[1]HU Xingchen,LI Yan,CHEN Zijian,et al.Review of the research of granular fuzzy rule-based modeling[J].CAAI Transactions on Intelligent Systems,2024,19(1):22-35.[doi:10.11992/tis.202306034]
Copy

Review of the research of granular fuzzy rule-based modeling

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 19 Number of periods: 2024 1 Page number: 22-35 Column: 综述 Public date: 2024-01-05
Title:
Review of the research of granular fuzzy rule-based modeling
Author(s):
HU Xingchen1;  LI Yan1;  CHEN Zijian1;  LI Wentao2;  SHEN Yinghua3;  LIU Zhong1
1. School of Systems Engineering, National University of Defense Technology, Changsha 410073, China;
2. College of artificial intelligence, Southwest University, Chongqing 400715, China;
3. School of Economics and Business Administration, Chongqing University, Chongqing 400030, China
Keywords:
granular computing; information granule; fuzzy rule; fuzzy C-means clustering; granulation and degranulation; granularity; prototype; fuzzy set
CLC:
TP182
DOI:
10.11992/tis.202306034
Abstract:
The purpose of this paper is to explore the main research and construction method for granular fuzzy rule model, and make a systematic analysis and summary of it. Granular computing is an emerging theoretical system that simulates patterns of human thinking and solves complex problems, and the granular model based on it explores a new direction for the description and problem solving of complex nonlinear system. Among which the granular fuzzy rule-based model incorporates information granule into existing fuzzy rule-based modeling methods to achieve granular-level system modeling for data analysis and inference at a higher level. This paper first briefly introduces the basics of fuzzy clustering and fuzzy rule-based models, next summarizes the construction method of information granules and discusses corresponding evaluation methods. Further, the design architecture and optimization method are summarized.
References:
[1] 苗夺谦, 张清华, 钱宇华, 等. 从人类智能到机器实现模型: 粒计算理论与方法[J]. 智能系统学报, 2016, 11(6): 743–757
MIAO Duoqian, ZHANG Qinghua, QIAN Yuhua, et al. From human intelligence to machine implementation model: theories and applications based on granular computing[J]. CAAI transactions on intelligent systems, 2016, 11(6): 743–757
[2] NORI H, JENKINS S, KOCH P, et al. Interpretml: a unified framework for machine learning interpretability[J]. (2019?09?19)[2023?06?15]. https://arxiv.org/abs/1909.09223v1.pdf.
[3] 焦李成. 类脑感知与认知的挑战与思考[J]. 智能系统学报, 2022, 17(1): 213–216
JIAO Licheng. Challenges and reflections on brain-like perception and cognition[J]. CAAI transactions on intelligent systems, 2022, 17(1): 213–216
[4] WANG Guoyin, YANG Jie, XU Ji. Granular computing: from granularity optimization to multi-granularity joint problem solving[J]. Granular computing, 2017, 2(3): 105–120.
[5] ZADEH L A. Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic[J]. Fuzzy sets and systems, 1997, 90(2): 111–127.
[6] YAO Y. Perspectives of granular computing[C]//2005 IEEE International Conference on Granular Computing. Piscataway: IEEE, 2005: 85?90.
[7] HOBBS J R. Granularity[M]. Amsterdam: Elsevier, 1990: 542?545.
[8] LIN T Y. Neighborhood systems and relational databases[C]//Proceedings of the 1988 ACM sixteenth annual conference on Computer science. New York: ACM, 1988: 725.
[9] LIN T Y. Granular computing: fuzzy logic and rough sets[M]. Heidelberg: Physica-Verlag HD, 1999: 183?200.
[10] YAO Yiyu. A partition model of granular computing[M. Heidelberg: Springer Berlin Heidelberg, 2004: 232?253.
[11] PAWLAK Z. Rough set theory and its applications to data analysis[J]. Cybernetics and systems, 1998, 29(7): 661–688.
[12] ZADEH L A. Fuzzy logic = computing with words[J]. IEEE transactions on fuzzy systems, 1996, 4(2): 103–111.
[13] YAO Y Y. Granular computing: basic issues and possible solutions[J]. Proceedings of the joint conference on information sciences, 2000, 5(1): 186–189.
[14] WANG Guoyin, HU Feng, HUANG Hai, et al. A granular computing model based on tolerance relation[J]. The journal of China universities of posts and telecommunications, 2005, 12(3): 86–90.
