Shadowed Sets Research Articles

Suppressed possibilistic fuzzy c-means clustering based on shadow sets for noisy data with imbalanced sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images which are characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

Fuzziness-Based Three-Way Decision With Neighborhood Rough Sets Under the Framework of Shadowed Sets

Fuzziness-Based Three-Way Decision With Neighborhood Rough Sets Under the Framework of Shadowed Sets

Shadowed set approximations of L-fuzzy sets

Pedrycz shadowed sets are three-way approximations of fuzzy sets by transforming the infinite levels of fuzzy set membership grades in the unit interval [0,1] into three levels. The three levels represent qualitatively the sets of the white, grey, and black members of a shadowed set. In this paper, we generalize the notion of shadowed sets to the case of L-fuzzy sets by making three new contributions. First, we consider two representations of a shadowed set. One is a three-valued L-fuzzy set and the other is three pairwise disjoint sets. Second, we introduce two methods for constructing a shadowed set. One divides a finite lattice based on the notion of a pair of a set of designated core membership grades and a set of designated null membership grades. The other uses a pair of threshold sets, which generalizes the method that uses a pair of thresholds. We study formal properties of the two methods and show that they are equivalent. Finally, based on a distance function on a lattice, we present a simple method to build the sets of designated core and null membership grades.

Rough Fuzzy K-Means Clustering Based on Parametric Decision-Theoretic Shadowed Set with Three-Way Approximation

Rough Fuzzy K-Means Clustering Based on Parametric Decision-Theoretic Shadowed Set with Three-Way Approximation

SDHGCN: A Heterogeneous Graph Convolutional Neural Network Combined With Shadowed Set

SDHGCN: A Heterogeneous Graph Convolutional Neural Network Combined With Shadowed Set

M-MSSEU: source-free domain adaptation for multi-modal stroke lesion segmentation using shadowed sets and evidential uncertainty.

Due to the unavailability of source domain data encountered in unsupervised domain adaptation, there has been an increasing number of studies on source-free domain adaptation (SFDA) in recent years. To better solve the SFDA problem and effectively leverage the multi-modal information in medical images, this paper presents a novel SFDA method for multi-modal stroke lesion segmentation in which evidential deep learning instead of convolutional neural network. Specifically, for multi-modal stroke images, we design a multi-modal opinion fusion module which uses Dempster-Shafer evidence theory for decision fusion of different modalities. Besides, for the SFDA problem, we use the pseudo label learning method, which obtains pseudo labels from the pre-trained source model to perform the adaptation process. To solve the unreliability of pseudo label caused by domain shift, we propose a pseudo label filtering scheme using shadowed sets theory and a pseudo label refining scheme using evidential uncertainty. These two schemes can automatically extract unreliable parts in pseudo labels and jointly improve the quality of pseudo labels with low computational costs. Experiments on two multi-modal stroke lesion datasets demonstrate the superiority of our method over other state-of-the-art SFDA methods.

Constructing shadowed set based on game analysis of uncertainty and decision cost

As a three-way approximation scheme to deal with fuzzy set, shadowed set approximately divides fuzzy objects with uncertainty into elevated, reduced, and shadow areas by a pair of decision thresholds α,β, thus effectively reducing the uncertainty of information. However, the current construction of shadowed set is all based on a single principle, lacking the comprehensive consideration of multiple principles, and these construction principles focus on the rationality of semantic interpretation of model construction process and threshold determination, and lack of consideration of the validity of partition results. To resolve these issues, this paper proposes a new shadowed set model through the game analysis between uncertainty and decision cost (UC-GTSS). First, Combining shadowed set construction with game theory, UC-GTSS is proposed based on game competition mechanism. Through the game analysis of uncertainty and decision cost, the optimal α,β is found, and a game payoff fusion algorithm based on Topsis is proposed. Second, the definition of UC-GTSS model expression, game player, strategy, payoff function, equilibrium analysis, optimization α,β determination and the influence of model parameters are analyzed and discussed. Third, the UC-GTSS model is extended and discussed based on the validity of the partition results, such as the game between approximate classification accuracy and coverage, the game between the Gini coefficient of the partition areas. Finally, through the analysis of algorithms, instances and data experiments, the construction process, validity, and rationality of UC-GTSS and its extended model are demonstrated.

