Study on sensible beginning divided-search enhanced Karnik-Mendel algorithms for centroid type-reduction of general type-2 fuzzy logic systems

Yang Chen; Chenxi Li; Yang Chen; Chenxi Li

doi:10.3934/math.2024580

AIMS Mathematics

2024, Volume 9, Issue 5: 11851-11876. doi: 10.3934/math.2024580

Previous Article Next Article

Research article

Study on sensible beginning divided-search enhanced Karnik-Mendel algorithms for centroid type-reduction of general type-2 fuzzy logic systems

Yang Chen ^,,
Chenxi Li

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China

Received: 20 December 2023 Revised: 23 January 2024 Accepted: 19 February 2024 Published: 26 March 2024
MSC : 68WXX, 94D05

General type-2 fuzzy logic systems (GT2 FLSs) on the basis of alpha-plane representation of GT2 fuzzy sets (FSs) have attracted considerable attention in recent years. For the kernel type-reduction (TR) block of GT2 FLSs, the enhanced Karnik-Mendel (EKM) algorithm is the most popular approach. This paper proposes the sensible beginning divided-search EKM (SBDEKM) algorithms for completing the centroid TR of GT2 FLSs. Computer simulations are provided to show the performances of the SBDEKM algorithms. Compared with EKM algorithms and sensible beginning EKM (SBEKM) algorithms, the SBDEKM algorithms have almost the same accuracies and better computational efficiency.
- sensible beginning divided-search EKM algorithms,
- general type-2 fuzzy logic systems,
- centroid type-reduction,
- simulation,
- efficiency
Citation: Yang Chen, Chenxi Li. Study on sensible beginning divided-search enhanced Karnik-Mendel algorithms for centroid type-reduction of general type-2 fuzzy logic systems[J]. AIMS Mathematics, 2024, 9(5): 11851-11876. doi: 10.3934/math.2024580

Related Papers:

Abstract

General type-2 fuzzy logic systems (GT2 FLSs) on the basis of alpha-plane representation of GT2 fuzzy sets (FSs) have attracted considerable attention in recent years. For the kernel type-reduction (TR) block of GT2 FLSs, the enhanced Karnik-Mendel (EKM) algorithm is the most popular approach. This paper proposes the sensible beginning divided-search EKM (SBDEKM) algorithms for completing the centroid TR of GT2 FLSs. Computer simulations are provided to show the performances of the SBDEKM algorithms. Compared with EKM algorithms and sensible beginning EKM (SBEKM) algorithms, the SBDEKM algorithms have almost the same accuracies and better computational efficiency.

