Development of Granular Fuzzy Relation Equations Based on a Subset of Data

Dan Wang; Xiubin Zhu; Witold Pedycz; Zhenhua Yu; Zhiwu Li

doi:10.1109/JAS.2021.1004054

Volume 8 Issue 8

Aug. 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(8): 1416-1427

D. Wang, X. B. Zhu, W. Pedycz, Z. H. Yu, and Z. W. Li, "Development of Granular Fuzzy Relation Equations Based on a Subset of Data," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1416-1427, Aug. 2021. doi: 10.1109/JAS.2021.1004054

Citation:

D. Wang, X. B. Zhu, W. Pedycz, Z. H. Yu, and Z. W. Li, "Development of Granular Fuzzy Relation Equations Based on a Subset of Data," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1416-1427, Aug. 2021. doi: 10.1109/JAS.2021.1004054

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Development of Granular Fuzzy Relation Equations Based on a Subset of Data

doi: 10.1109/JAS.2021.1004054

Dan Wang^1
,,
Xiubin Zhu^2
,,
Witold Pedycz^{2, 3, 4
,},
Zhenhua Yu^{1
,
,},
Zhiwu Li^{2, 5
,
,}

1.
School of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an 710054, China
2.
School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China
3.
Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada
4.
Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5.
the Institute of Systems Engineering, Macau University of Science and Technology, Macau, China

Funds: This work was supported by the National Natural Science Foundation of China (62006184, 62076189, 61873277)

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Author Bio:
Dan Wang received the B.S. degree and Ph.D. degree from Xidian University, in 2013 and 2019, respectively. She is currently an Associate Professor with the School of Computer Science and Technology, Xi’an University of Science and Technology. She was a Visiting Researcher with the University of Alberta, Edmonton, AB, Canada, from Jan. 2016 to Sept. 2019. Her research interests include computational intelligence, data mining, granular computing, and fuzzy system modeling

Xiubin Zhu received the B.S. degree in computer science and technology from Xi’an Shiyou University in 2004, the M.S. and Ph.D. degrees in computer software and theory, control theory and control engineering from Xidian University in 2007 and 2018, respectively. He is currently an Associate Professor with the School of Electro-Mechanical Engineering, Xidian University. His research interests include granular computing, data mining, and pattern recognition

Witold Pedrycz (M’88–SM’90–F’98) received the B.S. degree from the Silesian Technical University in 1977, the M.S. and Ph.D. degrees from the Silesian University of Technology, Gliwice, Poland, in 1980, and 1984, respectively. He is currently a Professor and Canada Research Chair (CRC) in computational intelligence in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. He is also with the Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland. In 2009, Dr. Pedrycz was elected a foreign member of the Polish Academy of Sciences. He is a Fellow of the Royal Society of Canada, recipient of the IEEE Canada Computer Engineering Medal, Cajastur Prize for Soft Computing from the European Centre for Soft Computing, Killam Prize, and Fuzzy Pioneer Award from the IEEE Computational Intelligence Society. His main research directions involve computational intelligence, fuzzy modeling and granular computing, knowledge discovery and data mining, fuzzy control, pattern recognition, knowledge-based neural networks, relational computing, and software engineering. He has published numerous papers in this area. He is also an author of 15 research monographs covering various aspects of computational intelligence, data mining, and software engineering. Dr. Pedrycz is intensively involved in editorial activities. He is an Editor-in-Chief of Information Sciences, Editor-in-Chief of WIREs Data Mining and Knowledge Discovery (Wiley), and Int. J. of Granular Computing (Springer). He currently serves as a member of a number of editorial boards of other international journals

Zhenhua Yu received the B.S. degree and M.S. degree from Xidian University in 1999 and 2003, respectively, and the Ph.D. degree from Xi’an Jiaotong University in 2006. He is currently a Professor with the Institute of Systems Security and Control, College of Computer Science and Technology, Xi’an University of Science and Technology. He has authored more than 20 technical papers for conferences and journals, and holds two invention patents. His research mainly focuses on cyber-physical systems, machine learning, and system security