Effect of Storage Time on the Physical, Chemical, and Rheological Properties of Blueberry Jam: Experimental Measurements and Artificial Neural Network Simulation.

Reversible data hiding (RDH) is crucial in modern data security, ensuring confidentiality and tamper-proofness in various industries like copyright protection, medical imaging, and digital forensics. As technology advances, RDH techniques become essential, but the trade-off between embedding capacity and visual quality must be heeded. In this paper, the relative correlation between the pixel's local complexity and its directional prediction error is employed to enhance an efficient RDH without using a location map. An embedding process based on multiple cumulative peak region localization (MCPRL) is proposed to hide information in the 3D-directional prediction error histogram with a lower local complexity value and avoid the underflow/overflow problems. The carrier image is divided into three color channels, and then each channel is split into two non-overlapping sets: blank and shadow. Two half-directional prediction errors (the blank set and the shadow set) are constructed to generate a full-directional prediction error for each color channel belonging to the host image. The local complexity value and directional prediction error are critical metrics in the proposed embedding process to improve security and robustness. By utilizing these metrics to construct a 3D stego-Blank Set, the 3D stego-shadow Set will be subsequently constructed using the 3D blank set. The proposed technique outperforms other state-of-the-art techniques in terms of embedding capacity, image quality, and robustness against attacks without an extra location map. The experimental results illustrate the effectiveness of the proposed method for various 3D RDH techniques.

Adaptive 3D Reversible Data Hiding Technique Based on the Cumulative Peak Bins in the Histogram of Directional Prediction Error

Reversible data hiding (RDH) is crucial in modern data security, ensuring confidentiality and tamper-proofness in various industries like copyright protection, medical imaging, and digital forensics. As technology advances, RDH techniques become essential, but the trade-off between embedding capacity and visual quality must be heeded. In this paper, the relative correlation between the pixel’s local complexity and its directional prediction error is employed to enhance an efficient RDH without using a location map. An embedding process based on multiple cumulative peak region localization (MCPRL) is proposed to hide information in the 3D-directional prediction error histogram with a lower local complexity value and avoid the underflow/overflow problems. The carrier image is divided into three color channels, and then each channel is split into two non-overlapping sets: blank and shadow. Two half-directional prediction errors (the blank set and the shadow set) are constructed to generate a full-directional prediction error for each color channel belonging to the host image. The local complexity value and directional prediction error are critical metrics in the proposed embedding process to improve security and robustness. By utilizing these metrics to construct a 3D stego-Blank Set, the 3D stego-shadow Set will be subsequently constructed using the 3D blank set. The proposed technique outperforms other state-of-the-art techniques in terms of embedding capacity, image quality, and robustness against attacks without an extra location map. The experimental results illustrate the effectiveness of the proposed method for various 3D RDH techniques.

Three-way decisions based on hesitant sets over three-way decision spaces

The concept of hesitant set was introduced by Hu, which purpose is to unify hesitant fuzzy sets, interval-valued hesitant fuzzy sets, shadowed sets etc. This paper discusses the construction of decision evaluation functions and three-way decisions based on hesitant sets over three-way decision spaces. First, this paper presents the construction methods of decision evaluation functions based on hesitant sets over semi-three-way decision spaces and quasi-three-way decision spaces. Second, this paper presents some transformation methods of decision evaluation functions based on hesitant sets from semi-three-way decision spaces and quasi-three-way decision spaces to three-way decision spaces. Third, this paper presents three-way decisions based on hesitant sets. Numerous examples are given to support this paper’s argument on the existence of semi-(quasi-)decision evaluation functions and significance of the transformation methods.