References

[1]	J. M. Mendel, R. I. John, F. L. Liu, Interval type-2 fuzzy logic systems made simple, IEEE T. Fuzzy Sys., 14 (2006), 808–821. https://doi.org/10.1109/TFUZZ.2006.879986 doi: 10.1109/TFUZZ.2006.879986
[2]	D. R. Wu, J. M. Mendel, Uncertainty measures for interval type-2 fuzzy sets, Inform. Sci., 177 (2007), 5378–5393. https://doi.org/10.1016/j.ins.2007.07.012 doi: 10.1016/j.ins.2007.07.012
[3]	A. Khosravi, S. Nahavandi, Load forecasting using interval type-2 fuzzy logic systems: Optimal type reduction, IEEE T. Indust. Inform., 10 (2014), 1055–1063. https://doi.org/10.1109/TII.2013.2285650 doi: 10.1109/TII.2013.2285650
[4]	J. M. Mendel, F. L. Liu, D. Y. Zhai, Alpha-plane representation for type-2 fuzzy sets: Theory and applications, IEEE T. Fuzzy Syst., 17 (2009), 1189–1207. https://doi.org/10.1109/TFUZZ.2009.2024411 doi: 10.1109/TFUZZ.2009.2024411
[5]	C. Wagner, H. Hagras, Toward general type-2 fuzzy logic systems based on zSlices, IEEE T. Fuzzy Syst., 18 (2010), 637–660. https://doi.org/10.1109/TFUZZ.2010.2045386 doi: 10.1109/TFUZZ.2010.2045386
[6]	F. L. Liu, An efficient centroid type-reduction strategy for general type-2 fuzzy logic system, Inf. Sci., 178 (2008), 2224–2236. https://doi.org/10.1016/j.ins.2007.11.014 doi: 10.1016/j.ins.2007.11.014
[7]	J. M. Mendel, General type-2 fuzzy logic systems made simple: A tutorial, IEEE T. Fuzzy Syst., 22 (2014), 1162–1182. https://doi.org/10.1109/TFUZZ.2013.2286414 doi: 10.1109/TFUZZ.2013.2286414
[8]	C. I. Gonzalez, P. Melin, J. R. Castro, O. Mendoza, O. Castillo, An improved sobel edge detection method based on generalized type-2 fuzzy logic, Soft Comput., 20 (2016), 773–784. https://doi.org/10.1007/s00500-014-1541-0 doi: 10.1007/s00500-014-1541-0
[9]	P. Melin, C. I. Gonzalez, J. R. Castro, O. Mendoza, O. Castillo, Edge-detection method for image processing based on generalized type-2 fuzzy logic, IEEE T. Fuzzy Syst., 22 (2014), 1515–1525. https://doi.org/10.1109/TFUZZ.2013.2297159 doi: 10.1109/TFUZZ.2013.2297159
[10]	M. A. Sanchez, O. Castillo, J. R. Castro, Generalized type-2 fuzzy systems for controlling a mobile robot and a performance comparison with interval type-2 and type-1 fuzzy systems, Expert Syst. Appl., 42 (2015), 5904–5914. https://doi.org/10.1016/j.eswa.2015.03.024 doi: 10.1016/j.eswa.2015.03.024
[11]	O. Castillo, L. Amador-Angulo, J. R. Castro, M. Garcia-Valdez, A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems, Inform. Sci., 354 (2016), 257–274. https://doi.org/10.1016/j.ins.2016.03.026
[12]	Y. Chen, D. Z. Wang, W. Ning, Forecasting by TSK general type-2 fuzzy logic systems optimized with genetic algorithms, Opt. Contr. Appl. Meth., 39 (2018), 393–409. https://doi.org/10.1002/oca.2353 doi: 10.1002/oca.2353
[13]	Y. Chen, C. X. Li, J. X. Yang, Design and application of Nagar-Bardini structure-based interval type-2 fuzzy logic systems optimized with the combination of backpropagation algorithms and recursive least square algorithms, Expert Syst. Appl., 211 (2023), 1–10. https://doi.org/10.1016/J.ESWA.2022.118596 doi: 10.1016/J.ESWA.2022.118596
[14]	Y. Chen, D. Z. Wang, Forecasting by general type-2 fuzzy logic systems optimized with QPSO algorithms, Int. J. Contr. Auto. Syst., 15 (2017), 2950–2958. https://doi.org/10.1007/s12555-017-0793-0 doi: 10.1007/s12555-017-0793-0
[15]	L. X. Wang, A new look at type-2 fuzzy sets and type-2 fuzzy logic systems, IEEE T. Fuzzy Syst., 25 (2017), 693–706. https://doi.org/10.1109/tfuzz.2016.2543746 doi: 10.1109/tfuzz.2016.2543746
[16]	D. R. Wu, J. M. Mendel, Enhanced Karnik-Mendel algorithms, IEEE T. Fuzzy Syst., 17 (2009), 923–934. https://doi.org/10.1109/TFUZZ.2008.924329 doi: 10.1109/TFUZZ.2008.924329
[17]	J. M. Mendel, On KM algorithms for solving type-2 fuzzy sets problems, IEEE T. Fuzzy Syst., 21 (2013), 426–446. https://doi.org/10.1109/TFUZZ.2012.2227488 doi: 10.1109/TFUZZ.2012.2227488
