Fuzzy Math
Bingxin Li; Xuefeng Zhang; Xin Zhao
Volume 21, Issue 3 , May and June 2024, Pages 1-17
Abstract
The problem of robust nonfragile H∞filtering for fuzzy fractional order (FFO) systems 0 < α < 1 with uncertainties is studied. First, a new sufficient condition of H∞ control for fractional order systems is given to overcome the shortcoming of solving the complex matrix. Then, ...
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The problem of robust nonfragile H∞filtering for fuzzy fractional order (FFO) systems 0 < α < 1 with uncertainties is studied. First, a new sufficient condition of H∞ control for fractional order systems is given to overcome the shortcoming of solving the complex matrix. Then, based on the condition and the linear matrix inequality (LMI) approach, the conditions of robust H∞ control for FFO systems are proposed, which can guarantee the prescribed noise attenuation level in the H∞ sense. Furthermore, the FFO filter is constructed, and sufficient conditions are proposed for FFO filter systems. Finally, two examples are given to verify the effectiveness of our conditions.
Fuzzy Math
Muhammad Akram; Muhammad Bilal; Mohammadreza Shahriari; Tofigh Allahviranloo
Volume 21, Issue 3 , May and June 2024, Pages 19-36
Abstract
This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. ...
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This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology’s liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposedmethodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics.
Optimization
Mohammadreza Jahangiri; Alireza Nazemi
Volume 21, Issue 3 , May and June 2024, Pages 37-63
Abstract
In the proposed manuscript, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is gainedusing a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOPby RNN's, we establish a new scheme to solve the problem. By reducing theoriginal program ...
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In the proposed manuscript, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is gainedusing a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOPby RNN's, we establish a new scheme to solve the problem. By reducing theoriginal program to an interval problem and then weighting problem, the Karush--Kuhn--Tucker (KKT)conditions are presented. Moreover, we apply the KKT conditions into a RNN as a efficient tool to solve the problem. Besides, the convergence properties and thestability analysis of the system model are provided. In the final step, several simulation examples are verified to support the obtained results. Reported results are compared with some other previous neural networks.
Approximate Reasoning
R.A. Aliev; S.R. Abizada; Rahib Abiyev
Volume 21, Issue 3 , May and June 2024, Pages 65-76
Abstract
Many dynamic processes are characterized by parametric or structural uncertainties due to internal and externaldisturbances. Existing deterministic models could not handle the uncertainties inherent in these processes. A valuablealternative to control these processes is the use of a type-3 fuzzy system. ...
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Many dynamic processes are characterized by parametric or structural uncertainties due to internal and externaldisturbances. Existing deterministic models could not handle the uncertainties inherent in these processes. A valuablealternative to control these processes is the use of a type-3 fuzzy system. Since type-3 fuzzy systems use threedimensionalmembership functions, they have more capacity to model uncertainties. This paper introduces the designof a type-3 fuzzy logic system (FLS) for the control of dynamic plants. Utilizing type-3 fuzzy logic, the architectureof the type-3 fuzzy control system (T3FCS) is proposed. The knowledge base of the controller is constructed and itsdesign stages are presented. The inference mechanism of type-3 FLS is developed using α slices and interval type-3membership functions. The proposed type-3 FLS is utilized for controlling nonlinear dynamic plants. The modelingof the proposed T3FCS is performed and transient response characteristic is derived using different stepwise excitationsignals. A comparison of the designed system with the type-1 FLS-based system is provided. The obtained simulationresult demonstrates the efficiency of using the proposed type-3 FLS in the control of dynamic systems characterized byuncertainties.
Fuzzy Math
Zhi-qiang Liu
Volume 21, Issue 3 , May and June 2024, Pages 77-90
Abstract
Based on the classical works of Clifford inducing partial order from semigroups, recently, Gupta and Jayaram explored the order $\sqsubseteq_{F}$ from an associative operation $F$ through \emph{local left identity} (\textbf{LLI}). Inspired by their works, we further present an order $\sqsubseteq^{*}_F$ ...