Anti-unwinding adaptive super-twisting attitude control for spacecraft

This article addresses the attitude maneuver control without unwinding based on variable gain(i.e. adaptive) super-twisting algorithm and the modified Rodrigues parameters(MRPs). First, a selection logic for the MRP set and its shadow set is designed in order to construct an attitude control system model for rigid spacecraft. Second, a nonlinear sliding function is presented, and on the sliding phase, finite-time convergence and anti-unwinding performance are guaranteed. As a result, a first order sliding mode controller is created to ensure finite-time convergence and anti-unwinding performance on the reaching phase. To alleviate the chattering and improve convergence speed, an adaptive super-twisting algorithm is presented, and the finite-time convergence and anti-unwinding performance are guaranteed on the reaching phase. Furthermore, the adaptive gains are designed based on dual-layer adaptive law, which allows the gains to be increased and decreased as appropriate. It is further demonstrated that when the controller gains are time-varying according to adaptive law, the convergence property and anti-unwinding performance are guaranteed. Numerical simulations are carried out to illustrate the closed-loop system's performance under the proposed control scheme.

A New Decision-Making Framework for Site Selection of Electric Vehicle Charging Station With Heterogeneous Information and Multigranular Linguistic Terms

As a key technology to perform sustainable development in transportation, electric vehicles have been largely welcomed due to their advantages in energy savings and low carbon emission. The main step in promoting these vehicles is the selection of the appropriate electric vehicle charging station (EVCS) site. EVCS site selection is a laborious task because it involves a series of conflicting quantitative and qualitative criteria from several dimensions. The quantitative criteria are usually expressed by numerical data, while qualitative criteria are commonly represented by linguistic terms. Furthermore, the linguistic terms generated by different decision makers are usually defined on multigranular linguistic term sets. In this article, we present a new decision-making framework to select sustainable EVCS sites within the context of heterogeneous information and multigranular linguistic terms. First, three information transformation mechanisms are defined to unify the heterogeneous information and multigranular linguistic terms into interval-valued belief structures. Afterward, shadowed sets theory is utilized to reflect the personalized individual semantics of linguistic terms. Then, with the aid of the evidential reasoning (ER) algorithm, a new information fusion method is proposed to generate the interval-valued expected utilities of alternatives. Subsequently, an improved minimax regret approach is developed to compare and rank the interval-valued expected utilities. The proposed decision-making framework is then implemented to solve a case study for EVCS site selection. Further analysis and comparisons with other methods are also conducted to show the applicability and feasibility of the current proposal.

Improved Multileader Optimization with Shadow Encryption for Medical Images in IoT Environment

Nowadays, security plays an important role in Internet of Things (IoT) environment especially in medical services’ domains like disease prediction and medical data storage. In healthcare sector, huge volumes of data are generated on a daily basis, owing to the involvement of advanced health care devices. In general terms, health care images are highly sensitive to alterations due to which any modifications in its content can result in faulty diagnosis. At the same time, it is also significant to maintain the delicate contents of health care images during reconstruction stage. Therefore, an encryption system is required in order to raise the privacy and security of healthcare data by not leaking any sensitive data. The current study introduces Improved Multileader Optimization with Shadow Image Encryption for Medical Image Security (IMLOSIE-MIS) technique for IoT environment. The aim of the proposed IMLOSIE-MIS model is to accomplish security by generating shadows and encrypting them effectively. To do so, the presented IMLOSIE-MIS model initially generates a set of shadows for every input medical image. Besides, shadow image encryption process takes place with the help of Multileader Optimization (MLO) with Homomorphic Encryption (IMLO-HE) technique, where the optimal keys are generated with the help of MLO algorithm. On the receiver side, decryption process is initially carried out and shadow image reconstruction process is conducted. The experimentation analysis was carried out on medical images and the results inferred that the proposed IMLOSIE-MIS model is an excellent performer compared to other models. The comparison study outcomes demonstrate that IMLOSIE-MIS model is robust and offers high security in IoT-enabled healthcare environment.

Induction of interval shadowed sets from the perspective of maintaining fuzziness

Shadowed sets, as a three-way approximation of fuzzy sets, employ two thresholds (α,β) to maintain the essence of fuzzy sets with reduced computing complexity and simpler semantic interpretation by allowing quantification of numeric membership grades into three parts: core, total exclusion, and complete uncertainty. An essential issue in inducing shadowed sets is determining the thresholds (α,β) and maintaining the consistency in fuzziness. However, it is found that the existing interval shadowed sets (ISS) have a significant fuzziness loss. In addition, the algorithm used to obtain the threshold pairs in ISS need to be further optimized. To this end, a novel method to induce interval shadowed sets based on a new objective function is proposed in this paper. Firstly, the shortcomings of the objective function and fuzziness loss of ISS are analyzed. Then, a new objective function is given, and interval shadowed sets with less fuzziness loss are induced based on this objective function. Afterwards, a fast algorithm is developed to obtain interval shadowed sets quickly. Finally, the rationality and validity of the proposed method are verified by experimental results.

