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Journal articles on the topic 'Resolution of fuzzy polynomial systems'

Author: Grafiati

Published: 25 May 2024

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1

Adil, Bouhouch, Er-Rafyg Aicha, and Ez-Zahout Abderrahmane. "Neural network to solve fuzzy constraint satisfaction problems." IAES International Journal of Artificial Intelligence (IJ-AI) 13, no. 1 (March 1, 2024): 228. http://dx.doi.org/10.11591/ijai.v13.i1.pp228-235.

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<p>It has been proven that solving the constraint satisfaction problem (CSP) is an No Polynomial hard combinatorial optimization problem. This holds true even in cases where the constraints are fuzzy, known as fuzzy constraint satisfaction problems (FCSP). Therefore, the continuous Hopfield neural network model can be utilized to resolve it. The original algorithm was developed by Talaavan in 2005. Many practical problems can be represented as a FCSP. In this paper, we expand on a neural network technique that was initially developed for solving CSP and adapt it to tackle problems that involve at least one fuzzy constraint. To validate the enhanced effectiveness and rapid convergence of our proposed approach, a series of numerical experiments are carried out. The results of these experiments demonstrate the superior performance of the new method. Additionally, the experiments confirm its fast convergence. Specifically, our study focuses on binary instances with ordinary constraints to test the proposed resolution model. The results confirm that both the proposed approaches and the original continuous Hopfield neural network approach exhibit similar performance and robustness in solving ordinary constraint satisfaction problems.</p>

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2

German, Oleg, and Sara Nasrh. "New Method for Optimal Feature Set Reduction." Informatics and Automation 19, no. 6 (December 11, 2020): 1198–221. http://dx.doi.org/10.15622/ia.2020.19.6.3.

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A problem of searching a minimum-size feature set to use in distribution of multidimensional objects in classes, for instance with the help of classifying trees, is considered. It has an important value in developing high speed and accuracy classifying systems. A short comparative review of existing approaches is given. Formally, the problem is formulated as finding a minimum-size (minimum weighted sum) covering set of discriminating 0,1-matrix, which is used to represent capabilities of the features to distinguish between each pair of objects belonging to different classes. There is given a way to build a discriminating 0,1-matrix. On the basis of the common solving principle, called the group resolution principle, the following problems are formulated and solved: finding an exact minimum-size feature set; finding a feature set with minimum total weight among all the minimum-size feature sets (the feature weights may be defined by the known methods, e.g. the RELIEF method and its modifications); finding an optimal feature set with respect to fuzzy data and discriminating matrix elements belonging to diapason [0,1]; finding statistically optimal solution especially in the case of big data. Statistically optimal algorithm makes it possible to restrict computational time by a polynomial of the problem sizes and density of units in discriminating matrix and provides a probability of finding an exact solution close to 1. Thus, the paper suggests a common approach to finding a minimum-size feature set with peculiarities in problem formulation, which differs it from the known approaches. The paper contains a lot of illustrations for clarification aims. Some theoretical statements given in the paper are based on the previously published works. In the concluding part, the results of the experiments are presented, as well as the information on dimensionality reduction for the coverage problem for big datasets. Some promising directions of the outlined approach are noted, including working with incomplete and categorical data, integrating the control model into the data classification system.

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3

Chen, Ying-Jen, Hua O. Wang, Motoyasu Tanaka, Kazuo Tanaka, and Hiroshi Ohtake. "Discrete polynomial fuzzy systems control." IET Control Theory & Applications 8, no. 4 (March 6, 2014): 288–96. http://dx.doi.org/10.1049/iet-cta.2013.0645.

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4

Qiu, Yu, Hong Yang, Yan-Qing Zhang, and Yichuan Zhao. "Polynomial regression interval-valued fuzzy systems." Soft Computing 12, no. 2 (May 23, 2007): 137–45. http://dx.doi.org/10.1007/s00500-007-0189-4.