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Based on the classical works of Clifford inducing partial order from semigroups, recently, Gupta and Jayaram explored the order $\sqsubseteq_{F}$ from an associative operation $F$ through \emph{local left identity} (\textbf{LLI}). Inspired by their works, we further present an order $\sqsubseteq^{*}_F$ obtained from non-commutative operation $F$ which has the \emph{local right identity} (\textbf{LRI}) since the non-commutativity of $F$ implies that the local left and right identity may be different for each element, which means that both orders may not coincide in the same domain. Firstly, we determine an equivalent characterization for two orders induced by non-commutative operation $F$. Secondly, we investigate both orders induced by semi-t-operators and deeply study their properties. Finally, we characterize both orders obtained from semi-uninorm (resp. semi-nullnorm) under the condition that semi-uninorm (resp. semi-nullnorm) is locally continuous.
Industrial Engineering
Abbas Parchami; Vahid Amirzadeh; Hamideh Iranmanesh; Fatemeh Ghaderi
Volume 21, Issue 3 , May and June 2024, Pages 91-101
Abstract
Process monitoring using control charts is a common quality control method to plot the manufacturing process data and compare it to the control limits in the manufacturing process. Construction of the statistical control charts is recently suggested on the basis of the flexible triangular fuzzy quality ...
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Process monitoring using control charts is a common quality control method to plot the manufacturing process data and compare it to the control limits in the manufacturing process. Construction of the statistical control charts is recently suggested on the basis of the flexible triangular fuzzy quality rather than common interval-valued quality. Two new percentile-based approaches are investigated in this paper to construct mean and range control charts for the degree of belonging observations to the triangular fuzzy quality. A real-world case study about automobile engine piston rings is presented to show the performance of the proposed control charts.
Fuzzy Math
Dongxue Jiang; Hua-Wen Liu
Volume 21, Issue 3 , May and June 2024, Pages 103-121
Abstract
Uninorms are a special type of associative aggregation functions, which have received widespread attention in the theoretical and practical fields since their introduction. Durante and Sarkoci introduced the migrativity property in 2008. Afterwards, this property was widely applied in numerous fields ...
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Uninorms are a special type of associative aggregation functions, which have received widespread attention in the theoretical and practical fields since their introduction. Durante and Sarkoci introduced the migrativity property in 2008. Afterwards, this property was widely applied in numerous fields like image processing and decision analysis, which has sparked a series of studies. There have been a large number of research results on the migrativity involving uninorms, but the work has mainly focused on the uninorms internal on the boundary. In this paper, we will concentrate on the uninorms not internal on the boundary. First, we discuss the characterization of the α-migrativity of conjunctive uninorms over continuous t-norms according to the value of α. Then, the consequences of the α-migrativity of disjunctive uninorms over continuous t-conorms can be obtained dually.
Fuzzy Math
Eunsuk Yang
Volume 21, Issue 3 , May and June 2024, Pages 123-136
Abstract
Micanorm-based logics with a weak form of associativity are introduced and their completeness results are addressed. More concretely, first the basic wa$_{t}$-uninorm logic \textbf{WA$_{\textbf{t}}$BUL} and its axiomatic extensions are introduced as $[0, t]$-continuous wa$_{t}$-uninorm analogues of the ...
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Micanorm-based logics with a weak form of associativity are introduced and their completeness results are addressed. More concretely, first the basic wa$_{t}$-uninorm logic \textbf{WA$_{\textbf{t}}$BUL} and its axiomatic extensions are introduced as $[0, t]$-continuous wa$_{t}$-uninorm analogues of the logics based the $[0, 1)$-continuous uninorms. Next algebraic structures characterizing the logics are introduced along with algebraic completeness results. Third, wa$_{t}$-uninorms are introduced as uninorms with weak $t$-associativity instead of associativity and associated properties are discussed. Finally, by virtue of Yang--style construction, it is verified that the logics based on wa$_{t}$-uninorms are complete on unit real interval $[0, 1]$, i.e., so called \emph{standard} complete.
Engineering
M. Syed Ali; B. Vigneshwar; G. Rajchakit; B. Priya; G. k. Thakur
Volume 21, Issue 3 , May and June 2024, Pages 137-154
Abstract
We present an event-triggered filtering design based on Takagi-Sugeno (T-S) fuzzy models for nonlinear conic-type networks. Discrete event-triggered systems (ETS) can save communication resources when they are dynamic. Firstly, we construct a appropriate event-triggered $H_{\infty}$ filtering design ...
