Fuzzy approximation
Peng Zhang; Shulin Cui; Beibei Du
Volume 22, Issue 1 , January and February 2025, Pages 1-21
Abstract
In this paper, we define the possibilistic mean, variance and covariance with different risk attitudes and analyses their mathematical property. The mean and variance of the portfolio model are calculated by the fuzzy numbers, which are predicted by the Long-Short Term Memory networks (LSTM), Convolutional ...
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In this paper, we define the possibilistic mean, variance and covariance with different risk attitudes and analyses their mathematical property. The mean and variance of the portfolio model are calculated by the fuzzy numbers, which are predicted by the Long-Short Term Memory networks (LSTM), Convolutional Neural Networks (CNN), Support Vector Regression (SVR) and Random Forest (RF). Considering the borrowing constraints, transaction costs and threshold constraints, a new mean and variance fuzzy portfolio selection model with different risk attitudes based on Machine Learning is proposed. Based on the possibilistic measure, the proposed model is transformed into a quadratic programming problem, which is solved by the pivoting algorithm. Finally, the in-sample and out-of-sample comparison analyses of different constraints and different risk attitudes are provided to test the model and the algorithm.
Fuzzy Math
Chengyu Liang; Jiesheng Cui
Volume 22, Issue 1 , January and February 2025, Pages 23-33
Abstract
In this paper, the notions of (L,M)-fuzzy bornological convergence and separation in (L,M)-fuzzy bornological vector spaces are introduced. Some properties of (L,M)-fuzzy bornological convergence and separation are discussed. The relationships between (L,M)-fuzzy bornologial convergence and separation ...
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In this paper, the notions of (L,M)-fuzzy bornological convergence and separation in (L,M)-fuzzy bornological vector spaces are introduced. Some properties of (L,M)-fuzzy bornological convergence and separation are discussed. The relationships between (L,M)-fuzzy bornologial convergence and separation in (L,M)-fuzzy bornological vector spaces are proposed. Moreover, the relationships of bornological convergence and separation between the framework of (L,M)-fuzzy bornological vector spaces and L-bornological vector spaces are discussed.
Approximate Reasoning
Shudi Liang; Xue-ping Wang
Volume 22, Issue 1 , January and February 2025, Pages 35-47
Abstract
This article pays attention to the $\alpha$-migrativity of 2-uninorms with $\alpha\in [0,1]$ deeply. It describes the $\alpha$-migrativity of 2-uninorms completely, which generalizes and unifies some current existing characterizations for the $\alpha$-migrativity of triangular norms, triangular conorms, ...
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This article pays attention to the $\alpha$-migrativity of 2-uninorms with $\alpha\in [0,1]$ deeply. It describes the $\alpha$-migrativity of 2-uninorms completely, which generalizes and unifies some current existing characterizations for the $\alpha$-migrativity of triangular norms, triangular conorms, uninorms, nullnorms, uni-nullnorms and null-uninorms, respectively.
Engineering
Fatemeh Ghaderi; Abbas Parchami; Vahid Amirzadeh; Hamideh Iranmanesh
Volume 22, Issue 1 , January and February 2025, Pages 49-69
Abstract
The primary objective of statistical quality control is to ensure that products or services meet predetermined standards while minimizing variation and instability in processes. Control charts are indispensable tools in quality control, playing a crucial role in enhancing and improving process quality. ...
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The primary objective of statistical quality control is to ensure that products or services meet predetermined standards while minimizing variation and instability in processes. Control charts are indispensable tools in quality control, playing a crucial role in enhancing and improving process quality. Given their significance, incorporating fuzzy quality into control charts introduces flexibility into product quality assessment. In this paper, we design mean (¯ X) and range (R) control charts based on fuzzy quality, as opposed to traditional crisp or precise quality. We construct quantile-based control charts for the degree of membership of observations to triangular fuzzy quality using parameter estimation in the beta distribution. Specifically, we propose two novel methods for constructing¯ X and R control charts, namely, the method of moments and maximum likelihood estimation, both based on triangular fuzzy quality.
Optimization
Nisha Pokharna; Indira P. Tripathi
Volume 22, Issue 1 , January and February 2025, Pages 71-91
Abstract
In this paper, an interval fractional optimization problem with directionally differentiable functions is considered, and the d-invexity concept is introduced for interval-valued functions. Slater's constraint qualification and pre-invex directional derivative assumption are used to establish the necessary ...