[18]	X. W. Liu, J. M. Mendel, D. R. Wu, Study on enhanced Karnik-Mendel algorithms: initialization explanations and computation improvements, Inform. Sci., 184 (2012), 75–91. https://doi.org/10.1016/j.ins.2011.07.042 doi: 10.1016/j.ins.2011.07.042
[19]	X. L. Liu, S. P. Wan, Combinatorial iterative algorithms for computing the centroid of an interval type-2 fuzzy set, IEEE T. Fuzzy Syst., 28 (2020), 607–617. https://doi.org/10.1109/TFUZZ.2019.2911918 doi: 10.1109/TFUZZ.2019.2911918
[20]	J. M. Mendel, X. W. Liu, Simplified interval type-2 fuzzy logic systems, IEEE T. Fuzzy Syst., 21 (2013), 1056–1069. https://doi.org/10.1109/TFUZZ.2013.2241771 doi: 10.1109/TFUZZ.2013.2241771
[21]	C. Chen, R. John, J. Twycross, J. M. Garibaldi, A direct approach for determining the switch points in the Karnik-Mendel algorithm, IEEE T. Fuzzy Syst., 26 (2018), 1079–1085. https://doi.org/10.1109/tfuzz.2017.2699168 doi: 10.1109/tfuzz.2017.2699168
[22]	Z. Zhang, X. Zhao, Y. Qin, H. Si, L. Zhou, Interval type-2 fuzzy TOPSIS approach with utility theory for subway station operational risk evaluation, J. Ambient Intel. Human. comput., 13 (2022), 4849–4863. https://doi.org/10.1007/s12652-021-03182-0 doi: 10.1007/s12652-021-03182-0
[23]	X. L. Liu, Y. C. Lin, New efficient algorithms for the centroid of an interval type-2 fuzzy set, Inform. Sci., 570 (2021), 1–19. https://doi.org/10.1016/j.ins.2021.04.032 doi: 10.1016/j.ins.2021.04.032
[24]	Y. Chen, J. X. Wu, J. Lan, Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems, AIMS Math., 5 (2020), 6149–6168. https://doi.org/10.3934/math.2020395 doi: 10.3934/math.2020395
[25]	J. H. Wang, W. Ji, X. K. Fang, S. S. Gu, Improvement of enhanced Karnik-Mendel algorithm for interval type-2 fuzzy sets, Contr. Deci., 28 (2013), 1165–1172. https://doi.org/10.13195/j.kzyjc.2013.08.002 doi: 10.13195/j.kzyjc.2013.08.002
[26]	Y. Chen, D. Z. Wang, S. C. Tong, Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: With combination of BP algorithms and KM algorithms, Neurocomputing, 174 (2016), 1133–1146. https://doi.org/10.1016/j.neucom.2015.10.032 doi: 10.1016/j.neucom.2015.10.032
[27]	Y. Chen, D. Z. Wang, Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms, Trans. Inst. Meas. Contr., 41 (2019), 2886–2896. https://doi.org/10.1177/0142331218816753 doi: 10.1177/0142331218816753
[28]	G. M. Méndez, M. D. L. A. Hernandez, Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems, Inform. Sci., 220 (2013), 149–169. https://doi.org/10.1016/j.ins.2012.01.024 doi: 10.1016/j.ins.2012.01.024
[29]	Y. Chen, J. X. Yang, C. X. Li, Design of Takagi Sugeno Kang type interval type-2 fuzzy logic systems optimized with hybrid algorithms, Int. J. Fuzzy Syst., 25 (2023), 868–879. https://doi.org/10.1007/S40815-022-01410-Z doi: 10.1007/S40815-022-01410-Z
[30]	Y. Chen, Study on non-iterative algorithms for center-of-sets type-reduction of Takagi-Sugeno-Kang type general type-2 fuzzy logic systems, Compl. Intell. Syst., 9 (2023), 4015–4023. https://doi.org/10.1007/s40747-022-00927-y doi: 10.1007/s40747-022-00927-y
[31]	Y. Chen, Study on centroid type-reduction of general type-2 fuzzy logic systems with sensible beginning weighted enhanced Karnik-Mendel algorithms, Soft Comput., 27 (2023), 9261–9279. https://doi.org/10.1007/S00500-023-08269-8 doi: 10.1007/S00500-023-08269-8
[32]	Y. Chen, J. X. Yang, C. X. Li, Design of reasonable initialization weighted enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems, AIMS Math., 7 (2022), 9846–9870. https://doi.org/10.3934/math.2022549 doi: 10.3934/math.2022549
[33]	Y. Chen, D. Z. Wang, Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted Nie-Tan algorithms, Soft Comput., 22 (2018), 7659–7678. https://doi.org/10.1007/s00500-018-3551-9 doi: 10.1007/s00500-018-3551-9
