進階搜尋


下載電子全文  
系統識別號 U0026-2611201318050000
論文名稱(中文) 直覺式模糊集評估指標與區間值排序函數
論文名稱(英文) Developing Measures and Interval-valued Ranking Functions based on Intuitionistic Fuzzy Sets
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 1
出版年 102
研究生(中文) 涂謙誠
研究生(英文) Chien-Cheng Tu
學號 R38981073
學位類別 博士
語文別 英文
論文頁數 83頁
口試委員 指導教授-陳梁軒
口試委員-王泰裕
口試委員-謝中奇
口試委員-陳世彬
召集委員-陳振明
中文關鍵字 直覺式模糊集  區間值直覺式模糊集  評估指標  雙重兩極性  排序函數 
英文關鍵字 intuitionistic fuzzy set  interval-valued intuitionistic fuzzy set  measure  dual bipolar  ranking function 
學科別分類
中文摘要 在Atanassov(1986)所提出的直覺式模糊集(IFS)的諸多評估指標之中,如鄰近度,基數,距離,相似度,關聯性以及評估函數,經常可應用於處理許多相關問題;然而區間值的資料型態似乎能廣義的使用於IFS,因而衍生出區間值直覺式模糊集(IvIFS)的排序議題,其困難來自於其同時具有區間值的歸屬程度與區間值的非歸屬程度之特殊性。本論文提出了迥異於過去觀點的上述IFS相關評估指標定義以及IvIFS排序函數。首先提出的是基於自身IFS相較於其他的IFS所呈現出來的相對程度所定義的四項函數,稱之為優越性(superiority),非劣等性(non-inferiority),明確性(determinacy)與非猶豫性(non-hesitancy),藉此以組成了所謂雙重兩極性(dual bipolar)尺度,也就是介於優越至於非劣等以及明確至於非猶豫的雙重尺度。此時根據雙重兩極性尺度所提出的直覺式模糊集(IFS)評估指標便根據相關公理加以定義。更憑藉圖形的呈現加以驗證存在於過去與本論文提出的評估指標之間的一致程度。其次此種以IvIFS表示的排序函數乃是藉由其自身凌駕於或者是不被凌駕於其它的IvIFS作為考量依據,而且是以IFS的雙重屬性與凌駕(dominance)概念為基礎。此排序函數的設計除了使用IFS之歸屬度與非歸屬度的臨界值之外,還將IvIFS之間以彼此相對的凌駕程度納入考量。此外本論文針對兩個IvIFS之間一旦滿足四項提出之排序函數就形成特有的偶配對(dual couple)關係加以定義,且證明提出的五項排序函數能夠完全區別所有之IvIFS,所提出的評估指標以及排序函數皆能夠顯現出IFS與IvIFS的獨有特質。此外,藉由配置不同程度之雙重兩極性尺度與不同比例的相對凌駕程度將決策者態度植入IFS評估指標與IvIFS排序函數。最終藉由四個範例驗證IFS評估指標與IvIFS排序函數的應用性與效能展現。
英文摘要 Measures of intuitionistic fuzzy sets (IFSs), such as subsethood, cardinality, distance, similarity, correlation, and evaluation functions, are often used in application problems. The interval-valued data used by IFSs can express the comprehensive uncertainty of IFSs. However, the ranking of interval-valued intuitionistic fuzzy sets (IvIFSs) is difficult since they include the interval values of membership and non-membership. This research investigates such measures of IFS and ranking functions for IvIFSs from various perspectives. Firstly, based on the relative relations of an IFS to other IFSs, four functions, namely superiority, non-inferiority, determinacy, and non-hesitancy, are constructed, which consist of dual bipolar scales, namely (superiority, non-inferiority) and (determinacy, non-hesitancy). Then, the proposed measures of IFSs are axiomatically defined using the dual bipolar scales. Geometrical demonstrations in general show consistency between the proposed measures and existing ones. Secondly, the proposed ranking functions consider the degree to which an IvIFS dominates and is not dominated by other IvIFSs. Based on the bivariate framework and the dominance concept, the functions incorporate not only the boundary values of membership and non-membership, but also the relative relations among IvIFSs in comparisons. The relationship for two IvIFSs that satisfy the dual couple is defined based on four proposed ranking functions. Importantly, the five proposed ranking functions can achieve a full ranking for all IvIFSs. Therefore, the proposed measures and ranking functions can highlight the significant features of IFSs and IvIFSs. In addition, the attitude of decision-makers is also implanted in measures of IFSs and ranking functions of IvIFSs to allocate the importance in the dual bipolar scales and the various kinds of dominance respectively. Four examples are used to demonstrate the applicability and performance of the proposed measures of IFSs and ranking functions of IvIFSs.