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In this paper, an interval fractional optimization problem with directionally differentiable functions is considered, and the d-invexity concept is introduced for interval-valued functions. Slater's constraint qualification and pre-invex directional derivative assumption are used to establish the necessary optimality conditions. Further, sufficient optimality conditions are derived under the d-invexity assumption, considering the LU-solution concept. As an application of interval fractional problems, a portfolio optimization problem with uncertain return and risk parameters subject to interval liquidity constraints is considered, and an optimal solution is obtained using the results developed in this paper. Also, the portfolio optimization problem is solved using the proposed global criteria method for interval optimization problems and two methods available in the literature. Moreover, to check the efficiency of the proposed method, a comparison between different methods is presented. Throughout the paper, non-trivial examples are presented at appropriate places to provide a better understanding of the results developed.
Engineering
Mohammad reza Mohammadi; Mahdi Pourgholi; Mojtaba Nouri Manzar
Volume 22, Issue 1 , January and February 2025, Pages 93-110
Abstract
In this paper, a practical adaptive cruise control system (ACC) with two controller levels is addressed. The upper-level control scheme consists of distance and speed controllers. This controller generates the desired acceleration profile that must be followed as closely as possible by the lower-level ...
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In this paper, a practical adaptive cruise control system (ACC) with two controller levels is addressed. The upper-level control scheme consists of distance and speed controllers. This controller generates the desired acceleration profile that must be followed as closely as possible by the lower-level controller. A fuzzy adaptive output feedback controller with very high precision produces this desired acceleration. Furthermore, an adaptive observer estimates the states that can’t be measured. The lower-level controller adjusts the throttle and brake actuators. Also, in the lower level, the active disturbance rejection controller (ADRC) eliminates all of the internal and external disturbances applied to the car. The ADRC parameters are tuned via the particle swarm genetic optimization algorithm. The closed-loop stability and semi-globally uniformly ultimately boundedness of all the signals is proved. Also, the asymptotic convergence of the ADRC controller estimation error to zero is insured. To show the effectiveness of the proposed method, the proposed algorithm is compared with a predictive controller, and the performance superiority of the proposed method is demonstrated.
Decision Making
Muhammad Akram; Farwa Ilyasa
Volume 22, Issue 1 , January and February 2025, Pages 111-130
Abstract
This study pioneers an innovative decision-making framework, integrating interval rough numbers with the elimination and choice translating reality method, enhanced by the level-based weight assessment approach, specifically designed to assess sustainable mining technologies. The proposed model overcomes ...
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This study pioneers an innovative decision-making framework, integrating interval rough numbers with the elimination and choice translating reality method, enhanced by the level-based weight assessment approach, specifically designed to assess sustainable mining technologies. The proposed model overcomes the limitations of traditional multi-criteria decision-making methods by effectively addressing uncertainty and imprecision through interval rough numbers. In contrast to the conventional versions of outranking methods, which proceed upon the principles of concordance and discordance sets, the proposed approach has the additional potential tometiculously handle the pseudo criteria to facilitate the proper examination of the outranking relations. By closely evaluating each criterion’s explicit behavior in reference to the veto, preference, and indifference threshold values, the suggested technique has the advantage of being able to infer preferences in terms of strong and weak preference relations. The level-based weight assessment technique ensures a systematic and balanced determination of criteria weights, reflecting their relative importance. A comprehensive case study on sustainable mining technology evaluation demonstrates the efficacy and robustness of our approach, yielding more preciseand consistent decision outcomes. A comparison study with existing techniques is carried out to elucidate the validity, rationality, superiority, and effectiveness of the results.
Fuzzy Math
Li Lingqiang; Jin Qiu
Volume 22, Issue 1 , January and February 2025, Pages 131-134
Abstract
Han and Pang (IJFS 2024) introduced important L-convergence structures based on L-ordered co-Scott closed sets, extending strong L-concave structures. Since L-ordered co-Scott closed sets and L-convergence structures rely on L-order, while strong L-concavestructures depend on pointwise order, the relationship ...
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Han and Pang (IJFS 2024) introduced important L-convergence structures based on L-ordered co-Scott closed sets, extending strong L-concave structures. Since L-ordered co-Scott closed sets and L-convergence structures rely on L-order, while strong L-concavestructures depend on pointwise order, the relationship between them is still not clearenough. To clarify this, we provide characterizations of both using pointwise orders, re-vealing that the definition of L-ordered co-Scott closed sets can be simplified, as its strat-ified condition can be derived from the L-ordered condition. This finding will streamlineproofs in Han and Pang’s paper, as these conditions have been repeatedly verified. Addi-tionally, our insights will aid in accurately establishing the relationships between variouslattice-valued co-Scott closed sets and lattice-valued concave structures.