Zhiwu Li (M’06–SM’07–F’16) received the B.S. degree in mechanical engineering, the M.S. degree in automatic control, and the Ph.D. degree in manufacturing engineering from Xidian University in 1989, 1992, and 1995, respectively. He joined Xidian University in 1992. He was a Visiting Professor with the University of Toronto, Toronto, ON, Canada, the Technion-Israel Institute of Technology, Haifa, Israel, the Martin-Luther University of Halle-Wittenburg, Halle, Germany, Conservatoire National des Arts et Métiers, Paris, France, Meliksah Universitesi, Kayseri, Turkey. He is currently with the Institute of Systems Engineering, Macau University of Science and Technology, Macau, China. His current research interests include Petri net theory and application, supervisory control of discrete-event systems, workflow modeling and analysis, system reconfiguration, game theory, and data and process mining. Dr. Li was a recipient of an Alexander von Humboldt Research Grant, Alexander von Humboldt Foundation, Germany. He is listed in Marquis Who’s Who in the World, 27th Edition, 2010. He serves as a Frequent Reviewer for 70+ international journals, including Automatica and a number of the IEEE Transactions as well as many international conferences. He is the Founding Chair of Xi’an Chapter of IEEE Systems, Man, and Cybernetics Society. He is a member of Discrete-Event Systems Technical Committee of the IEEE Systems, Man, and Cybernetics Society, and IFAC Technical Committee on Discrete-Event and Hybrid Systems, from 2011 to 2014
Corresponding author: Zhenhua Yu, e-mail: zhenhuayu@xust.edu.cn; Zhiwu Li, e-mail: zhwli@xidian.edu.cn
Received Date: 2020-12-20
Revised Date: 2021-02-26
Accepted Date: 2021-03-28

Available Online: 2021-04-07

Abstract

Abstract

Developing and optimizing fuzzy relation equations are of great relevance in system modeling, which involves analysis of numerous fuzzy rules. As each rule varies with respect to its level of influence, it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance. In this study, we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules. The subset of rules is selected by maximizing their performance of the obtained solutions. The originality of this study is conducted in the following ways. Starting with developing granular fuzzy relation equations, an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules (the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations), which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency. Then, the particle swarm optimization (PSO) is implemented to solve a multi-objective optimization problem, in which not only an optimal subset of rules is selected but also a parameter ε for specifying a level of information granularity is determined. A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance. A visible improvement of particle swarm optimization (about 78.56% of the encoding mechanism of particle swarm optimization, or 90.42% of particle swarm optimization with an exploration operator) is gained over the method conducted without using the particle swarm optimization algorithm.
- A subset of data,
- granular fuzzy relation equations,
- interval-valued fuzzy relation,
- particle swarm optimization (PSO)