論文目次 摘 要 I
Abstract II
Acknowledgements III
List of Tables VI
List of Figures VII
Chapter 1 Introduction 1
1.1 Background 1
1.2 Measures and ranking functions 3
1.3 Motivation and objectives 5
1.4 Organization 5
Chapter 2 Preliminaries 7
2.1 Basic definitions 7
2.2 Measures and Operators 10
2.3 Ranking functions of IvIFSs 14
Chapter 3 Dual bipolar measures of IFSs 20
3.1 Motivations 20
3.2 Measures 23
3.2.1 Subsethood for IFSs 24
3.2.2 Cardinality for IFSs 25
3.2.3 Distance and Similarity Measures for IFSs 26
3.2.4 Correlation measure for IFSs 31
3.2.5 Evaluation Functions for IFSs 32
Chapter 4 Ranking functions of IvIFSs 35
4.1 Composite score function 36
4.2 Composite accuracy function 39
4.3 Definiteness function 40
4.4 Exactness function 41
4.5 Vagueness function 42
4.6 Discussion of properties 43
4.7 Ranking procedure 44
Chapter 5 Numerical illustrations 47
5.1 Multi-attribute decision-making problem by IFSs 47
5.2 Medical diagnosis problem by IFSs 50
5.3 Adaptive Ranking Orders of IvIFSs 52
5.4 Comparative Ranking Orders of Subtle IvIFSs 54
Chapter 6 Conclusions 60
Bibliography 62
Appendix 68
A-I: Proof of Theorem 3-1 68
A-II: Proof of Corollary 3-1 71
A-III: Proof of Theorem 3-2 74
A-IV: Proof of Theorem 3-3 75
A-V: Proof of Theorem 3-4 75
A-VI: Proof of Theorem 4-1 78
A-VII: Proof of Theorem 4-2 78
A-VIII: Proof of Theorem 4-3 81
參考文獻 Atanassov, K. T. (1983), Intuitionistic fuzzy sets, in VII ITKR's Session, edited, Sofia.
Atanassov, K. T. (1986), “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 20(1), pp. 87-96.
Atanassov, K. T. (1993), “Norms and metrics over intuitionistic fuzzy sets,” BUSEFAL, 55, pp. 11-20.
Atanassov, K. T. (1994), “Operators over interval valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 64(2), pp. 159-174.
Atanassov, K. T. (1999), Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Heidelberg.
Atanassov, K. T. (2012), On intuitionistic fuzzy sets theory, 292 pp., Springer Publishing Company, Incorporated.
Atanassov, K. T., & G. Gargov (1989), “Interval valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 31(3), pp. 343-349.
Atanassova, L. C. (1995), “Remark on the cardinality of the intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 75(3), pp. 399-400.
Bandler, W., & L. Kohout (1980), “Fuzzy power sets and fuzzy implication operators,” Fuzzy Sets and Systems, 4(1), pp. 13-30.
Barrenechea, E., H. Bustince, M. Pagola, & J. Fernandez (2010), “Construction of interval-valued fuzzy entropy invariant by translations and scalings,” Soft Computing, 14(9), pp. 945-952.
Burillo, P., & H. Bustince (1995), “Intuitionistic fuzzy relations. (Part I),” Mathware & Soft Computing, 2, pp. 5-38.