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We present an event-triggered filtering design based on Takagi-Sugeno (T-S) fuzzy models for nonlinear conic-type networks. Discrete event-triggered systems (ETS) can save communication resources when they are dynamic. Firstly, we construct a appropriate event-triggered $H_{\infty}$ filtering design an error dynamic system. A generalized performance index is developed next, which addresses the $L_{2}-L_{\infty}$ and $H_{\infty}$ fuzzy filtering problems with network transmission delay. Further, an suitable Lyapunov-Krasovskii function is chosen to derive the stability condition of the conic-type error dynamic system and fulfills the given $H_{\infty}$ performance level. A linear matrix inequality (LMI) provides the necessary conditions for the result to be obtained. In addition, numerical examples are presented to verify the proposed new design method.
Fuzzy Math
Xiaofei Yang; Leyao Jia; Yingcang Ma; Xiaolong Xin; Mohammad Mehdi Zahedi
Volume 21, Issue 3 , May and June 2024, Pages 155-175
Abstract
Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method ...
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Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method is applied to the fuzzy clustering algorithm, and a robust semi-supervised fuzzy clustering algorithm is proposed. Firstly, fully considering prior knowledge, our models integrate pointwise constraints and pairwise constraints into a unified framework to improve the clustering performance of the fuzzy clustering algorithm. Secondly, in order to alleviate the impact of outliers, the robust performance of the models is considered by introducing an adaptive loss function into the models. Thirdly, our models can capture the global structures and the local manifold structures of data sets. Finally, a simple and efficient algorithm is proposed to solve the models, which ensures that the obtained solution is sparse and satisfies the constraint conditions in our models. Compared with five representative methods, experimental results on public datasets, such as text dataset (dbworld), voice dataset (Isolet), image datasets (YALE, Umist), chemical dataset (wine) and biological datasets (colon, TOX-171), show the effectiveness of the proposed models.
Fuzzy modelling
Zahra Behdani; majid darehmiraki
Volume 21, Issue 3 , May and June 2024, Pages 177-192
Abstract
Both traditional and fuzzy regression analyses have demonstrated the significant characteristics of the least-squares methodology as a method for parameter estimation.} The presence of outliers in the sample and/or minor variations in the dataset might impact the behaviour and characteristics of the ...
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Both traditional and fuzzy regression analyses have demonstrated the significant characteristics of the least-squares methodology as a method for parameter estimation.} The presence of outliers in the sample and/or minor variations in the dataset might impact the behaviour and characteristics of the least-squares estimators (LSE). In contrast, robust approaches provide estimators of the parameters that are resilient to the aforementioned unfavourable effects. This study aims to expand upon the Theil-Sen estimator in fuzzy regression analysis, with the objective of obtaining consistent findings even when outliers are present. \rd{ We demonstrate the effectiveness of the suggested technique through simulation experiments and real-world examples, comparing it to commonly used fuzzy regression models. The applicative examples are based on hydrology and atmospheric environment datasets. We also show the sensitivity analysis of the estimated parameters using a Monte-Carlo simulation study, demonstrating the effectiveness of the suggested estimators in comparison to other established approaches in the field of fuzzy regression analysis. The results showed that the Theil-Sen estimator (TSE) is very effective in cases where there are outliers, and the calculation error is smaller compared to other methods.
Fuzzy Math
John Mordeson; Davender Malik; Sunil Mathew
Volume 21, Issue 3 , May and June 2024, Pages 193-200
Abstract
In this paper, we evaluate the fuzzy similarity measuresof different country rankings with respect to the most dangerous and safestfor women. We find that the fuzzy similarity measures are high. We developsome theoretical results concerning fuzzy similarity measures. The goal of the paper is to examine ...
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In this paper, we evaluate the fuzzy similarity measuresof different country rankings with respect to the most dangerous and safestfor women. We find that the fuzzy similarity measures are high. We developsome theoretical results concerning fuzzy similarity measures. The goal of the paper is to examine the similarity of the rankings of countries with respect to the most dangerous countries for women to live and the peace and security of the countries for women. We determine a formula for the difference of rankings of the fuzzy similarity measure of two rankings A and B and the opposite of A and B.