[15] 胡峰, 黄海, 王国胤, 等. 不完备信息系统的粒计算方法[J]. 小型微型计算机系统, 2005, 26(8): 1335–1339
HU Feng, HUANG Hai, WANG Guoyin, et al. Granular computing in incomplete information systems[J]. Mini-micro systems, 2005, 26(8): 1335–1339
[16] 张铃, 张钹. 模糊相容商空间与模糊子集[J]. 中国科学:信息科学, 2011, 41(1): 1–11
ZHANG Ling, ZHANG Bo. Fuzzy tolerance quotient spaces and fuzzy subsets[J]. Scientia sinica (informationis), 2011, 41(1): 1–11
[17] ZHANG Yanping, ZHANG Ling, WU Tao. Description method of different granularity world?Business Space Law[J]. Chinese journal of computers, 2004, 27(3): 328–333.
[18] 王国胤, 张清华, 马希骜, 等. 知识不确定性问题的粒计算模型[J]. 软件学报, 2011, 22(4): 676–694
WANG Guoyin, ZHANG Qinghua, MA Xiao, et al. Granular computing models for knowledge uncertainty[J]. Journal of software, 2011, 22(4): 676–694
[19] 李道国, 苗夺谦, 张红云. 粒度计算的理论、模型与方法[J]. 复旦学报(自然科学版), 2004, 43(5): 837–841
LI Daoguo, MIAO Duoqian, ZHANG Hongyun. The theory models and approaches of granular computing[J]. Journal of Fudan University, 2004, 43(5): 837–841
[20] 苗夺谦, 胡声丹. 基于粒计算的不确定性分析[J]. 西北大学学报(自然科学版), 2019, 49(4): 487–495
MIAO Duoqian, HU Shengdan. Uncertainty analysis based on granular computing[J]. Journal of Northwest University (natural science edition), 2019, 49(4): 487–495
[21] LEITE D, COSTA P, GOMIDE F. Evolving granular neural networks from fuzzy data streams[J]. Neural networks, 2013, 38: 1–16.
[22] SONG Mingli, WANG Yongbin. A study of granular computing in the agenda of growth of artificial neural networks[J]. Granular computing, 2016, 1(4): 247–257.
[23] 罗建豪, 吴建鑫. 基于深度卷积特征的细粒度图像分类研究综述[J]. 自动化学报, 2017, 43(8): 1306–1318
LUO Jianhao, WU Jianxin. A survey on fine-grained image categorization using deep convolutional features[J]. Acta automatica sinica, 2017, 43(8): 1306–1318
[24] 任俊伟, 曾诚, 肖丝雨, 等. 基于会话的多粒度图神经网络推荐模型[J]. 计算机应用, 2021, 41(11): 3164–3170
REN Junwei, ZENG Cheng, XIAO Siyu, et al. Session-based recommendation model of multi-granular graph neural network[J]. Journal of computer applications, 2021, 41(11): 3164–3170
[25] PEDRYCZ W, HOMENDA W. From fuzzy cognitive maps to granular cognitive maps[J]. IEEE transactions on fuzzy systems, 2014, 22(4): 859–869.
[26] WANG Yihan, YU Fusheng, HOMENDA W, et al. The trend-fuzzy-granulation-based adaptive fuzzy cognitive map for long-term time series forecasting[J]. IEEE transactions on fuzzy systems, 2022, 30(12): 5166–5180.
[27] FALCON R, NáPOLES G, BELLO R, et al. Granular cognitive maps: a review[J]. Granular computing, 2019, 4(3): 451–467.
[28] QIN Jindong, MARTíNEZ L, PEDRYCZ W, et al. An overview of granular computing in decision-making: extensions, applications, and challenges[J]. Information fusion, 2023, 98: 101833.
[29] LIU Keyu, YANG Xibei, FUJITA H, et al. An efficient selector for multi-granularity attribute reduction[J]. Information sciences, 2019, 505: 457–472.
[30] YANG Xin, LI Tianrui, LIU Dun, et al. A temporal-spatial composite sequential approach of three-way granular computing[J]. Information sciences, 2019, 486: 171–189.
[31] LIU Dun, YANG Xin, LI Tianrui. Three-way decisions: beyond rough sets and granular computing[J]. International journal of machine learning and cybernetics, 2020, 11(5): 989–1002.
[32] SONG Mingli, LI Yan, PEDRYCZ W. Time series prediction with granular neural networks[J]. Neurocomputing, 2023, 546: 126328.
