Properties, Improvements and Propagation of Compatibility Measurementbetween IntervalValued Fuzzy Sets
XU WeiHong1,2,3, ZENG ShuiLing1,2, YANG JingYu2, YE YouPei2
1.College of Mathematics and Computer Science, Jishou University, Jishou 416000 2.Department of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094 3.College of Computer and Communications Engineering, Changsha University of Science and Technology, Changsha 410077
Abstract：The properties of compatibility measurement between intervalvalued fuzzy sets are analyzed, and the existing compatibility measurement is improved into a new formula, so called harmoniousness, which overcomes the unsymmetry and inherits other basic characteristics of the compatibility. How fuzzy inference methods propagate the compatibility and harmoniousness is also discussed. In practical applications, when antecedent and consequence of a known rule are normal fuzzy sets, the harmoniousness between input and the antecedent is not bigger than the one between output and the consequence by Zadeh’s Compositional Rule of Inference. Our research is advantageous to neatening fuzzy rule database based on intervalvalued fuzzy sets as well as analysis and choice of fuzzy inference methods.
[1] Wang X Z, Baets B D, Kerre E. A Comparative Study of Similarity Measures. Fuzzy Sets and Systems, 1995, 73(2): 259-268 [2] Liang Y, Zhang W X. The Degree of the Consistency on Fuzzy Rules and the Method to Delete Rules. Chinese Journal of Computers, 1997, 20(10): 949-952 (in Chinese) (梁 怡,张文修.模糊规则的谐调度与矛盾规则的排除方法.计算机学报, 1997, 20(10): 949-952) [3] Zhang J J, Ou J P, et al. Method of Optimizing Fuzzy Control Roles Based on Compatibility of Fuzzy Subsets. Fuzzy Systems and Mathematics, 2002, 16(4):81-88 (in Chinese) (张吉礼,欧进萍,等. 基于模糊集相容性的模糊控制规则优化方法. 模糊系统与数学, 2002, 16(4): 81-88) [4] Liu W Y. The Fuzzy Data Dependencies Based on the Semantic Proximity. Chinese Journal of Computers, 1997, 20 (8): 725-730 (in Chinese) (刘惟一. 基于语义贴近度的模糊数据依赖. 计算机学报, 1997, 20(8): 725-730) [5] Feng N Q. Research on Fuzzy Measure of Fuzzy Concept. Pattern Recognition and Artificial Intelligence, 2002,15 (3): 290-294 (in Chinese) (冯乃勤. 模糊概念的模糊度研究. 模式识别与人工智能, 2002, 15(3): 290-294) [6]Wang S T. Fuzzy Inference Theory and Fuzzy Expert Systems. Shanghai, China: Shanghai Science and Technological Documents Publishing House, 1994 (in Chinese) (王士同. 模糊推理理论与模糊专家系统.上海:上海科技文献出版社,1994) [7]Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(2): 338-358 [8]Li W H, Wang Z S, et al. Interval-Valued Fuzzy C-Means Clustering Neural Networks Based on Interval-Valued Fuzzy Logic Neurons. Acta Electronica Sinica, 1998, 26(10): 99-103 (in Chinese) (李文化,王智顺,等. 基于区间值模糊逻辑神经元的区间值模糊C-均值聚类神经网络. 电子学报,1998, 26(10): 99-103) [9]Gorzalczany M B. An Interval-Valued Fuzzy Inference Method-Some Basic Properties. Fuzzy Sets and Systems, 1989, 31(2): 243-251 [10]Chen S M, Hsiao W H. Bidirectional Approximate Reasoning for Rule-Based Systems Using Interval-Valued Fuzzy Sets. Fuzzy Sets and Systems, 2000, 113(2): 185-203 [11]Yuan B, Pan Y, Wu W M. On Normal Form Based Interval- Valued Fuzzy Sets and Their Applications to Approximate Reasoning. International Journal of General Systems, 1995, 23(3): 241-254 [12]Wang G J. Triple-Implication Algorithm and Interval -Valued Fuzzy Inference. Science in China (Series E), 2000, 30(4): 331-340 (in Chinese) (王国俊. 三I方法与区间值模糊推理. 中国科学E辑, 2000, 30(4): 331-340) [13]Xu W H, Ye Y P, Yang J Y. Research on the Properties of a Compositional Rule of Fuzzy Inference with Parameters. Pattern Recognition and Artificial Intelligence, 2002, 15(4): 397-402 (in Chinese) (徐蔚鸿 ,叶有培, 杨静宇. 带参数的模糊推理合成法则的性质研究.模式识别与人工智能, 2002, 15(4): 397-402)
2006, Vol. 19 
