Linguistic-Valued Intuitionistic Fuzzy 2-Tuple Representation Model
ZOU Li1,2,ZHANG Yun-Xia1,Gao Wei1
1.School of Computer and Information Technology, Liaoning Normal University, Dalian 116081 2.State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093
Abstract：A kind of linguistic-valued intuitionistic fuzzy 2-tuple representation model is proposed based on the linguistic truth-valued intuitionistic fuzzy lattice. The operations and the properties of linguistic-valued intuitionistic fuzzy pair are discussed. Based on the proposed model, a kind of linguistic-valued intuitionistic fuzzy aggregation approach is defined. Arithmetic mean aggregation operator and weighted average aggregation operator are given respectively. Using the aggregation operations of the linguistic-valued intuitionistic fuzzy pairs, the information loss is reduced in the process of the aggregation for linguistic-valued intuitionisttic fuzzy pair. A recognition process of disease diagnosis is given to illustrate that the proposed approach is more effective for pattern recognition under a fuzzy environment with both positive evidence and negative evidence.
[1] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338-353 [2] Xu Z S. Intuitionistic Fuzzy Information Aggregation Theory and Application. Beijing, China: Science Press, 2008 (in Chinese) (徐泽水.直觉模糊信息集成理论及应用.北京:科学出版社, 2008) [3] Zou L, Liu X, Ruan D, et al. Linguistic Truth-Valued Intuitionistic Fuzzy Algebra. Journal of Multiple-Valued Logic and Soft Computing, 2012, 18: 445-456 [4] Zhang Z H, Yang J Y, Ye Y P, et al. Interval Valued Intuitionistic Fuzzy Sets with Parameters and Its Application in Pattern Recognition. Computer Science, 2011, 38(9): 215-219 (in Chinese) (张振华,杨静宇,叶有培,等.带参数区间值直觉模糊集及其在模式识别中的应用.计算机科学, 2011, 38(9): 215-219) [5] Zadeh L A. Fuzzy Logic=Computing with Words. IEEE Trans on Fuzzy Systems, 1996, 4(2): 103-111 [6] Mendel J M, John R I, Liu F L. Interval Type-2 Fuzzy Logic Systems Made Simple. IEEE Trans on Fuzzy Systems, 2006, 14(6): 808-821 [7] Xu Z S. Group Decision Making Based on Multiple Types of Linguistic Preference Relations. Information Sciences, 2008, 178(2): 452-467 [8] Novák V. A Formal Theory of Intermediate Quantifiers. Fuzzy Sets and Systems, 2008, 159(10): 1229-1246 [9] Pei Z, Ruan D, Liu J, et al. Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Application. Paris, France: Atlantis Press, 2010 [10] Pei Z, Xu Y, Ruan D, et al. Extracting Complex Linguistic Data Summaries from Personnel Database via Simple Linguistic Aggregations. Information Sciences, 2009, 179(14): 2325-2332 [11] Herrera F, Martinez L. A 2-Tuple Fuzzy Linguistic Representation Model for Computing with Words. IEEE Trans on Fuzzy Systems, 2000, 8(6): 746-752 [12] Zhang X Z, Zhu Q, Pei Z. Linguistic Set-Valued Decision Making Based on LWA Operator // Proc of the IEEE International Conference on Industrial Engineering and Engineering Management. Macao, China, 2010: 2353-2356 [13] Li X H. The Study and Application of Electromagnetic Environment Evaluation Based on Linguistic Decision Model. Master Dissertation. Chengdu, China: Xihua University, 2009 (in Chinese) (李西慧.基于语言决策模型的电磁环境评价研究与应用.硕士学位论文.成都:西华大学, 2009) [14] Zou L, Liu X, Pei Z, et al. A New Linguistic Aggregation Operator for Group Decision Making // Cao B Y, Xie X J, eds. Fuzzy Engineering and Operations Research. Berlin, Germany: Springer-Verlag, 2012: 85-95 [15] Park J H, Park J M, Kwun Y C. 2-Tuple Linguistic Harmonic Operators and their Applications in Group Decision Making. Knowledge-Based Systems, 2013, 44: 10-19 [16] Wan S P. 2-Tuple Linguistic Hybrid Arithmetic Aggregation Operators and Application to Multi-attribute Group Decision Making. Knowledge-Based Systems, 2013, 45: 31-40 [17] Rodriguez R M, Martinez L. An Analysis of Symbolic Linguistic Computing Models in Decision Making. International Journal of General Systems, 2013, 42(1): 121-136 [18] Gramajo S, Martinez L. A Linguistic Decision Support Model for QoS Priorities in Networking. Knowledge-Based Systems, 2012, 32: 65-75 [19] Pei Z, Shi P. Fuzzy risk Analysis Based on Linguistic Aggregation Operators. International Journal of Innovative Computing, Information and Control, 2011, 7(12): 7105-7117 [20] Badaracco M, Martinez L. A Fuzzy Linguistic Algorithm for Adaptive Test in Intelligent Tutoring System Based on Competences. Expert Systems with Applications, 2013, 40(8): 3073-3086 [21] Pei Z, Ruan D, Liu J, et al. A Linguistic Aggregation Operator with Three Kinds of Weights for Nuclear Safeguards Evaluation. Knowledge-Based Systems, 2012, 28: 19-26 [22] Yan L, Ruan Y L, Pei Z. Linguistic Interval 2-Tuple Power Average Operator and its Application. Journal of Shang Dong University: Engineering Science, 2013, 43(1): 115-122 (in Chinese) (晏 力,阮艳丽,裴 峥.语言值区间二元组能量平均算子及其应用.山东大学学报:工学版, 2013, 43(1): 115-122) [23] Zhang H M. Some Interval-Valued 2-Tuple Linguistic Aggregation Operators and Application in Multi-attribute Group Decision Making. Applied Mathematical Modelling, 2013, 37(6): 4269-4282 [24] Atanassov K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96 [25] Xu Y, Li X B, Liu J, et al. Determination of α-Resolution for Lattice-Valued First-Order Logic Based on Lattice Implication Algebra // Proc of the International Conference on Intelligent Systems and Knowledge Engineering. Chengdu, China, 2007: 1567-1573 [26] Xu Y, Chen S W, Ma J. Linguistic Truth-Valued Lattice Implication Algebra and Its Properties // Proc of the IMACS Multiconference on Computational Engineering in Systems Applications. Beijing, China, 2006: 1413-1418 [27] He X X, Xu Y, Liu J, et al. On Compatibilities of α-Lock Resolution Method in Linguistic Truth-Valued Lattice-Valued Logic. Soft Computing, 2012, 16(4): 699-709 [28] Li Z, Shi P, Zheng Z, et al. On an Algebra of Linguistic Truth-Valued Intuitionistic Lattice-Valued Logic. Journal of Intelligent & Fuzzy Systems, 2012, 24(3): 447-457
2014, Vol. 27 