[33] PEDRYCZ W, BARGIELA A. An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering[J]. IEEE transactions on systems, man, and cybernetics, part B (cybernetics), 2012, 42(3): 582–590.
[34] PEDRYCZ W. Granular computing for data analytics: a manifesto of human-centric computing[J]. CAA journal of automatica sinica, 2018, 5(6): 1025–1034.
[35] PEDRYCZ W, VALENTE DE OLIVEIRA J. A development of fuzzy encoding and decoding through fuzzy clustering[J]. IEEE transactions on instrumentation and measurement, 2008, 57(4): 829–837.
[36] ZHANG Liyong, ZHONG Wanxie, ZHONG Chongquan, et al. Fuzzy C-Means clustering based on dual expression between cluster prototypes and reconstructed data[J]. International journal of approximate reasoning, 2017, 90: 389–410.
[37] ZHU Xiubin, PEDRYCZ W, LI Zhiwu. Fuzzy clustering with nonlinearly transformed data[J]. Applied soft computing, 2017, 61: 364–376.
[38] PEDRYCZ A, HIROTA K, PEDRYCZ W, et al. Granular representation and granular computing with fuzzy sets[J]. Fuzzy sets and systems, 2012, 203: 17–32.
[39] WANG Hai, XU Zeshui, PEDRYCZ W. An overview on the roles of fuzzy set techniques in big data processing: trends, challenges and opportunities[J]. Knowledge-based systems, 2017, 118: 15–30.
[40] WANG Guoyin. Extension of rough set under incomplete information systems[C]//2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE’02. Proceedings (Cat. No. 02CH37291). Piscataway: IEEE, 2002: 1098?1103.
[41] 韩祯祥, 张琦, 文福拴. 粗糙集理论及其应用综述[J]. 控制理论与应用, 1999, 16(2): 153–157
HAN Zhenxiang, ZHANG Qi, WEN Fushuan. A survey on rough set theory and its application[J]. Control theory & applications, 1999, 16(2): 153–157
[42] LI Deyi, LIU Changyu, GAN Wenyan. A new cognitive model: cloud model[J]. International journal of intelligent systems, 2009, 24(3): 357–375.
[43] WANG Guoyin, XU Changlin, LI Deyi. Generic normal cloud model[J]. Information sciences, 2014, 280: 1–15.
[44] An A, Stefanowski J, Ramanna S, et al. Rough sets, fuzzy sets, data mining and granular computing[C]//Proceedings of RSFDGrC2007, LNAI4482, Berlin:Springer-Verlag, 2007:.
[45] DESCHRIJVER G. Arithmetic operators in interval-valued fuzzy set theory[J]. Information sciences, 2007, 177(14): 2906–2924.
[46] CASTILLO O, MELIN P, KACPRZYK J, et al. Type-2 fuzzy logic: theory and applications[C]//2007 IEEE International Conference on Granular Computing (GRC 2007). Piscataway: IEEE, 2007: 145?145.
[47] JI W, PANG Y, JIA X, et al. Fuzzy rough sets and fuzzy rough neural networks for feature selection: a review[J]. Wiley interdisciplinary reviews:data mining and knowledge discovery, 2021, 11(3): e1402.
[48] XU W, WANG Q, ZHANG X. Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space[J]. International journal of fuzzy systems, 2011, 13(4).
[49] 张钹, 张铃. 问题求解理论及应用[M]. 北京: 清华大学出版社, 1990.
ZHANG Bai, ZHANG Ling. Theory and application of problem sSolving [M]. Beijing: Tsinghua University Press, 1990. (in Chinese)
[50] 张铃, 张钹. 模糊商空间理论(模糊粒度计算方法)[J]. 软件学报, 2003, 14(4): 770–776
ZHANG Ling, ZHANG Bo. Theory of fuzzy quotient space (methods of fuzzy granular computing)[J]. Journal of software, 2003, 14(4): 770–776
[51] 李德毅, 刘常昱, 杜鹢, 等. 不确定性人工智能[J]. 软件学报, 2004, 15(11): 1583–1594
LI Deyi, LIU Changyu, DU Yi, et al. Artificial intelligence with uncertainty[J]. Journal of software, 2004, 15(11): 1583–1594
[52] 王国胤, 云模型与粒计算[M]. 北京：科学出版社，2012.
WANG Guoyin. Cloud model and particle computing[M]. Beijing: Science Press, 2012.