[34]	Y. Chen, D. Z. Wang, Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted enhanced Karnik-Mendel algorithms, Soft Comput., 22 (2018), 1361–1380. https://doi.org/10.1007/s00500-017-2938-3 doi: 10.1007/s00500-017-2938-3
[35]	Y. Chen, Study on centroid type-reduction of general type-2 fuzzy logic systems with sensible beginning weighted enhanced Karnik-Mendel algorithms, Soft Comput., 27 (2023), 9261–9279. https://doi.org/10.1007/S00500-023-08269-8 doi: 10.1007/S00500-023-08269-8
[36]	D. R. Wu, Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: Overview and comparisons, IEEE T. Fuzzy Syst., 21 (2013), 80–99. https://doi.org/10.1109/TFUZZ.2012.2201728 doi: 10.1109/TFUZZ.2012.2201728
[37]	J. W. Li, R. John, S. Coupland, G. Kendall, On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets, IEEE T. Fuzzy Syst., 26 (2018), 1036–1039. https://doi.org/10.1109/TFUZZ.2017.2666842 doi: 10.1109/TFUZZ.2017.2666842
[38]	S. Greenfield, F. Chiclana, Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set, Int. J. Approx. Reason., 54 (2013), 1013–1033. https://doi.org/10.1016/j.ijar.2013.04.013 doi: 10.1016/j.ijar.2013.04.013
[39]	S. Greenfield, F. Chiclana, S. Coupland, R. John, The collapsing method of defuzzification for discretised interval type-2 fuzzy sets, Inform. Sci., 179 (2009), 2055–2069. https://doi.org/10.1016/j.ins.2008.07.011 doi: 10.1016/j.ins.2008.07.011
[40]	Y. Chen, Study on weighted-based noniterative algorithms for computing the centroids of general type-2 fuzzy sets, Int. J. Fuzzy Syst., 24 (2022), 587–606. https://doi.org/10.1007/S40815-021-01166-Y doi: 10.1007/S40815-021-01166-Y
[41]	C. Chen, D. Wu, J. M. Garibaldi, R. I. John, J. Twycross, J. M. Mendel, A comprehensive study of the efficiency of type-reduction algorithms, IEEE T. Fuzzy Syst., 29 (2020), 1556–1566. https://doi.org/10.1109/TFUZZ.2020.2981002 doi: 10.1109/TFUZZ.2020.2981002
[42]	M. A. Khanesar, A. Jalalian, O. Kaynak, H. Gao, Improving the speed of center of sets type reduction in interval type-2 fuzzy systems by eliminating the need for sorting, IEEE T. Fuzzy Syst., 25 (2017), 1193–1206. https://doi.org/10.1109/TFUZZ.2016.2602392 doi: 10.1109/TFUZZ.2016.2602392
[43]	Y. Chen, C. X. Li, J. X. Yang, Design of discrete noniterative algorithms for center-of-sets type reduction of general type-2 fuzzy logic systems, Int. J. Fuzzy Syst., 24 (2022), 2024–2035. https://doi.org/10.1007/S40815-022-01256-5 doi: 10.1007/S40815-022-01256-5
[44]	F. Gaxiola, P. Melin, F. Valdez, J. R. Castro, O. Castillo, Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Appl. Soft Comput., 38 (2016), 860–871. https://doi.org/10.1016/j.asoc.2015.10.027 doi: 10.1016/j.asoc.2015.10.027
[45]	H. Mo, F. Y. Wang, M. Zhou, R. Li, Z. Xiao, Footprint of uncertainty for type-2 fuzzy sets, Inform. Sci., 272 (2014), 96–110. https://doi.org/10.1016/j.ins.2014.02.092 doi: 10.1016/j.ins.2014.02.092
[46]	F. Y. Wang, H. Mo, Some fundamental issues on type-2 fuzzy sets, Acta Auto. Sin., 43 (2017), 1114–1141. https://doi.org/10.16383/j.aas.2017.c160638 doi: 10.16383/j.aas.2017.c160638
[47]	C. H. Hsu, C. F. Juang, Evolutionary robot wall-following control using type-2 fuzzy controller with species-de-activated continuous ACO, IEEE T. Fuzzy Syst., 21 (2013), 100–112. https://doi.org/10.1109/TFUZZ.2012.2202665 doi: 10.1109/TFUZZ.2012.2202665
[48]	N. Mansoureh, F. Z. M. Hossein, B. Susan, A multilayer general type-2 fuzzy community detection model in large-scale social networks, IEEE T. Fuzzy Syst., 30 (2022), 4494–4503. https://doi.org/10.1109/TFUZZ.2022.3153745 doi: 10.1109/TFUZZ.2022.3153745
[49]	E. Ontiveros, P. Melin, O. Castillo, Comparative study of interval type-2 and general type-2 fuzzy systems in medical diagnosis, Inform. Sci., 525 (2020), 37–53. https://doi.org/10.1016/j.ins.2020.03.059 doi: 10.1016/j.ins.2020.03.059

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)