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References

[1]	L. A. Zadeh, “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy Sets and Systems, vol. 90, no. 2, pp. 111–127, Sept. 1997. doi: 10.1016/S0165-0114(97)00077-8
[2]	X. B. Zhu, W. Pedrycz, and Z. W. Li, “A design of granular Takagi-Sugeno fuzzy model through the synergy of fuzzy subspace clustering and optimal allocation of information granularity,” IEEE Trans. Fuzzy Systems, vol. 26, no. 5, pp. 2499–2509, Oct. 2018. doi: 10.1109/TFUZZ.2018.2813314
[3]	X. C. Hu, W. Pedrycz, and D. H. Wang, “Fuzzy rule-based models with randomized development mechanisms,” Fuzzy Sets and Systems, vol. 361, pp. 71–87, Apr. 2019. doi: 10.1016/j.fss.2018.09.001
[4]	X. M. Zhao, H. Mo, K. F. Yan, and L. X. Li, “Type-2 fuzzy control for driving state and behavioral decisions of unmanned vehicle,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 178–186, Jan. 2020.
[5]	Z. H. Ding, Y. Zhou, and M. C. Zhou, “Modeling self-adaptive software systems by fuzzy rules and Petri nets,” IEEE Trans. Fuzzy Systems, vol. 26, no. 2, pp. 967–984, Apr. 2018. doi: 10.1109/TFUZZ.2017.2700286
[6]	J. Yen and L. Wang, “Simplifying fuzzy rule-based models using orthogonal transformation methods,” IEEE Trans. Systems,Man,and Cybernetics,Part B (Cybernetics), vol. 29, no. 1, pp. 13–24, Feb. 1999.
[7]	A. Skowron and J. Stepaniuk, “Information granules: Towards foundations granular computing,” Int. J. Intelligent Systems, vol. 16, no. 1, pp. 57–85, Dec. 2000.
[8]	W. Pedrycz, G. Succi, A. Sillitti, and J. Llgazi, “Data description: A general framework of information granules,” Knowledge-Based Systems, vol. 80, pp. 98–108, May 2015. doi: 10.1016/j.knosys.2014.12.030
[9]	X. B. Zhu, W. Pedrycz, and Z. W. Li, “Granular data description: Designing ellipsoidal information granules,” IEEE Trans. Cybernetics, vol. 47, no. 12, pp. 4475–4484, Dec. 2017. doi: 10.1109/TCYB.2016.2612226
[10]	L. A. Zadeh, “Is there a need for fuzzy logic?” Information Science, vol. 178, no. 13, pp. 2751–2779, Jul. 2008. doi: 10.1016/j.ins.2008.02.012
[11]	L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, Jun. 1965. doi: 10.1016/S0019-9958(65)90241-X
[12]	L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3–28, Jan. 1978. doi: 10.1016/0165-0114(78)90029-5
[13]	M. Setnes, R. Babuska, and H. B. Verbruggen, “Rule-based modeling: Precision and transparency,” IEEE Trans. Systems,Man,and Cybernetics,Part C (Applications and Reviews), vol. 28, no. 1, pp. 165–169, Feb. 1998. doi: 10.1109/5326.661100
[14]	Y. Cui, H. E, W. Pedrycz, and Z. W. Li, “Augmentation of rule-based models with a granular quantification of results,” Soft Computing, vol. 23, pp. 12745–12759, Feb. 2019. doi: 10.1007/s00500-019-03825-7
[15]	X. B. Li, Z. H. Yu, Z. W. Li, and N. Q. Wu, “Group consensus via pinning control for a class of heterogeneous multi-agent systems with input constraints,” Information Sciences, vol. 542, pp. 247–262, Jan. 2021.
[16]	L. Yang, Z. H. Yu, M. A. El-Meligy, A. M. El-Sherbeeny, and N. Q. Wu, “On multiplexity-aware influence spread in social networks,” IEEE Access, vol. 8, pp. 106705–106713, Jun. 2020.
[17]	S. Zhou, Z. H. Yu, E. S. A. Nasr, H. A. Mahmoud, E. M. Awwad, and N. Q. Wu, “Homomorphic encryption of supervisory control systems using automata,” IEEE Access, vol. 8, pp. 147185–147198, Aug. 2020.
[18]	E. Sanchez, “Resolution of composite fuzzy relation equations,” Information and Control, vol. 30, pp. 38–48, 1976. doi: 10.1016/S0019-9958(76)90446-0
[19]	W. Pedrycz, “On generalized fuzzy relational equations and their applications,” J. Mathematical Analysis and Applications, vol. 107, pp. 520–536, May 1985. doi: 10.1016/0022-247X(85)90329-4