[53] MAGDALENA L. Fuzzy rule-based systems[M]. Heidelberg: Springer Berlin Heidelberg, 2015: 203?218.
[54] PEDRYCZ W. From fuzzy models to granular fuzzy models[J]. International journal of computational intelligence systems, 2016, 9(suppl 1): 35.
[55] CASILLAS J, CORDON O, DEL JESUS M J, et al. Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction[J]. IEEE transactions on fuzzy systems, 2005, 13(1): 13–29.
[56] CORDóN O. A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: designing interpretable genetic fuzzy systems[J]. International journal of approximate reasoning, 2011, 52(6): 894–913.
[57] XU R, WUNSCHII D. Survey of clustering algorithms[J]. IEEE transactions on neural networks, 2005, 16(3): 645–678.
[58] BARALDI A, BLONDA P. A survey of fuzzy clustering algorithms for pattern recognition. I[J]. IEEE transactions on systems, man and cybernetics, part B (cybernetics), 1999, 29(6): 778–785.
[59] BEZDEK J C, EHRLICH R, FULL W. FCM: the fuzzy c-means clustering algorithm[J]. Computers & geosciences, 1984, 10(2/3): 191–203.
[60] SUGANYA R, SHANTHI R. Fuzzy c-means algorithm-a review[J]. International journal of scientific and research publications, 2012, 2(11): 1.
[61] DING Yi, FU Xian. Kernel-based fuzzy c-means clustering algorithm based on genetic algorithm[J]. Neurocomputing, 2016, 188: 233–238.
[62] HANYU E, CUI Ye, PEDRYCZ W, et al. Enhancements of rule-based models through refinements of Fuzzy C-Means[J]. Knowledge-based systems, 2019, 170: 43–60.
[63] Zhao F, Li G, Guo H, et al. Rule-based models via the axiomatic fuzzy set clustering and their granular aggregation[J]. Applied Soft Computing, 2022, 130: 109692.
[64] ANGELOV P P, FILEV D P. An approach to online identification of Takagi-Sugeno fuzzy models[J]. IEEE transactions on systems, man, and cybernetics part B, cybernetics:a publication of the IEEE systems, man, and cybernetics society, 2004, 34(1): 484–498.
[65] HU Xingchen, PEDRYCZ W, WANG Xianmin. From fuzzy rule-based models to their granular generalizations[J]. Knowledge-based systems, 2017, 124: 133–143.
[66] ZHANG X, ZHU Z, ZHAO Y, et al. Self-supervised deep low-rank asignment model for prototype selection[C]//IJCAI. 2018: 3141?3147.
[67] Wang S, Mao W, Wei P, et al. Knowledge structure driven prototype learning and verification for fact checking[J]. Knowledge-Based Systems, 2022, 238: 107910.
[68] LIN Shuai, LIU Chen, ZHOU Pan, et al. Prototypical graph contrastive learning[J]. IEEE transactions on neural networks and learning systems, 2021, 35(2): 2747–2758.
[69] CHEN Min, MIAO Duoqian. Interval set clustering[J]. Expert systems with applications, 2011, 38(4): 2923–2932.
[70] MOORE R E, KEARFOTT R B, CLOUD M J. Introduction to interval analysis[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2009.
[71] ALEFELD G, HERZBERGER J. Introduction to interval computation[M]. Herzberger: Academic press, 2012.
[72] ZHANG Qinghua, XIE Qin, WANG Guoyin. A survey on rough set theory and its applications[J]. CAAI transactions on intelligence technology, 2016, 1(4): 323–333.
[73] CAO Bin, ZHAO Jianwei, LV Zhihan, et al. Multiobjective evolution of fuzzy rough neural network via distributed parallelism for stock prediction[J]. IEEE transactions on fuzzy systems, 2020, 28(5): 939–952.
[74] YANG Jilin, YAO Yiyu. A three-way decision based construction of shadowed sets from atanassov intuitionistic fuzzy sets[J]. Information sciences, 2021, 577: 1–21.
[75] ZHANG Qinghua, CHEN Yuhong, YANG Jie, et al. Fuzzy entropy: a more comprehensible perspective for interval shadowed sets of fuzzy sets[J]. IEEE transactions on fuzzy systems, 2020, 28(11): 3008–3022.
[76] BOSE A, MALI K. Gradual representation of shadowed set for clustering gene expression data[J]. Applied soft computing, 2019, 83: 105614.
