statistics Executive Yuan, ROC. (In Chinese).
[39]	Xavier de Groote. (1994). Flexibility and product variety in lot-sizing models. European Journal of Operational Research, Vol. 75, 264-274.
[40]	Yao, J. S. and Lin, F. T. (2002). Constructing a fuzzy flow-shop sequencing model based on statistical data. International journal of Approximate Reasoning, Vol. 29, No. 3, 471-487.
[41]	Yao, J. S. and Wu, K. M. (2000). Ranking fuzzy number based on decomposition principle and signed distance. Fuzzy Sets and Systems, Vol. 116, 275-288.
[42]	Yao, J. S. and Yu, M. M. (2004). Decision making based on statistical data, signed distance and compositional rule of inference. International journal of Uncertainty Fuzziness and Knowledge-based Systems, Vol. 12, No. 2, 161-190.
[43]	Yao, J. S. Huang, W. T. and Huang, T. T. (2005). Fuzzy flexibility and product variety in lot-sizing. Journal of Information Science and Engineering, Accepted.
[44]	Yeh, C. H. and Kuo, Y. L. (2003). Evaluating passenger services of Asia-Pacific international airports. Transportation Research Part E, Vol. 39, 35-48.
[45]	Yu, M. M. and Yao J. S. (2001). Modification of concordance analysis based on statistical data and ranking of level 1-  fuzzy numbers. International journal of Uncertainty Fuzziness and Knowledge-based Systems, Vol. 9, No. 3, 313-340.
[46]	Zadeh, L. A. (1965). Fuzzy sets. Information and Control, Vol. 8, 338-353.
[47]	Zimmermann, H. J. (1991). Fuzzy Set Theory and Its Applications, Boston: Kluwer Academic Publishers. 2nd ed.