Fuzzy Math
Enrique de Amo; David García-Fernández; José Juan Quesada-Molina; Manuel Úbeda-Flores
Volume 22, Issue 1 , January and February 2025, Pages 135-146
Abstract
The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula. We start establishing relationships in the bivariate and trivariate cases, which will help to understand the extension to the multivariate ...
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The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula. We start establishing relationships in the bivariate and trivariate cases, which will help to understand the extension to the multivariate case. Several examples are provided.
Engineering
Lakhdar SAIHI; Brahim Berbaoui
Volume 22, Issue 1 , January and February 2025, Pages 147-168
Abstract
This paper presents the design and evaluation of a Photovoltaic-Unified Power Quality Conditioner (PV-UPQC) with series and shunt compensators connected via a DC link. The shunt compensator extracts power from the PV array, compensates harmonic currents and reactive power, and operates at the maximum ...
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This paper presents the design and evaluation of a Photovoltaic-Unified Power Quality Conditioner (PV-UPQC) with series and shunt compensators connected via a DC link. The shunt compensator extracts power from the PV array, compensates harmonic currents and reactive power, and operates at the maximum power point (MPP) under real solar conditions in Adrar, Algeria. Hybrid Neuro-Fuzzy (HNF) integrated with Integral Sliding Mode Control (ISM-C) address chattering issues, improving energy extraction and power quality under variable conditions. Grey Wolf Optimizer (GWO) tunes controller (HNF-ISM-C) parameters, with simulations demonstrating the superiority of HNF-ISM-C over conventional methods. The proposed system significantly enhances power quality, especially under fluctuating irradiation and temperature conditions. The results highlight the robustness and effectiveness of the optimized control strategy in real-world applications.
Neda Doodman; Mohammad Amini; Hadi Jabbari; Ali Dolati
Volume 22, Issue 1 , January and February 2025, Pages 169-183
Abstract
This paper explores an extension of the bivariate Schur-constant model, introducing an additional parameter to its associated Archimedean copula for greater flexibility. We analyze the dependence properties of the proposed model and illustrate our findings with several examples. Furthermore, provide ...
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This paper explores an extension of the bivariate Schur-constant model, introducing an additional parameter to its associated Archimedean copula for greater flexibility. We analyze the dependence properties of the proposed model and illustrate our findings with several examples. Furthermore, provide a likelihood ratio test to compare the performance of the extended Archimedean copula with that of the traditional Archimedean subfamily. Two real-data analysis are also included.
Soft/Rough sets
Ahmed Khalil; Shenggang Li; Hai-Long Yang
Volume 22, Issue 1 , January and February 2025, Pages 185-207
Abstract
A $\beta$-soft fuzzy complement neighborhood is the initial concept proposed by Zhang and Zhan (International Journal of Machine Learning and Cybernetics 10(2019) 1487-1502), which we will refer to in this study as $\circledast$-$\beta$- soft fuzzy complement neighborhood. In the present paper, we first ...
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A $\beta$-soft fuzzy complement neighborhood is the initial concept proposed by Zhang and Zhan (International Journal of Machine Learning and Cybernetics 10(2019) 1487-1502), which we will refer to in this study as $\circledast$-$\beta$- soft fuzzy complement neighborhood. In the present paper, we first introduce three new approximation types based on $\beta$-soft fuzzy covering via $\circledast$-$\beta$-soft fuzzy complement neighborhood, along with several essential features and examples. The new approximation types are significant because they satisfy the inclusion property (i.e., the upper approximation contains the lower approximation, which is one of the essential features of rough set models). In addition, we update some algorithms to a very easy-to-understand state. As a result, improved decision-making procedures will be observable and trustworthy in order to arrive at the optimal choice. Second, we offer a novel idea of $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and then present three other new approximation types based on $\beta$-soft fuzzy covering via $\circledcirc$-$\beta$ soft fuzzy complement neighborhood, besides outlining some of its key characteristics and giving some examples. On the theoretical side, by using three other new approximations via $\circledcirc$-$\beta$-FCN${\mathscr A},$ we also study some basic fuzzy topology properties. Third, we use $\circledcirc$-$\beta$-FCN${\mathscr A}$ to construct a new method that can be applied to the MADM field. We illustrate this method using a real-world problem: a candidate seeking employment in a company. Finally, to demonstrate the advantages of the proposed work, we will compare our proposed method with published $\beta$-soft fuzzy MADM methods.