Burillo, P., & H. Bustince (1996), “Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets,” Fuzzy Sets and Systems, 78(3), pp. 305-316.
Bustince, H., E. Barrenechea, & M. Pagola (2008), “Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant,” Pattern Recognition Letters, 29(4), pp. 525-536.
Bustince, H., E. Barrenechea, M. Pagola, J. Fernandez, C. Guerra, P. Couto, & P. Melo-Pinto (2011), “Generalized Atanassov's intuitionistic fuzzy index: Construction of Atanassov's fuzzy entropy from fuzzy implication operators,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(01), pp. 51-69.
Bustince, H., & P. Burillo (1995), “Correlation of interval-valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 74(2), pp. 237-244.
Bustince, H., & P. Burillo (1996), “Vague sets are intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 79(3), pp. 403-405.
Bustince, H., M. Pagola, & E. Barrenechea (2007), “Construction of fuzzy indices from fuzzy DI-subsethood measures: Application to the global comparison of images,” Information Sciences, 177(3), pp. 906-929.
Chen, S. M. (1997), “Similarity measures between vague sets and between elements,” Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 27(1), pp. 153-158.
Chen, S. M., & J. M. Tan (1994), “Handling multicriteria fuzzy decision-making problems based on vague set theory,” Fuzzy Sets and Systems, 67(2), pp. 163-172.
Chen, S. M., M. W. Yang, & C. J. Liau (2011), ”A new method for multicriteria fuzzy decision making based on ranking interval-valued intuitionistic fuzzy values”, International Conference on Machine Learning and Cybernetics Jul.
Cornelis, C., C. Van der Donck, & E. Kerre (2003), “Sinha–Dougherty approach to the fuzzification of set inclusion revisited,” Fuzzy Sets and Systems, 134(2), pp. 283-295.
Dubois, D., & H. Prade (2008), “An introduction to bipolar representations of information and preference,” International Journal of Intelligent Systems, 23(8), pp. 866-877.
Dubois, D., & H. Prade (2009), “An overview of the asymmetric bipolar representation of positive and negative information in possibility theory,” Fuzzy Sets and Systems, 160(10), pp. 1355-1366.
Fan, J., W. Xie, & J. Pei (1999), “Subsethood measure: new definitions,” Fuzzy Sets and Systems, 106(2), pp. 201-209.
Galar, M., J. Fernandez, G. Beliakov, & H. Bustince (2011), “Interval-valued fuzzy sets applied to stereo matching of color images,” Image Processing, IEEE Transactions on, 20(7), pp. 1949-1961.
Gau, W. L., & D. J. Buehrer (1993), “Vague sets,” IEEE Transactions on Systems, Man, and Cybernetics, 23(2), pp. 610-614.
Gerstenkorn, T., & J. Mańko (1991), “Correlation of intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 44(1), pp. 39-43.
Herrera, F., & E. Herrera Viedma (2000), “Linguistic decision analysis: steps for solving decision problems under linguistic information,” Fuzzy Sets and Systems, 115(1), pp. 67-82.
Hong, D. H. (1998), “A note on correlation of interval-valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 95(1), pp. 113-117.
Hong, D. H., & C. H. Choi (2000), “Multicriteria fuzzy decision-making problems based on vague set theory,” Fuzzy Sets and Systems, 114(1), pp. 103-113.
Hung, W. L., & J. W. Wu (2002), “Correlation of intuitionistic fuzzy sets by centroid method,” Information Sciences, 144(1-4), pp. 219-225.
Lakshmana Gomathi Nayagam, V., & S. Geetha (2011), “Ranking of interval-valued intuitionistic fuzzy sets,” Applied Soft Computing, 11(4), pp. 3368-3372.
Lakshmana Gomathi Nayagam, V., S. Muralikrishnan, & G. Sivaraman (2011), “Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets,” Expert Systems with Applications, 38(3), pp. 1464-1467.
Lee, W. (2009), ”A novel method for ranking interval-valued Intuitionistic fuzzy numbers and its application to decision making”, International Conference on Intelligent Human-Machine Systems and Cybernetics, Aug.