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5

Aubry, Philippe, Jérémy Marrez, and Annick Valibouze. "Computing real solutions of fuzzy polynomial systems." Fuzzy Sets and Systems 399 (November 2020): 55–76. http://dx.doi.org/10.1016/j.fss.2020.01.004.

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6

OH, S., W. PEDRYCZ, and S. ROH. "Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons." Information Sciences 176, no. 23 (December 4, 2006): 3490–519. http://dx.doi.org/10.1016/j.ins.2005.11.009.

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7

Ku, Cheung-Chieh, Chein-Chung Sun, Shao-Hao Jian, and Wen-Jer Chang. "Passive Fuzzy Controller Design for the Parameter-Dependent Polynomial Fuzzy Model." Mathematics 11, no. 11 (May 28, 2023): 2482. http://dx.doi.org/10.3390/math11112482.

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This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent NTV systems. According to the Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of the PDPF model. Furthermore, the passive theory is applied to achieve performance, constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions, which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller, such that the NTV system is robustly stable and passive. Finally, two examples are applied to demonstrate the effectiveness of the proposed stability criterion.

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8

Kharrati, Hamed, Sohrab Khanmohammadi, Witold Pedrycz, and Ghasem Alizadeh. "Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems." Mathematical Problems in Engineering 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/273631.

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This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

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9

Shen, Yu-Hsuan, Ying-Jen Chen, Fan-Nong Yu, Wen-June Wang, and Kazuo Tanaka. "Descriptor Representation-Based Guaranteed Cost Control Design Methodology for Polynomial Fuzzy Systems." Processes 10, no. 9 (September 7, 2022): 1799. http://dx.doi.org/10.3390/pr10091799.

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This paper presents a descriptor representation-based guaranteed cost design methodology for polynomial fuzzy systems. This methodology applies the descriptor representation for presenting the closed-loop system of the polynomial fuzzy model with a parallel distributed compensation (PDC) based fuzzy controller. By the utility of descriptor representation, the guaranteed cost control (GCC) design analysis can utilize polynomial fuzzy slack matrices for obtaining less conservative results. The proposed GCC design is presented as the sum-of-squares (SOS) conditions. The application of polynomial fuzzy slack matrices leads to the double fuzzy summation issue in the control design. Accordingly, the copositive relaxation works out the problem well and is adopted in the control design analysis. The GCC design minimizes the upper limit of a predesignated cost function. According to the performance function, two simulation examples are provided to demonstrate the validity of the proposed GCC design. In these two examples, the proposed design obtains superior results.

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10

Nasiri, Alireza, Sing Kiong Nguang, Akshya Swain, and Dhafer Almakhles. "Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach." International Journal of Systems Science 49, no. 3 (December 21, 2017): 557–66. http://dx.doi.org/10.1080/00207721.2017.1407006.

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11

Zhou, Qi, Ziran Chen, Xinchen Li, and Yabin Gao. "Quantized control for polynomial fuzzy discrete-time systems." Complexity 21, no. 2 (September 26, 2014): 325–32. http://dx.doi.org/10.1002/cplx.21607.

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12

Chibani, Ali, Mohammed Chadli, and Naceur Benhadj Braiek. "A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs." International Journal of Control, Automation and Systems 14, no. 1 (February 2016): 323–30. http://dx.doi.org/10.1007/s12555-014-0406-8.

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13

KO, K. H., T. SAKKALIS, and N. M. PATRIKALAKIS. "RESOLUTION OF MULTIPLE ROOTS OF NONLINEAR POLYNOMIAL SYSTEMS." International Journal of Shape Modeling 11, no. 01 (June 2005): 121–47. http://dx.doi.org/10.1142/s021865430500075x.

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14

Hosseini Rostami, Seyyed Mohammad, Babak Sheikhi, Ahmad Jafari, and Mohammadreza Darvish. "Modeling and Control of Electrical Power and Energy Produced by a Synchronous Generator Using Polynomial Fuzzy Systems and Sum-Of-Squares Approach." Journal of Computational and Theoretical Nanoscience 18, no. 6 (June 1, 2021): 1653–66. http://dx.doi.org/10.1166/jctn.2021.9732.

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The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e., stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T-S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T-S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

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15

Hosseini Rostami, Seyyed Mohammad, Babak Sheikhi, Ahmad Jafari, and Mohammadreza Darvish. "Modeling and Control of Electrical Power and Energy Produced by a Synchronous Generator Using Polynomial Fuzzy Systems and Sum-Of-Squares Approach." Journal of Computational and Theoretical Nanoscience 18, no. 6 (June 1, 2021): 1653–66. http://dx.doi.org/10.1166/jctn.2021.9732.

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The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e., stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T-S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T-S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

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16

Hosseini Rostami, Seyyed Mohammad, Babak Sheikhi, Ahmad Jafari, and Mohammadreza Darvish. "Modeling and Control of Electrical Power and Energy Produced by a Synchronous Generator Using Polynomial Fuzzy Systems and Sum-Of-Squares Approach." Journal of Computational and Theoretical Nanoscience 18, no. 6 (June 1, 2021): 1653–66. http://dx.doi.org/10.1166/jctn.2021.9732.

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The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e., stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T-S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T-S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

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17

Lam, H. K., L. D. Seneviratne, and X. Ban. "Fuzzy control of non-linear systems using parameter-dependent polynomial fuzzy model." IET Control Theory & Applications 6, no. 11 (2012): 1645. http://dx.doi.org/10.1049/iet-cta.2011.0310.

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18

Sala, Antonio. "On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems." Annual Reviews in Control 33, no. 1 (April 2009): 48–58. http://dx.doi.org/10.1016/j.arcontrol.2009.02.001.

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19

OH, SUNG-KWUN, DONG-WON KIM, and WITOLD PEDRYCZ. "HYBRID FUZZY POLYNOMIAL NEURAL NETWORKS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 03 (June 2002): 257–80. http://dx.doi.org/10.1142/s0218488502001478.

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We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x) " where A is fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data.

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20

Farahani, Hamed, Sajjad Rahmany, Abdolali Basiri, and Ali Abbasi Molai. "Resolution of a system of fuzzy polynomial equations using eigenvalue method." Soft Computing 19, no. 2 (February 28, 2014): 283–91. http://dx.doi.org/10.1007/s00500-014-1249-1.

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21

Castro, Juan R., Oscar Castillo, Mauricio A. Sanchez, Olivia Mendoza, Antonio Rodríguez-Diaz, and Patricia Melin. "Method for Higher Order polynomial Sugeno Fuzzy Inference Systems." Information Sciences 351 (July 2016): 76–89. http://dx.doi.org/10.1016/j.ins.2016.02.045.

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22

Farahani, Hamed, and Hossein Jafari. "SOLVING FULLY FUZZY POLYNOMIAL EQUATIONS SYSTEMS USING EIGENVALUE METHOD." Advances in Fuzzy Sets and Systems 24, no. 1 (June 30, 2019): 29–54. http://dx.doi.org/10.17654/fs024010029.

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23

Lam, H. K., and J. C. Lo. "Output Regulation of Polynomial-Fuzzy-Model-Based Control Systems." IEEE Transactions on Fuzzy Systems 21, no. 2 (April 2013): 262–74. http://dx.doi.org/10.1109/tfuzz.2012.2211365.

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24

Meng, Aiwen, Hak-Keung Lam, Yan Yu, Xiaomiao Li, and Fucai Liu. "Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems." IEEE Transactions on Fuzzy Systems 26, no. 3 (June 2018): 1600–1612. http://dx.doi.org/10.1109/tfuzz.2017.2736964.

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25

Yu, Gwo-Ruey, Yong-Dong Chang, and Chih-Heng Chang. "Synthesis of Polynomial Fuzzy Model-Based Designs with Synchronization and Secure Communications for Chaos Systems with H∞ Performance." Processes 9, no. 11 (November 22, 2021): 2088. http://dx.doi.org/10.3390/pr9112088.

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This paper presents the sum of squares (SOS)-based fuzzy control with H∞ performance for a synchronized chaos system and secure communications. To diminish the influence of the extrinsic perturbation, SOS-based stability criteria of the polynomial fuzzy system are derived by using the polynomial Lyapunov function. The perturbation decreasing achievement is indexed in a H∞ criterion. The submitted SOS-based stability criteria are more relaxed than the existing linear matrix inequality (LMI)-based stability criteria. The cryptography scheme based on an n-shift cipher is combined with synchronization for secure communications. Finally, numerical simulations illustrate the perturbation decay accomplishment of the submitted polynomial fuzzy compensator.

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26

Ashar, Alissa Ully, Motoyasu Tanaka, and Kazuo Tanaka. "Stabilization and Robust Stabilization of Polynomial Fuzzy Systems: A Piecewise Polynomial Lyapunov Function Approach." International Journal of Fuzzy Systems 20, no. 5 (December 14, 2017): 1423–38. http://dx.doi.org/10.1007/s40815-017-0435-6.

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27

Lam, H. K., Mohammad Narimani, Hongyi Li, and Honghai Liu. "Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems Using Switching Polynomial Lyapunov Function." IEEE Transactions on Fuzzy Systems 21, no. 5 (October 2013): 800–813. http://dx.doi.org/10.1109/tfuzz.2012.2230005.

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Sadykova, Zulfira F., and Vladimir A. Abaev. "POLYNOMIAL APPROXIMATION OF FUZZY DATA AND SOLUTION OF FUZZY SYSTEMS OF LINEAR EQUATIONS." SOFT MEASUREMENTS AND COMPUTING 2, no. 63 (2023): 53–65. http://dx.doi.org/10.36871/2618-9976.2023.02.004.

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A large number of tasks in the economy are aimed at processing little formalized data. These can be tasks of analysis, planning, forecasting in the economy. The solution of these problems is reduced to the formalization of the data flow into a functional dependence. The definition of functional dependence is reduced to the approximation of data by a mathematical function. It is convenient to represent poorly formalized data as fuzzy numbers and reduce the solution of the approximation problem to the calculation of systems of fuzzy linear equations. This is achieved by developing the apparatus of software systems operating with calculations of fuzzy matrices. We have implemented computational approaches using the Zadeh principle and ordered fuzzy numbers.

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Abbasi Molai, Ali, Abdolali Basiri, and Sajjad Rahmany. "Resolution of a system of fuzzy polynomial equations using the Gröbner basis." Information Sciences 220 (January 2013): 541–58. http://dx.doi.org/10.1016/j.ins.2012.07.029.

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CHAKRABORTY, CHANDAN, and DEBJANI CHAKRABORTY. "FUZZY LINEAR AND POLYNOMIAL REGRESSION MODELLING OF ‘IF-THEN’ FUZZY RULEBASE." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 02 (April 2008): 219–32. http://dx.doi.org/10.1142/s0218488508005145.

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In developing so called fuzzy expert systems, fuzzy rule bases have been considered with greater importance. In fact, a fuzzy rule base is a knowledgebase that models human cognitive factors. Fuzzy rules are linguistic ‘IF-THEN’ constructions where ‘IF’ part consists of a set of fuzzy variables and ‘THEN’ part includes a dependent fuzzy variable. In order to identify the underlying mathematical structure in the fuzzy rule base, we develop fuzzy linear and fuzzy polynomial regression techniques in this paper. And the estimation of model parameters is also shown using least-square approach. Finally, examples are illustrated to demonstrate the proposed model.

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Sung-Kwun Oh, W. Pedrycz, and Ho-Sung Park. "Genetically optimized fuzzy polynomial neural networks." IEEE Transactions on Fuzzy Systems 14, no. 1 (February 2006): 125–44. http://dx.doi.org/10.1109/tfuzz.2005.861620.

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32

Sala, Antonio, and Thierry M. Guerra. "Stability Analysis of Fuzzy Systems: membership-shape and polynomial approaches." IFAC Proceedings Volumes 41, no. 2 (2008): 5605–10. http://dx.doi.org/10.3182/20080706-5-kr-1001.00945.

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Chen, Taolue, Tingting Han, and Yongzhi Cao. "Polynomial-time algorithms for computing distances of fuzzy transition systems." Theoretical Computer Science 727 (May 2018): 24–36. http://dx.doi.org/10.1016/j.tcs.2018.03.002.

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Liu, FuChun. "Polynomial-time verification of diagnosability of fuzzy discrete event systems." Science China Information Sciences 57, no. 6 (March 7, 2014): 1–10. http://dx.doi.org/10.1007/s11432-013-4945-z.

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Lendek, Zs, J. Lauber, T. M. Guerra, R. Babuška, and B. De Schutter. "Adaptive observers for TS fuzzy systems with unknown polynomial inputs." Fuzzy Sets and Systems 161, no. 15 (August 2010): 2043–65. http://dx.doi.org/10.1016/j.fss.2010.03.010.

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Seok-Beom Roh, W. Pedrycz, and Sung-Kwun Oh. "Genetic Optimization of Fuzzy Polynomial Neural Networks." IEEE Transactions on Industrial Electronics 54, no. 4 (August 2007): 2219–38. http://dx.doi.org/10.1109/tie.2007.894714.

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Chen, Xiaoxing, and Manfeng Hu. "Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems." Abstract and Applied Analysis 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3273480.

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Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.

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Narimani, Mohammand, and H. K. Lam. "SOS-Based Stability Analysis of Polynomial Fuzzy-Model-Based Control Systems Via Polynomial Membership Functions." IEEE Transactions on Fuzzy Systems 18, no. 5 (October 2010): 862–71. http://dx.doi.org/10.1109/tfuzz.2010.2050890.

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Abdollahzade, Majid, and Reza Kazemi. "A Developed Local Polynomial Neuro-Fuzzy Model for Nonlinear System Identification." International Journal on Artificial Intelligence Tools 24, no. 03 (June 2015): 1550004. http://dx.doi.org/10.1142/s0218213015500049.

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This paper proposes a local polynomial model tree (LPMT) learning technique for prediction and identification of nonlinear systems and processes. The proposed LPMT learning algorithm is applied to a local polynomial neuro fuzzy (LPNF) model, which includes local polynomial models (LPMs), as Taylor series expansion of any unknown function. . The LPMT algorithm is established based on the concept of hierarchical binary tree and heuristically partitions the input space into smaller subdomains through axis-orthogonal splits. The proposed learning algorithm starts from a single local polynomial model and then refines the LPNF model by increasing the degree of the worstperforming LPM or by further partitioning of the input space. During the learning procedure, the validity functions automatically form a partition of unity and therefore normalization side effects, e.g. reactivation and poor extrapolation performance, are prevented. The LPNF model, trained by the proposed LPMT algorithm, is used for prediction and identification of the nonlinear processes and systems in three case studies. The obtained results and comparisons to other methods revealed the promising performance of the proposed model.

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Oh, Sung-Kwun, and Witold Pedrycz. "Fuzzy Polynomial Neuron-Based Self-Organizing Neural Networks." International Journal of General Systems 32, no. 3 (June 2003): 237–50. http://dx.doi.org/10.1080/0308107031000090756.

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41

Mewada, Hiren, Amit V. Patel, Jitendra Chaudhari, Keyur Mahant, and Alpesh Vala. "Composite fuzzy-wavelet-based active contour for medical image segmentation." Engineering Computations 37, no. 9 (June 6, 2020): 3525–41. http://dx.doi.org/10.1108/ec-11-2019-0529.

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Purpose In clinical analysis, medical image segmentation is an important step to study the anatomical structure. This helps to diagnose and classify abnormality in the image. The wide variations in the image modality and limitations in the acquisition process of instruments make this segmentation challenging. This paper aims to propose a semi-automatic model to tackle these challenges and to segment medical images. Design/methodology/approach The authors propose Legendre polynomial-based active contour to segment region of interest (ROI) from the noisy, low-resolution and inhomogeneous medical images using the soft computing and multi-resolution framework. In the first phase, initial segmentation (i.e. prior clustering) is obtained from low-resolution medical images using fuzzy C-mean (FCM) clustering and noise is suppressed using wavelet energy-based multi-resolution approach. In the second phase, resultant segmentation is obtained using the Legendre polynomial-based level set approach. Findings The proposed model is tested on different medical images such as x-ray images for brain tumor identification, magnetic resonance imaging (MRI), spine images, blood cells and blood vessels. The rigorous analysis of the model is carried out by calculating the improvement against noise, required processing time and accuracy of the segmentation. The comparative analysis concludes that the proposed model withstands the noise and succeeds to segment any type of medical modality achieving an average accuracy of 99.57%. Originality/value The proposed design is an improvement to the Legendre level set (L2S) model. The integration of FCM and wavelet transform in L2S makes model insensitive to noise and intensity inhomogeneity and hence it succeeds to segment ROI from a wide variety of medical images even for the images where L2S failed to segment them.

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Mugambi, E. M., Andrew Hunter, Giles Oatley, and Lee Kennedy. "Polynomial-fuzzy decision tree structures for classifying medical data." Knowledge-Based Systems 17, no. 2-4 (May 2004): 81–87. http://dx.doi.org/10.1016/j.knosys.2004.03.003.

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Firouzkouhi, Narjes, Abbas Amini, Chun Cheng, Mehdi Soleymani, and Bijan Davvaz. "Fundamental relations and identities of fuzzy hyperalgebras." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 2265–74. http://dx.doi.org/10.3233/jifs-210994.

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Abstract:

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

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Ammar, Imen Iben, Hamdi Gassara, Ahmed El Hajjaji, and Mohamed Chaabane. "New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay." International Journal of Fuzzy Systems 20, no. 4 (December 27, 2017): 1057–68. http://dx.doi.org/10.1007/s40815-017-0425-8.

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Elias, Leandro J., Flávio A. Faria, Rayza Araujo, and Vilma A. Oliveira. "Stability conditions of TS fuzzy systems with switched polynomial Lyapunov functions." IFAC-PapersOnLine 53, no. 2 (2020): 6352–57. http://dx.doi.org/10.1016/j.ifacol.2020.12.1768.

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Li, Lizhen, and Kazuo Tanaka. "Relaxed Sum-of-squares Approach to Stabilization of Polynomial Fuzzy Systems." International Journal of Control, Automation and Systems 19, no. 8 (June 16, 2021): 2921–30. http://dx.doi.org/10.1007/s12555-020-0242-y.

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Sanjaya, Bomo W., Bambang Riyanto Trilaksono, and Arief Syaichu-Rohman. "H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach." Journal of Engineering and Technological Sciences 46, no. 2 (July 2014): 152–69. http://dx.doi.org/10.5614/j.eng.technol.sci.2014.46.2.3.

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Jang, Yong Hoon, Han Sol Kim, Young Hoon Joo, and Jin Bae Park. "Robust H∞Disturbance Attenuation Control of Continuous-time Polynomial Fuzzy Systems." Journal of Institute of Control, Robotics and Systems 22, no. 6 (June 1, 2016): 429–34. http://dx.doi.org/10.5302/j.icros.2016.16.0030.

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Boroujeni, Marziyeh, Abdolali Basiri, Sajjad Rahmany, and Annick Valibouze. "Finding solutions of fuzzy polynomial equations systems by an Algebraic method." Journal of Intelligent & Fuzzy Systems 30, no. 2 (February 9, 2016): 791–800. http://dx.doi.org/10.3233/ifs-151801.

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Pakkhesal, Sajjad, and Iman Mohammadzaman. "Less conservative output-feedback tracking control design for polynomial fuzzy systems." IET Control Theory & Applications 12, no. 13 (September 4, 2018): 1843–52. http://dx.doi.org/10.1049/iet-cta.2017.1271.

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