Computing with Words in Generalized Interval Type-2 Fuzzy Sets
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摘要: 普通的模糊集合是点值为二维的一型模糊集合,二型模糊集合(Type-2 fuzzy sets, T2 FS)是点值为三维的模糊集合, T2 FS比相应的一型难以理解和计算. 为了让人们更好地理解T2 FS并推广其应用, 本文提出了广义区间二型模糊集合(Generalized interval type-2 fuzzy sets, GIT2 FS)的定义, 并将其分成三类:离散型、半离散型及连续型,分别给出相应的数学表达式与扩展原理公式,并得到了GIT2 FS在两种不同的模糊逻辑算子下的词计算.
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关键词:
- 广义区间二型模糊集合 /
- 扩展原理 /
- 词计算 /
- 不确定覆盖域
Abstract: The conventional fuzzy sets are type-1 fuzzy sets whose point-values are two-dimensional, and the point-values of type-2 fuzzy sets (T2 FSs) are three-dimensional. So it is more difficult for T2 FS to be understood and computed than the corresponding type-1. To make T2 FS be better understood and extensively applied, in this paper, we present the definition of generalized interval type-2 fuzzy sets (GIT2 FSs), and divide them into three types: discrete type, partial discrete type, and continuous type. Then, the corresponding mathematical representation of every type is given to get the extension principle formula of GIT2 FS. Lastly, computing methods are proposed to discuss computing with words of GIT2 FS by two different fuzzy logic operators. -
[1] Zadeh L A. Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 1996, 4(2): 103-111[2] Adolfo R de Soto. A hierarchical model of a linguistic variable. Information Sciences, 2011, 181(20): 4394-4408[3] Cao Y Z, Chen G Q. A fuzzy petri-nets model for computing with words. IEEE Transactions on Fuzzy Systems, 2010, 18(3): 486-499[4] Aisbett J, Rickard J T, Morgenthaler D. Multivariate modeling and type-2 fuzzy sets. Fuzzy Sets and Systems, 2011, 163(1): 78-95[5] Wu D R, Mendel J M. Computing with words for hierarchical decision making applied to evaluating a weapon system. IEEE Transactions on Fuzzy Systems, 2010, 18(3): 441-460[6] Herrera F, Alonso S, Chiclana F, Herrera-Viedma E. Computing with words in decision making: foundations, trends and prospects. Fuzzy Optimization and Decision Making, 2009, 8(4): 337-364[7] Mo H, Wang F Y. Linguistic dynamic systems based on computing with words and their stabilities. Science in China Series F - Information Sciences, 2009, 52(5): 780-796[8] Wang F Y. Outline of a computational theory for linguistic dynamic systems: toward computing with words. International Journal of Intelligent Control and Systems, 1998, 2(2): 211-224[9] Wang Fei-Yue. Fundamental issues in research of computing with words and linguistic dynamic systems. Acta Automatica Sinica, 2005, 31(6): 844-852 (王飞跃. 词计算和语言动力学系统的基本问题和研究. 自动化学报, 2005, 31(6): 844-852)[10] Rubin S H. Computing with words. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, 1999, 29(4): 518-524[11] Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, 1973, SCM-3(1): 28-44[12] Li Jia-Ning, Yi Jian-Qiang, Zhao Dong-Bin, Xi Guang-Cheng. A new fuzzy identification approach for complex systems based on neural-fuzzy inference network. Acta Automatica Sinica, 2006, 32(5): 695-703[13] Mendel J M. Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Upper-Saddle River, NJ: Prentice-Hall PTR, 2001[14] Wang F Y. Modeling, analysis and synthesis of linguistic dynamic systems: a computational theory. In: Proceedings of IEEE International Workshop on Architecture for Semiotic Modeling and Situation Control in Large Complex Systems. Monterey, CA: IEEE, 1995. 173-178[15] Mendel J M, John R I B. Type-2 fuzzy sets made simple. IEEE Transactions on Fuzzy Systems, 2002, 10(2): 117-127[16] Uncu O, Turksen I B. Discrete interval type 2 fuzzy system models using uncertainty in learning parameters. IEEE Transactions on Fuzzy Systems, 2007, 15(1): 90-106[17] Pan Yong-Ping, Huang Dao-Ping, Sun Zong-Hai. Overview of type-2 fuzzy logic control. Control Theory and Application, 2011, 28(1): 13-23 (潘永平, 黄道平, 孙宗海. Ⅱ型模糊控制综述. 控制理论与应用, 2011, 28(1): 13-23)[18] Zhang Wei-Bin, Hu Huai-Zhong, Liu Wen-Jiang. Traffic flow forecast based on type-2 fuzzy logic approach. Journal of Xi'an Jiaotong University, 2007, 41(10): 1160-1164 (张伟斌, 胡怀中, 刘文江. 基于二型模糊逻辑的交通流量预测. 西安交通大学学报, 2007, 41(10): 1160-1164)[19] Li Cheng-Dong, Yi Jian-Qiang, Yu Yi, Zhao Dong-Bin. Inverse control of cable-driven parallel mechanism using type-2 fuzzy neural network. Acta Automatica Sinica, 2010, 36(3): 459-464 (李成栋, 易建强, 余意, 赵冬斌. 柔索驱动并联机构的二型模糊神经逆控制. 自动化学报, 2010, 36(3): 459-464)[20] Hagras H. Type-2 FLCs: a new generation of fuzzy controllers. IEEE Computational Intelligence Magazine, 2007, 2(1): 30-43[21] Lin P Z, Lin C M, Hsu C F, Lee T T. Type-2 fuzzy controller design using a sliding-mode approach for application to DC-DC converters. IEEE Proceedings: Electric Power Applications, 2005, 152(6): 1482-1488[22] Mo Hong, Wang Fei-Yue, Zhao Liang. LDS trajectories under one-to-one mapping in interval type-2 fuzzy sets. Pattern Recognition and Artificial Intelligence, 2010, 23(2): 144-147 (莫红, 王飞跃, 赵亮. 一一映射下区间二型模糊集合的语言动力学轨迹. 模式识别与人工智能, 2010, 23(2): 144-147)[23] Mo Hong, Wang Fei-Yue, Xiao Zhi-Quan, Chen Qian. Stabilities of linguistic dynamic systems based on interval type-2 fuzzy sets. Acta Automatica Sinica, 2011, 37(8): 1018-1024(莫红, 王飞跃, 肖志权, 陈茜. 基于区间二型模糊集合的语言动力系统稳定性. 自动化学报, 2011, 37(8): 1018-1024)[24] Wu D R, Mendel J M. Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Transactions on Fuzzy Systems, 2007, 15(6): 1145-1161[25] Mendel J M. An architecture for making judgments using computing with words. International Journal of Applied Mathematics and Computer Sciences, 2002, 12(3): 325-335[26] Wu Q H, Yu D, Xie Z X, Liu J F. Fuzzy probabilistic approximation spaces and their information measures. IEEE Transactions on Fuzzy Systems, 2006, 14(2): 191-201[27] Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 1975, 8(3): 199-249[28] Wang Xiao-Bo. Decomposition theorem of type-2 fuzzy sets. Fuzzy Mathematics, 1983, (1): 9-13 (王晓波. 2型Fuzzy 集的分解定理. 模糊数学, 1983, (1): 9-13)[29] Zadeh L A. Soft computing and fuzzy logic. IEEE Software, 1994, 11(6): 48-56
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