Li, D. F. (2010a), “Linear programming method for MADM with interval-valued intuitionistic fuzzy sets,” Expert Systems with Applications, 37(8), pp. 5939-5945.
Li, D. F. (2010b), “Mathematical-programming approach to matrix games with payoffs represented by Atanassov's interval-valued intuitionistic fuzzy sets,” Fuzzy Systems, IEEE Transactions on, 18(6), pp. 1112-1128.
Li, D. F. (2010c), “TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets,” Fuzzy Systems, IEEE Transactions on, 18(2), pp. 299-311.
Li, D. F. (2011a), “Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information,” Applied Soft Computing, 11(4), pp. 3402-3418.
Li, D. F. (2011b), “Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations,” Fuzzy Optimization and Decision Making, 10(1), pp. 45-58.
Li, D. F. (2011c), “The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets,” Mathematical and Computer Modelling, 53(5–6), pp. 1182-1196.
Li, D. F. (2011d), “Linear programming approach to solve interval-valued matrix games,” Omega, 39(6), pp. 655-666.
Li, D. F. (2011e), “Notes on "Linear programming technique to solve two-person matrix games with interval pay-offs",” Asia-Pacific Journal of Operational Research, 28(06), pp. 705-737.
Li, D. F., J. X. Nan, & M. J. Zhang (2012), “Interval programming models for matrix games with interval payoffs,” Optimization Methods and Software, 27(1), pp. 1-16.
Liu, X. D., S. H. Zheng, & F. L. Xiong (2005), “Entropy and subsethood for general interval-valued intuitionistic fuzzy sets,” Lecture Notes in Artificial Intelligence, 3613, pp. 42-52.
Marinov, E., E. Szmidt, J. Kacprzyk, & R. Tcvetkov (2012), ”A modified weighted Hausdorff distance between intuitionistic fuzzy sets”, Intelligent Systems (IS), 2012 6th IEEE International Conference, 6-8 Sept. 2012.
Meimei, X., X. Zeshui, & L. Huchang (2013), “Preference Relations Based on Intuitionistic Multiplicative Information,” Fuzzy Systems, IEEE Transactions on, 21(1), pp. 113-133.
Mondal, K. T., & S. K. Samanta (2001), “Topology of interval-valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 119(3), pp. 483-494.
Papageorgiou, E. I., & D. K. Iakovidis (2013), “Intuitionistic fuzzy cognitive maps,” Fuzzy Systems, IEEE Transactions on, 21(2), pp. 342-354.
Park, D. G., Y. C. Kwun, J. H. Park, & I. Y. Park (2009), “Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems,” Mathematical and Computer Modelling, 50(9-10), pp. 1279-1293.
Sinha, D., & E. R. Dougherty (1993), “Fuzzification of set inclusion: Theory and applications,” Fuzzy Sets and Systems, 55(1), pp. 15-42.
Szmidt, E., & J. Kacprzyk (2000), “Distances between intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 114(3), pp. 505-518.
Szmidt, E., & J. Kacprzyk (2001), “Entropy for intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 118(3), pp. 467-477.
Szmidt, E., & J. Kacprzyk (2004a), ”A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning”, Artificial Intelligence and Soft Computing - Icaisc 2004, Zakopane, Poland.
Szmidt, E., & J. Kacprzyk (2004b), ”Similarity of intuitionistic fuzzy sets and the Jaccard coefficient”, Proceedings of Tenth Int. Conf. IPMU'2004, Perugia, 4-9 July 2004.
Szmidt, E., & J. Kacprzyk (2005), “New measures of entropy for intuitionistic fuzzy sets,” Notes on Intuitionistic Fuzzy Sets, 11(2), pp. 12-20.
Tanev, D. (1995), “On an intuitionistic fuzzy norm,” Notes on Intuitionistic Fuzzy Sets, 1(1), pp. 25-26.
Vlachos, I. K., & G. D. Sergiadis (2007a), “Intuitionistic fuzzy information - Applications to pattern recognition,” Pattern Recognition Letters, 28(2), pp. 197-206.