[20]	Y. K. Wu and S. M. Guu, “An efficient procedure for solving a fuzzy relational equation with max–archimedean t-norm composition,” IEEE Trans. Fuzzy Systems, vol. 16, no. 1, pp. 73–84, Feb. 2008. doi: 10.1109/TFUZZ.2007.902018
[21]	X. P. Yang, H. T. Lin, X. G. Zhou, and B. Y. Cao, “Addition-min fuzzy relation inequalities with application in BitTorrent-like peer-to-peer file sharing system,” Fuzzy Sets and Systems, vol. 343, pp. 126–140, Jul. 2018. doi: 10.1016/j.fss.2017.04.002
[22]	X. C. Hu, W. Pedrycz, and X. M. Wang, “Granular fuzzy rule-based models: A study in a comprehensive evaluation and construction of fuzzy models,” IEEE Trans. Fuzzy Systems, vol. 25, no. 5, pp. 1342–1355, Oct. 2017. doi: 10.1109/TFUZZ.2016.2612300
[23]	M. Fang, T. Y. Zhou, J. Yin, Y. Wang, and D. C. Tao, “Data subset selection with imperfect multiple labels,” IEEE Trans. Neural Networks and Learning Systems, vol. 30, no. 7, pp. 2212–2221, Nov. 2018.
[24]	J. Y. Kim, S. M. Park, K. E. Ko, and K. B. Sim, “A binary PSO-based optimal EEG channel selection method for a motor imagery based BCI system,” Communications in Computer and Information Science, vol. 310, pp. 245–252, 2012.
[25]	S. J. Liao, Q. X. Zhu, and Y. H. Qian, “Feature-granularity selection with variable costs for hybrid data,” Soft Computing, vol. 23, pp. 13105–13126, Feb. 2019. doi: 10.1007/s00500-019-03854-2
[26]	J. Loetamonphong and S. C. Fang, “An efficient solution procedure for fuzzy relation equations with max-product composition,” IEEE Trans. Fuzzy Systems, vol. 7, no. 4, pp. 441–445, Aug. 1999. doi: 10.1109/91.784204
[27]	Y. K. Wu, S. M. Guu, and J. Y. C. Liu, “An accelerated approach for solving fuzzy relation equations with a linear objective function,” IEEE Trans. Fuzzy Systems, vol. 10, no. 4, pp. 552–558, Nov. 2002. doi: 10.1109/TFUZZ.2002.800657
[28]	L. Luoh, W. J. Wang, and Y. K. Liaw, “Matrix-pattern-based computer algorithm for solvng fuzzy relation equations,” IEEE Trans. Fuzzy Systems, vol. 11, no. 1, pp. 100–108, Feb. 2003. doi: 10.1109/TFUZZ.2002.806322
[29]	A. P. Rotshtein and H. B. Rakytyanska, “Diagnosis problem solving using fuzzy relations,” IEEE Trans. Fuzzy Systems, vol. 16, no. 3, pp. 664–675, Jun. 2008. doi: 10.1109/TFUZZ.2007.905908
[30]	F. Sun, X. B. Qu, X. P. Wang, and L. Zhu, “On pre-solution matrices of fuzzy relation equations over complete Brouwerian lattices,” Fuzzy Sets and Systems, vol. 383, pp. 34–53, Apr. 2020.
[31]	X. P. Yang, “Leximax minimum solution of addition-min fuzzy relation inequalities,” Information Science, vol. 524, pp. 184–198, Jul. 2020. doi: 10.1016/j.ins.2020.03.047
[32]	J. Loetamonphong and S. C. Fang, “Optimization of fuzzy relation equations with max-product composition,” Fuzzy Sets and Systems, vol. 118, no. 3, pp. 509–517, Mar. 2001. doi: 10.1016/S0165-0114(98)00417-5
[33]	A. Thapar, D. Pandey, and S. K. Gaur, “Optimization of linear objective function with max-t fuzzy relation equations,” Applied Soft Computing, vol. 9, no. 3, pp. 1097–1101, Jun. 2009. doi: 10.1016/j.asoc.2009.02.004
[34]	A. Ghodousian, “Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined bu Dubois-Prade family of t-norms,” J. Mathematical Analysis and Applications, vol. 503, pp. 291–306, Nov. 2019.
[35]	A. Ghodousian and A. Babalhavaeji, “An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition,” Applied Soft Computing, vol. 69, pp. 475–492, Aug. 2018. doi: 10.1016/j.asoc.2018.04.029