[77] LIU Xiaodong, PEDRYCZ W, CHAI Tianyou, et al. The development of fuzzy rough sets with the use of structures and algebras of axiomatic fuzzy sets[J]. IEEE transactions on knowledge and data engineering, 2009, 21(3): 443–462.
[78] HIROTA K. Concepts of probabilistic sets[J]. Fuzzy sets and systems, 1981, 5(1): 31–46.
[79] FUJITA H, GAETA A, LOIA V, et al. Hypotheses analysis and assessment in counterterrorism activities: a method based on OWA and fuzzy probabilistic rough sets[J]. IEEE transactions on fuzzy systems, 2020, 28(5): 831–845.
[80] SUN Junzi. The 1090 megahertz riddle: a guide to decoding mode S and ADS-B signals[M]. Delft: TU Delft OPEN, 2021.
[81] NACHMANI E, MARCIANO E, LUGOSCH L, et al. Deep learning methods for improved decoding of linear codes[J]. IEEE journal of selected topics in signal processing, 2018, 12(1): 119–131.
[82] PEDRYCZ W. An introduction to computing with fuzzy sets[J]. IEEE ASSP magazine, 2021: 190.
[83] HU Xingchen, PEDRYCZ W, WU Guohua, et al. Data reconstruction with information granules: an augmented method of fuzzy clustering[J]. Applied soft computing, 2017, 55: 523–532.
[84] GRAVES D, PEDRYCZ W. Kernel-based fuzzy clustering and fuzzy clustering: a comparative experimental study[J]. Fuzzy sets and systems, 2010, 161(4): 522–543.
[85] REYES-GALAVIZ O F, PEDRYCZ W. Enhancement of the classification and reconstruction performance of fuzzy C-means with refinements of prototypes[J]. Fuzzy sets and systems, 2017, 318: 80–99.
[86] XU Kaijie, PEDRYCZ W, LI Zhiwu, et al. Optimizing the prototypes with a novel data weighting algorithm for enhancing the classification performance of fuzzy clustering[J]. Fuzzy Sets and Systems, 2021, 413: 29–41.
[87] IZAKIAN H, PEDRYCZ W, JAMAL I. Clustering spatiotemporal data: an augmented fuzzy C-means[J]. IEEE transactions on fuzzy systems, 2013, 21(5): 855–868.
[88] IZAKIAN H, PEDRYCZ W. Anomaly detection in time series data using a fuzzy c-means clustering[C]//2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). Piscataway IEEE, 2013: 1513?1518.
[89] REYES-GALAVIZ O F, PEDRYCZ W. Granular fuzzy modeling with evolving hyperboxes in multi-dimensional space of numerical data[J]. Neurocomputing, 2015, 168: 240–253.
[90] ZHU Xiubin, PEDRYCZ W, LI Zhiwu. Granular representation of data: a design of families of ?-information granules[J]. IEEE transactions on fuzzy systems, 2018, 26(4): 2107–2119.
[91] ZHANG Rui, XU Kaijie, ZHU Shengqi, et al. Modeling of number of sources detection under nonideal conditions based on fuzzy information granulation[J]. IEEE transactions on aerospace and electronic systems, 2022: 1?10.
[92] PEDRYCZ W, HIROTA K. Fuzzy vector quantization with the particle swarm optimization: a study in fuzzy granulation-degranulation information processing[J]. Signal processing, 2007, 87(9): 2061–2074.
[93] LINDA O, MANIC M. General type-2 fuzzy C-means algorithm for uncertain fuzzy clustering[J]. IEEE transactions on fuzzy systems, 2012, 20(5): 883–897.
[94] ROH S B, OH S K, PEDRYCZ W, et al. Design methodology for radial basis function neural networks classifier based on locally linear reconstruction and conditional fuzzy C-means clustering[J]. International journal of approximate reasoning, 2019(106): 228–243.
[95] HU Xingchen, PEDRYCZ W, WANG Xianmin. Granular fuzzy rule-based models: a study in a comprehensive evaluation and construction of fuzzy models[J]. IEEE transactions on fuzzy systems, 2017, 25(5): 1342–1355.
[96] ZHU Xiubin, PEDRYCZ W, LI Zhiwu. A design of granular takagi–sugeno fuzzy model through the synergy of fuzzy subspace clustering and optimal allocation of information granularity[J]. IEEE transactions on fuzzy systems, 2018, 26(5): 2499–2509.