Vlachos, I. K., & G. D. Sergiadis (2007b), “Subsethood, entropy, and cardinality for interval-valued fuzzy sets—An algebraic derivation,” Fuzzy Sets and Systems, 158(12), pp. 1384-1396.
Wang, J. Q., & H. Y. Zhang (2013), “Multicriteria decision-making approach based on Atanassov's intuitionistic fuzzy sets with incomplete certain information on weights,” Fuzzy Systems, IEEE Transactions on, 21(3), pp. 510-515.
Wang, L. L., D. F. Li, & S. S. Zhang (2013), “Mathematical programming methodology for multiattribute decision making using interval-valued intuitionistic fuzzy sets,” Journal of Intelligent and Fuzzy Systems, 24(4), pp. 755-763.
Wang, X., & E. E. Kerre (2001), “Reasonable properties for the ordering of fuzzy quantities (I),” Fuzzy Sets and Systems, 118(3), pp. 375-385.
Wang, Z., K. W. Li, & W. Wang (2009), “An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights,” Information Sciences, 179(17), pp. 3026-3040.
Wei, C., P. Wang, & Y. Z. Zhang (2011a), “Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications,” Information Sciences, 181(19), pp. 4273-4286.
Wei, G. W. (2008), “Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting,” Knowledge-Based Systems, 21(8), pp. 833-836.
Wei, G. W., H. J. Wang, & R. Lin (2011b), “Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information,” Knowledge and Information Systems, 26(2), pp. 337-349.
Willmott, R. (1980), “Two fuzzier implication operators in the theory of fuzzy power sets,” Fuzzy Sets and Systems, 4(1), pp. 31-36.
Xu, Z. (2007a), “Intuitionistic fuzzy aggregation operators,” Fuzzy Systems, IEEE Transactions on, 15(6), pp. 1179-1187.
Xu, Z. (2007b), “Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making,” Control and Decision, 22(2), pp. 215-219.
Xu, Z. (2010), “A method based on distance measure for interval-valued intuitionistic fuzzy group decision making,” Information Sciences, 180(1), pp. 181-190.
Xu, Z., & J. Chen (2007), “An approach to group decision making based on interval-valued intuitioinistic judgment matrices,” Systems Engineering - Theory and Practice, 27(4), pp. 126-133.
Xu, Z., & R. R. Yager (2008), “Dynamic intuitionistic fuzzy multi-attribute decision making,” International Journal of Approximate Reasoning, 48(1), pp. 246-262.
Ye, J. (2009), “Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment,” Expert Systems with Applications, 36(3), pp. 6899-6902.
Ye, J. (2010), “Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets,” Applied Mathematical Modelling, 34(12), pp. 3864-3870.
Ye, J. (2012), “Multicriteria decision-making method using the dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets,” Applied Mathematical Modelling, 36(9), pp. 4466-4472.
Young, V. R. (1996), “Fuzzy subsethood,” Fuzzy Sets and Systems, 77(3), pp. 371-384.
Yu, D., Y. Wu, & T. Lu (2012), “Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making,” Knowledge-Based Systems, 30, pp. 57-66.
Zadeh, L. A. (1965), “Fuzzy sets,” Information and Control, 8(3), pp. 338-353.
Zadeh, L. A. (1975), “The concept of a linguistic variable and its application to approximate reasoning-I,” Information Sciences, 8(3), pp. 199-249.
Zeng, W., & P. Guo (2008), “Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship,” Information Sciences, 178(5), pp. 1334-1342.
Zeng, W. Y., & H. X. Li (2006), “Relationship between similarity measure and entropy of interval valued fuzzy sets,” Fuzzy Sets and Systems, 157(11), pp. 1477-1484.
Zhang, Q. S., S. Jiang, B. Jia, & S. Luo (2010), “Some information measures for interval-valued intuitionistic fuzzy sets,” Information Sciences, 180(24), pp. 5130-5145.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2016-01-23起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2017-01-23起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw