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Journal articles on the topic 'Fuzzy variance'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Tang, Wenjing, and Yitao Chen. "Variance and Semi-Variances of Regular Interval Type-2 Fuzzy Variables." Symmetry 14, no. 2 (2022): 278. http://dx.doi.org/10.3390/sym14020278.

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In this paper, we define the variance and semi-variances of regular interval type-2 fuzzy variables (RIT2-FVs) as well as derive a calculation formula of them based on the credibility distribution. Following the relationship between the variance and the semi-variances of the regular symmetric triangular interval type-2 fuzzy variables (RSTIT2-FVs), a special type of interval type-2 fuzzy variable is discovered and proved. Furthermore, for applying the two measures, we propose the operational law for the variance and semi-variances of the linear function of mutually independent RSTIT2-FVs. Some

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2

Zhang, Wei-Guo, and Ying-Luo Wang. "A Comparative Analysis of Possibilistic Variances and Covariances of Fuzzy Numbers." Fundamenta Informaticae 79, no. 1-2 (2007): 257–63. https://doi.org/10.3233/fun-2007-791-212.

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In this paper, we introduce a new crisp possibilistic variance and a new crisp possibilistic covariance of fuzzy numbers, which are different from those introduced by Carlsson and Fullér. We show that the possibilistic variance and covariance preserve many properties of variance and covariance in probability theory. Furthermore, we investigate the relationship between several crisp possibilistic variances and covariances of fuzzy numbers.

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P., Senthil Kumar, and Venkatesh A. "A MATHEMATICAL MODEL FOR THE EFFECT OF CORTICOSTERONE USING FUZZY EXPONENTIAL DISTRIBUTION." International Journal of Applied and Advanced Scientific Research 1, no. 1 (2016): 224–28. https://doi.org/10.5281/zenodo.223110.

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A fuzzy mathematical model was developed and used this model to calculate the expected mean and variance of Corticosterone level in the given time interval after lights onsets Releasing Hormone treatment. Formulae of fuzzy Exponential distribution and its α-cut sets were presented. Using fuzzy Exponential distribution, we showed that if the Lower α-cut of Mean and variance are increases when different alpha values and upper α-cut of Mean and variance are increases when different alpha values with respect to the time intervals.

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4

Ramasubramanian, S., and P. Mahendran. "Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable." Abstract and Applied Analysis 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/164795.

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L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

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5

Zainali, Z., M. G. Akbari, and H. Alizadeh Noughabi. "Intuitionistic fuzzy random variable and testing hypothesis about its variance." Soft Computing 19, no. 9 (2014): 2681–89. http://dx.doi.org/10.1007/s00500-014-1437-z.

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6

Wu, Hsien-Chung. "Analysis of variance for fuzzy data." International Journal of Systems Science 38, no. 3 (2007): 235–46. http://dx.doi.org/10.1080/00207720601157997.

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7

Pahade, Jagdish Kumar, and Manoj Jha. "Credibilistic variance and skewness of trapezoidal fuzzy variable and mean–variance–skewness model for portfolio selection." Results in Applied Mathematics 11 (August 2021): 100159. http://dx.doi.org/10.1016/j.rinam.2021.100159.

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8

Dzuche, Justin, Christian Deffo Tassak, Jules Sadefo Kamdem, and Louis Aimé Fono. "The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection." New Mathematics and Natural Computation 16, no. 02 (2020): 271–90. http://dx.doi.org/10.1142/s1793005720500167.

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Possibility, necessity and credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [L. Yang and K. Iwamura, Applied Mathematical Science 2(46) (2008) 2271–2288] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy variable based on that measure, namely, expected value, variance, semi-variance, skewness, kurtosis and semi-kurtosis. We determine some properties of these characteristics and we compu

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9

Yang, Mingrui, Wen Huang, and Dongyi Zou. "Fuzzy Pricing of European Options Based on Constant Elasticity of Variance Process." Journal of Statistics and Economics 1, no. 2 (2024): 199–205. http://dx.doi.org/10.62517/jse.202411229.

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Based on the assumption that the stock price follows the CEV process, this article uses fuzzy mathematics theory to discuss the price of European options. As the financial market is constantly fluctuating, the parameter of the stock price following the CEV process should not be a constant. Therefore, considering fuzzy interest rates, fuzzy stock prices, and fuzzy initial volatility, under the assumption of fuzzy parameters, the price of the obtained option is a fuzzy number. This article first derives the pricing formula for European options with stock prices following the CEV process. Then, u

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10

Heng, Aimin, Qian Chen, and Yingshuang Tan. "Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/635898.