[97] PEDRYCZ W, AL-HMOUZ R, BALAMASH A S, et al. Designing granular fuzzy models: a hierarchical approach to fuzzy modeling[J]. Knowledge-based systems, 2015, 76: 42–52.
[98] LI Yan, HU Xingchen, PEDRYCZ W, et al. Multivariable fuzzy rule-based models and their granular generalization: a visual interpretable framework[J]. Applied soft computing, 2023, 134: 109958.
[99] HU Xingchen, PEDRYCZ W, WANG Xianmin. Optimal allocation of information granularity in system modeling through the maximization of information specificity: a development of granular input space[J]. Applied soft computing, 2016, 42: 410–422.
[100] SONG Mingli, JING Yukai. Granular neural networks: the development of granular input spaces and parameters spaces through a hierarchical allocation of information granularity[J]. Information sciences, 2020, 517: 148–166.
[101] ZHONG Chunfu, PEDRYCZ W, WANG Dan, et al. Granular data imputation: a framework of Granular Computing[J]. Applied soft computing, 2016, 46: 307–316.
[102] HU Xingchen, PEDRYCZ W, WU Keyu, et al. Information Granule-based classifier: a development of granular imputation of missing data[J]. Knowledge-based systems, 2021, 214: 106737.
[103] LI Menghang, WANG Degang, SONG Wenyan. A design of direct granular model based on takagi-sugeno fuzzy model[C]//2020 7th International Conference on Information, Cybernetics, and Computational Social Systems (ICCSS). Piscataway IEEE, 2020: 457?462.
[104] ZHU Xiubin, PEDRYCZ W, LI Zhiwu. A granular approach to interval output estimation for rule-based fuzzy models[J]. IEEE transactions on cybernetics, 2022, 52(7): 7029–7038.
[105] SHEN Yinghua, PEDRYCZ W, JING Xuyang, et al. Identification of fuzzy rule-based models with output space knowledge guidance[J]. IEEE transactions on fuzzy systems, 2021, 29(11): 3504–3518.
[106] ZHANG Bowen, PEDRYCZ W, FAYEK A R, et al. Granular aggregation of fuzzy rule-based models in distributed data environment[J]. IEEE transactions on fuzzy systems, 2021, 29(5): 1297–1310.
[107] LU Wei, SHAN Dan, PEDRYCZ W, et al. Granular fuzzy modeling for multidimensional numeric data: a layered approach based on hyperbox[J]. IEEE transactions on fuzzy systems, 2019, 27(4): 775–789.
[108] LU Wei, PEDRYCZ W, YANG Jianhua, et al. Granular fuzzy modeling guided through the synergy of granulating output space and clustering input subspaces[J]. IEEE transactions on cybernetics, 2021, 51(5): 2625–2638.
[109] LU Wei, MA Cong, PEDRYCZ W, et al. Design of granular model: a method driven by hyper-box iteration granulation[J]. IEEE transactions on cybernetics, 2023, 53(5): 2899–2913.
[110] SONG Mingli, WANG Yongbin. Human centricity and information granularity in the agenda of theories and applications of soft computing[J]. Applied soft computing, 2015, 27: 610–613.
[111] LU Wei, ZHANG Liyong, PEDRYCZ W, et al. The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series[J]. Applied soft computing, 2016, 42: 38–52.
[112] ZUO Hua, ZHANG Guangquan, PEDRYCZ W, et al. Granular fuzzy regression domain adaptation in takagi–sugeno fuzzy models[J]. IEEE transactions on fuzzy systems, 2018, 26(2): 847–858.
[113] SONG Mingli, LIU Yapeng. A development framework of granular prototypes with an allocation of information granularity[J]. Information sciences, 2021, 573: 154–170.
[114] ZHU Xiubin, PEDRYCZ W, LI Zhiwu. A development of hierarchically structured granular models realized through allocation of information granularity[J]. IEEE transactions on fuzzy systems, 2021, 29(12): 3845–3858.
[115] 柳春华, 刘宏兵. 基于多目标优化的超盒粒计算分类算法[J]. 信阳师范学院学报(自然科学版), 2014, 27(1): 127–130
LIU Chunhua, LIU Hongbing. The hyperbox granular computing classification algorithm based on multi-objective optimization[J]. Journal of Xinyang Normal University (natural science edition), 2014, 27(1): 127–130
Similar References:

Memo

-

Last Update: 1900-01-01

Copyright © CAAI Transactions on Intelligent Systems