[36]	X. P. Yang, X. G. Zhou, and B. Y. Cao, “Min-max programming problem subject to addition-min fuzzy relation inequalities,” IEEE Trans. Fuzzy Systems, vol. 24, no. 1, pp. 111–119, May 2016. doi: 10.1109/TFUZZ.2015.2428716
[37]	N. Cao, M. Holcapek, and M. Stepnicka, “Extensions of fuzzy relational compositions based on generalized quantifiers,” Fuzzy Sets and Systems, vol. 339, pp. 73–98, May 2018. doi: 10.1016/j.fss.2017.04.009
[38]	W. Pedrycz, “Granular computing for data analytics: a manifesto of human-centric computing,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1025–1034, Nov. 2018. doi: 10.1109/JAS.2018.7511213
[39]	X. B. Zhu, W. Pedrycz, and Z. W. Li, “Granular models and granular outliers,” IEEE Trans. Fuzzy Systems, vol. 26, no. 6, pp. 3835–3846, Jun. 2018. doi: 10.1109/TFUZZ.2018.2849736
[40]	A. A. Ashtiani and M. B. Menhaj, “Introducing g-normal fuzzy relational models,” Soft Computing, vol. 19, no. 8, pp. 2163–2171, Jul. 2015. doi: 10.1007/s00500-014-1398-2
[41]	E. Schmitt, V. Bombardier, and L. Wendling, “Improving fuzzy rule classifier by extracting suitable features from capacities with respect to the choquet integral,” IEEE Trans. Systems,Man,and Cybernetics,Part B (Cybernetics), vol. 38, no. 5, pp. 1195–1206, Jul. 2008. doi: 10.1109/TSMCB.2008.925750
[42]	R. Alcalá, M. J. Gacto, F. Herrera, and J. Alcaláfdez, “A multi-objective genetic algorithm for tuning and rule selection to obtain accurate and compact linguistic fuzzy rule-based systems,” Int. J. Uncertainty Fuzziness and Knowledge Based Systems, vol. 15, no. 5, pp. 539–557, 2007.
[43]	S. M. Zhou, J. M. Garibaldi, R. I. John, and F. Chiclana, “On constructing parsimonious type-2 fuzzy logic systems via influential rule selection,” IEEE Trans. Fuzzy Systems, vol. 17, no. 3, pp. 654–667, Jul. 2008.
[44]	Y. L. Cao, H. Zhang, W. F. Li, M. C. Zhou, Y. Zhang, and W. A. Chaovalitwongse, “Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions,” IEEE Trans. Evolutionary Computation, vol. 23, no. 4, pp. 718–731, Dec. 2018.
[45]	J. Kennedy and R. C. Eberhart, “A discrete binary version of the particle swarm algorithm,” in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, Computational Cybernetics and Simulation, Orlando, FL, USA, Oct. 1997, pp. 4104–4108.
[46]	Y. D. Zhang, S. H. Wang, P. Phillips, and G. L. Ji, “Binary PSO with mutation operator for feature selection using decision tree applied to spam detection,” Knowledge-Based Systems, vol. 64, pp. 22–31, Jul. 2014. doi: 10.1016/j.knosys.2014.03.015
[47]	H. W. Lin, B. Zhao, D. R. Liu, and C. Alippi, “Data-based fault tolerant control for affine nonlinear systems through particle swarm optimized neural networks,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 954–964, Jul. 2020. doi: 10.1109/JAS.2020.1003225
[48]	J. Q. Zhang, X. X. Zhu, Y. H. Wang, and M. C. Zhou, “Dual-environmental particle swarm optimizer in noisy and noise-free environments,” IEEE Trans. Cybernetics, vol. 49, no. 6, pp. 2011–2021, Jun. 2019. doi: 10.1109/TCYB.2018.2817020
[49]	M. I. Menhas, M. R. Fei, L. Wang, and X. P. Fu, A Novel Hybrid Binary PSO Algorithm. Springer Berlin Heidelberg, 2011.

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Highlights

a novel framework of granular fuzzy relation equations based on the optimized subset of data.
an encoding mechanism of PSO are applied for selecting a subset of data.
numeric fuzzy relation is transformed to granular version with a level of information granularity.
the interpretability and accuracy are balanced by designing the granular mode.

Development of Granular Fuzzy Relation Equations Based on a Subset of Data

doi: 10.1109/JAS.2021.1004054

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