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Option pricing is irreversible, fuzzy, and flexible. The fuzzy measure which is used for real option pricing is a useful supplement to the traditional real option pricing method. Based on the review of the concepts of the mean and variance of trapezoidal fuzzy number and the combination with the Carlsson-Fuller model, the trapezoidal fuzzy variable can be used to represent the current price of land expropriation and the sale price of land on the option day. Fuzzy Black-Scholes option pricing model can be constructed under fuzzy environment and problems also can be solved and discussed through

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11

Ramli, Suhailywati, and Saiful Hafizah Jaaman. "MEDIAN-VARIANCE FUZZY WITH TRAPEZOIDAL FUZZY NUMBERS FOR PORTFOLIO SELECTION MODEL." Advances and Applications in Statistics 60, no. 1 (2020): 35–44. http://dx.doi.org/10.17654/as060010035.

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12

Gong, Yanbing, Lin Xiang, Shuxin Yang, and Hailiang Ma. "A New Method for Ranking Interval Type-2 Fuzzy Numbers Based on Mellin Transform." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 04 (2020): 591–611. http://dx.doi.org/10.1142/s0218488520500257.

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Interval type-2 fuzzy sets provide us with additional degrees of freedom to represent the uncertainty and the fuzziness of the real word than traditional type-1 fuzzy sets. Interval type-2 fuzzy numbers ranking has an important role in the decision making analysis. In this paper, the probatilistic mean value and variance of interval type-2 fuzzy numbers are proposed based on the Mellin transform for type-1 fuzzy numbers. The interval type-2 fuzzy number with the higher mean is ranked higher. If the mean values are equal the one with the smaller variance is judged higher rank. On this basis, so

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13

Kılıçman, Adem, and Jaisree Sivalingam. "Portfolio Optimization of Equity Mutual Funds—Malaysian Case Study." Advances in Fuzzy Systems 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/879453.

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We focus on the equity mutual funds offered by three Malaysian banks, namely Public Bank Berhad, CIMB, and Malayan Banking Berhad. The equity mutual funds or equity trust is grouped into four clusters based on their characteristics and categorized as inferior, stable, good performing, and aggressive funds based on their return rates, variance and treynor index. Based on the cluster analysis, the return rates and variance of clusters are represented as triangular fuzzy numbers in order to reflect the uncertainty of financial market. To find the optimal asset allocation in each cluster we develo

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14

GEORGESCU, IRINA, and JANI KINNUNEN. "A NEW NOTION OF POSSIBILISTIC COVARIANCE." New Mathematics and Natural Computation 09, no. 01 (2013): 1–11. http://dx.doi.org/10.1142/s1793005713500014.

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Possibilistic indicators of fuzzy numbers (expected value, variance, and covariance) are an efficient instrument in the modeling of uncertainty phenomena. Various models of uncertainty phenomena have led to several notions of variance and covariance. In particular, the possibilistic models of risk aversion previously studied by one of the authors imposed a notion of variance of a fuzzy number different from those existing in the literature. In this paper, a new notion of covariance of two fuzzy numbers corresponding to the possibilistic variance mentioned is studied. This possibilistic covaria

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15

Kang, Man-Ki, and Sung-Il Han. "Multivariate Analysis of Variance for Fuzzy Data." International Journal of Fuzzy Logic and Intelligent Systems 4, no. 1 (2004): 97–100. http://dx.doi.org/10.5391/ijfis.2004.4.1.097.

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16

Körner, Ralf. "On the variance of fuzzy random variables." Fuzzy Sets and Systems 92, no. 1 (1997): 83–93. http://dx.doi.org/10.1016/s0165-0114(96)00169-8.

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17

Huang, Xiaoxia. "Mean-variance model for fuzzy capital budgeting." Computers & Industrial Engineering 55, no. 1 (2008): 34–47. http://dx.doi.org/10.1016/j.cie.2007.11.015.

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18

Nourbakhsh, M., M. Mashinchi, and A. Parchami. "Analysis of variance based on fuzzy observations." International Journal of Systems Science 44, no. 4 (2013): 714–26. http://dx.doi.org/10.1080/00207721.2011.618640.

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19

Bonacic, Milena, Héctor López-Ospina, Cristián Bravo, and Juan Pérez. "A Fuzzy Entropy Approach for Portfolio Selection." Mathematics 12, no. 13 (2024): 1921. http://dx.doi.org/10.3390/math12131921.

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Portfolio management typically aims to achieve better returns per unit of risk by building efficient portfolios. The Markowitz framework is the classic approach used when decision-makers know the expected returns and covariance matrix of assets. However, the theory does not always apply when the time horizon of investments is short; the realized return and covariance of different assets are usually far from the expected values, and considering additional factors, such as diversification and information ambiguity, can lead to better portfolios. This study proposes models for constructing effici

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20

Chachi, Jalal. "On Distribution Characteristics of a Fuzzy Random Variable." Austrian Journal of Statistics 47, no. 2 (2018): 53–67. http://dx.doi.org/10.17713/ajs.v47i2.581.

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In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

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21

Subiantoro, Aries, F. Yusivar, B. Budiardjo, and M. I. Al-Hamid. "Identification and Control Design of Fuzzy Takagi-Sugeno Model for Pressure Process Rig." Advanced Materials Research 605-607 (December 2012): 1810–18. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.1810.

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The design of an intelligent controller based on fuzzy TS model for a pressure process rig is presented. The proposed controller consists of a fuzzy TS model, a feedback fuzzy TS model, and a low pass filter combined in an internal model control structure. The identification of the fuzzy TS model uses fuzzy clustering technique to mimic the nonlinearity characteristic of the process. Instead of least-squares algorithm, the instrumental variable method is used to estimate the consequent parameters of the fuzzy TS model in order to avoid inconsistency problem. The identified model is validated w

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22

Chen, Guohua, Zhijun Luo, Xiaolian Liao, Xing Yu, and Lian Yang. "mean–variance–skewness fuzzy portfolio selection model based on intuitionistic fuzzy optimization." Procedia Engineering 15 (2011): 2062–66. http://dx.doi.org/10.1016/j.proeng.2011.08.385.

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23

Emad Kareem, Rawya, and Mohammed Jasim Mohammed. "Fuzzy Bridge Regression Model Estimating via Simulation." Journal of Economics and Administrative Sciences 29, no. 136 (2023): 60–69. http://dx.doi.org/10.33095/jeas.v29i136.2607.

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The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor whe

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24

P. Pandian, P. Pandian, and D. Kalpanapriya D. Kalpanapriya. "Analysis of Variance For Crisp Data with Membership Grades of Fuzzy Sets." International Journal of Scientific Research 2, no. 12 (2012): 548–52. http://dx.doi.org/10.15373/22778179/dec2013/174.

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25

Chang, Wen-Jer, and Bo-Jyun Huang. "Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/687317.

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The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the correspondin

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26

Mohamad Hanapi, Amiratul L., Mahmod Othman, Rajalingam Sokkalingam, Nazirah Ramli, Abdullah Husin, and Pandian Vasant. "A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting." Applied Sciences 10, no. 6 (2020): 1949. http://dx.doi.org/10.3390/app10061949.

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Generalized autoregressive conditional heteroskedasticity (GARCH) is one of the most popular models for time-series forecasting. The GARCH model uses a maximum likelihood method for parameter estimation. For the likelihood method to work, there should be a known and specific distribution. However, due to uncertainties in time-series data, a specific distribution is indeterminable. The GARCH model is also unable to capture the influence of each variance in the observation because the calculation of the long-run average variance only considers the series in its entirety, hence the information on

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27

Appadoo, S. S., A. Kumar, and Y. Gajpal. "Generalized exponential trapezoidal fuzzy numbers based on variance." Journal of Information and Optimization Sciences 42, no. 7 (2021): 1409–24. http://dx.doi.org/10.1080/02522667.2021.1877403.

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28

Castillo, Sergio E. Pinto, Mike J. Grimble, and Reza Katebi. "SELF-TUNING NEURO-FUZZY GENERALIZED MINIMUM VARIANCE CONTROLLER." IFAC Proceedings Volumes 38, no. 1 (2005): 103–8. http://dx.doi.org/10.3182/20050703-6-cz-1902.01095.

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29

Huang, Xiaoxia. "Minimax mean-variance models for fuzzy portfolio selection." Soft Computing 15, no. 2 (2010): 251–60. http://dx.doi.org/10.1007/s00500-010-0654-3.

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30

Spadoni, Massimo, and Luciano Stefanini. "Computing the variance of interval and fuzzy data." Fuzzy Sets and Systems 165, no. 1 (2011): 24–36. http://dx.doi.org/10.1016/j.fss.2010.09.003.

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31

Näther, Wolfgang, and Andreas Wünsche. "On the Conditional Variance of Fuzzy Random Variables." Metrika 65, no. 1 (2006): 109–22. http://dx.doi.org/10.1007/s00184-006-0063-x.

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32

Kang, Man-Ki. "Correlation Test by Reduced-Spread of Fuzzy Variance." Communications for Statistical Applications and Methods 19, no. 1 (2012): 147–55. http://dx.doi.org/10.5351/ckss.2012.19.1.147.

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33

Ramos-Guajardo, Ana Belén, Ana Colubi, Gil González-Rodríguez, and María Ángeles Gil. "One-sample tests for a generalized Fréchet variance of a fuzzy random variable." Metrika 71, no. 2 (2009): 185–202. http://dx.doi.org/10.1007/s00184-008-0225-0.

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34

Sendi, Chokri. "Attitude Control of a Flexible Spacecraft via Fuzzy Optimal Variance Technique." Mathematics 10, no. 2 (2022): 179. http://dx.doi.org/10.3390/math10020179.

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This paper investigates the performance of a fuzzy optimal variance control technique for attitude stability and vibration attenuation with regard to a spacecraft made of a rigid platform and multiple flexible appendages that can be retargeted to the line of sight. The proposed technique addresses the problem of actuators’ amplitude and rate constraints. The fuzzy model of the spacecraft is developed based on the Takagi-Sugeno(T-S) fuzzy model with disturbances, and the control input is designed using the Parallel Distributed Compensation technique (PDC). The problem is presented as an optimiz

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35

Gu, Shanshan, Jianye Liu, Qinghua Zeng, Shaojun Feng, and Pin Lv. "Dynamic Allan Variance Analysis Method with Time-Variant Window Length Based on Fuzzy Control." Journal of Sensors 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/564041.

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To solve the problem that dynamic Allan variance (DAVAR) with fixed length of window cannot meet the identification accuracy requirement of fiber optic gyro (FOG) signal over all time domains, a dynamic Allan variance analysis method with time-variant window length based on fuzzy control is proposed. According to the characteristic of FOG signal, a fuzzy controller with the inputs of the first and second derivatives of FOG signal is designed to estimate the window length of the DAVAR. Then the Allan variances of the signals during the time-variant window are simulated to obtain the DAVAR of th

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36

Ostapenko, R. O., and I. A. Hodashinsky. "Setting a rule base for a fuzzy classifier using the grasshopper optimization algorithm and the clustering algorithm." Proceedings of Tomsk State University of Control Systems and Radioelectronics 25, no. 2 (2022): 31–36. http://dx.doi.org/10.21293/1818-0442-2022-25-2-31-36.

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The article presents a description of a hybrid algorithm for generating fuzzy rules for a fuzzy classifier using grasshopper optimization algorithm and the K-means data clustering algorithm. The performance of clustering was evaluated by three fitness functions: total variance, Davis–Bouldin index, and Calinski–Harabasz index. Triangular and Gaussian membership functions have been investigated. The efficiency of the generated fuzzy rule bases has been tested on real datasets. The best combination is to use the total variance as the fitness function and the Gaussian function as the membership f

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37

Gu, Yujie, Qingwei Hao, Jie Shen, Xiang Zhang, and Liying Yu. "Calculation formulas and correlation inequalities for variance bounds and semi-variances of fuzzy intervals." Journal of Intelligent & Fuzzy Systems 37, no. 4 (2019): 5689–705. http://dx.doi.org/10.3233/jifs-181408.

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38

Gu, Yujie, Qingwei Hao, Jie Shen, Xiang Zhang, and Liying Yu. "Calculation formulas and correlation inequalities for variance bounds and semi-variances of fuzzy intervals." Journal of Intelligent & Fuzzy Systems 36, no. 1 (2019): 353–69. http://dx.doi.org/10.3233/jifs-181467.

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39

Chang, Wen-Jer, Bo-Jyun Huang, and Po-Hsun Chen. "Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/598618.

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For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In orde

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40

Solatikia, Farnaz, Erdem Kiliç, and Gerhard Wilhelm Weber. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces." Organizacija 47, no. 2 (2014): 90–97. http://dx.doi.org/10.2478/orga-2014-0010.

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Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Ba

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41

Yano, Hitoshi. "Fuzzy decision making for fuzzy random multiobjective linear programming problems with variance covariance matrices." Information Sciences 272 (July 2014): 111–25. http://dx.doi.org/10.1016/j.ins.2014.02.101.

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42

Parsafard, Pouyan, Hadi Veisi, Niloofar Aflaki, and Siamak Mirzaei. "Text Classification based on DiscriminativeSemantic Features and Variance of Fuzzy Similarity." International Journal of Intelligent Systems and Applications 14, no. 2 (2022): 26–39. http://dx.doi.org/10.5815/ijisa.2022.02.03.

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Due to the rapid growth of the Internet, large amounts of unlabelled textual data are producing daily. Clearly, finding the subject of a text document is a primary source of information in the text processing applications. In this paper, a text classification method is presented and evaluated for Persian and English. The proposed technique utilizes variance of fuzzy similarity besides discriminative and semantic feature selection methods. Discriminative features are those that distinguish categories with higher power and the concept of semantic feature takes into the calculations the similarit

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43

Gogo, Kevin Otieno, Lawrence Nderu, and Makau Mutua. "Variances in knowledge-based interval type 2 Gaussian fuzzy on linear regression models." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 1807–20. http://dx.doi.org/10.3233/jifs-210568.

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Fuzzy logic is a branch of artificial intelligence that has been used extensively in developing Fuzzy systems and models. These systems usually offer artificial intelligence based on the predictive mathematical models used; in this case linear regression mathematical model. Interval type 2 Gaussian fuzzy logic is a fuzzy logic that utilizes Gaussian upper membership function and the lower membership function, with a footprint of uncertainty in between the Gaussian membership functions. The artificial intelligence solutions predicted by these interval type 2 fuzzy systems depends on the trainin

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44

Hidayah Mohamed Isa, Noor, Mahmod Othman, and Samsul Ariffin Abdul Karim. "Multivariate Matrix for Fuzzy Linear Regression Model to Analyse The Taxation in Malaysia." International Journal of Engineering & Technology 7, no. 4.33 (2018): 78. http://dx.doi.org/10.14419/ijet.v7i4.33.23490.

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A multivariate matrix is proposed to find the best factor for fuzzy linear regression (FLR) with symmetric triangular fuzzy numbers (TFNs). The goal of this paper is to select the best factor influence tax revenue among four variables. Eighteen years’ data of the variables from IndexMundi and World Bank Data. It is found that the model is successfully explained between independent variables and response variable. It is notices that sixty-six percent of the variance of tax revenue is explained by Gross Domestic Product, Inflation, Unemployment and Merchandise Trade. The introduction of multivar

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45

Noh, Sun-Young, Jin-Bae Park, and Young-Hoon Joo. "Optimal Fuzzy Filter for Nonlinear Systems with Variance Constraints." Journal of Korean Institute of Intelligent Systems 22, no. 5 (2012): 549–54. http://dx.doi.org/10.5391/jkiis.2012.22.5.549.

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46

Carlsson, Christer, and Robert Fullér. "On possibilistic mean value and variance of fuzzy numbers." Fuzzy Sets and Systems 122, no. 2 (2001): 315–26. http://dx.doi.org/10.1016/s0165-0114(00)00043-9.

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47

Fullér, Robert, and Péter Majlender. "On weighted possibilistic mean and variance of fuzzy numbers." Fuzzy Sets and Systems 136, no. 3 (2003): 363–74. http://dx.doi.org/10.1016/s0165-0114(02)00216-6.

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48

Pinto Castillo, Sergio E., Mike J. Grimble, and Reza Katebi. "Neuro-Fuzzy Generalized Minimum Variance Control of Nonlinear Systems." IFAC Proceedings Volumes 37, no. 21 (2004): 741–46. http://dx.doi.org/10.1016/s1474-6670(17)30559-1.

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49

Rezvani, S. "Ranking generalized exponential trapezoidal fuzzy numbers based on variance." Applied Mathematics and Computation 262 (July 2015): 191–98. http://dx.doi.org/10.1016/j.amc.2015.04.030.

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50

Li, Tiehong, Jin Li, Junbang Jiang, and Xinyu Liu. "Fuzzy PID control based on genetic algorithm optimization inverted pendulum system." Journal of Physics: Conference Series 2816, no. 1 (2024): 012001. http://dx.doi.org/10.1088/1742-6596/2816/1/012001.

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Abstract For the first-order inverted pendulum control system, a fuzzy PID control system based on the optimization of the genetic algorithm is proposed. The traditional genetic algorithm has the problem that the difference in the fuzzy subset parameter leads to a decrease in the interpretative ability of the fuzzy system. The main problem of the current genetic algorithm is the complexity of the computation and the low efficiency. Based on this problem, this paper proposes an improved genetic algorithm, i.e., it adopts the variance operator and adaptive change of the variance index and elite

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