Cross region safety monitoring method of distribution secondary system network under Internet of things

In order to ensure the safe transmission of the information of the secondary distribution system across the regional network, this paper studies a security monitoring method of the secondary distribution system across the regional network based on the Internet of things technology and the improved fuzzy clustering algorithm. The Internet of things technology is used to collect the information transmission in cross region network of the secondary power distribution system and store it in the database; Combined with the shadow set to improve the basic fuzzy C-means clustering algorithm, the improved fuzzy C-means clustering algorithm is obtained. The cross region information transmission in the clustering database is divided into two categories: security and risk, and the risk information obtained by clustering is divided into four risk types, so as to realize the security monitoring of information transmission in cross region network of secondary power distribution system. The results show that the average monitoring rate of this method can reach 93.93%, the information collection is efficient and accurate, the number of packet losses is low, and the clustering results are stable and reliable, which can ensure the safe information transmission of cross region network of the secondary power distribution system.

Unwinding-Free Fast Finite-Time Sliding Mode Satellite Attitude Tracking Control

A double-gimbal variable-speed control moment gyro (DGVSCMG) is considered for attitude control of a rigid satellite for track-to-track maneuver. Satellite attitude tracking control involves precision and time limit. In addition, satellite attitude control also faces rotation kinematic singularity, rotation unwinding, and control singularity associated with DGVSCMG. The rotation singularity and unwinding problems are solved using the body and shadow sets of the modified Rodrigues parameters. A nonlinear unwinding and kinematic singularity-free fast finite-time sliding mode tracking attitude control is proposed and designed for the satellite attitude control using a single unit of DGVSCMG. The issue of control singularity is addressed using constrained optimization to avoid gimbal lock. It is proved through five new propositions that the system states errors converge first to the sliding surface and then to the origin in fast finite-time with unwinding-free dynamics showing global stability of the system for the track-to-track maneuver. As a special case, it is shown that the proposed control is also applicable to rest-to-rest maneuver. Simulation results are presented and compared with a finite-time sliding control showing superiority of the proposed fast finite-time control in terms of time of convergence and unwinding and singularity-free angular motion.

Trade-off principle for standard shadowed sets and its generalization to five-regions

A shadowed set S interprets and makes decision with a fuzzy set F from its approximation regions and a tri-valued mapping μS:F⟶{0,0.5,1} on fuzzy membership grades. The original idea of shadowed sets is to balance the uncertainty of F in S by a principle of uncertainty relocation. This paper proposes a principle of making a trade-off between uncertainty for certainty to minimize the amount of unclassified data and maximize the number of items for which crisp decisions are made. We provide detailed derivations for determining the optimum partition threshold for a trade-off three-region shadowed set and generalized it to five-region model S5. We investigate the existence and uniqueness of the optimum partition threshold of S5. Also, we outline some application examples where five-region shadowed sets can be reasonably exploited, including fuzzy clustering, decision-making, etc. To deliver guidance on how to construct S5, several detailed numeric examples are also provided.

Semi-supervised shadowed sets for three-way classification on partial labeled data

Shadowed set divides a fuzzy set into three regions through fuzzy-rough transformation to denote acceptance, rejection and uncertain decision. Based on the tri-partition property, shadowed sets are utilized to implement the machine learning methods for uncertain data analysis. The extant uncertain machine learning methods with shadowed sets include the unsupervised clustering on only unlabeled data and the supervised classification on only labeled data. However, for the partial labeled data containing both labeled and unlabeled data instances, the studies of uncertain learning methods with shadowed sets are very limited. Aiming at the requirement, in this paper, we propose a novel semi-supervised shadowed set on partial labeled data and thereby construct semi-supervised shadowed neighborhoods to implement the three-way classification of uncertain data. To construct the semi-supervised shadowed set, we reformulate the objective function of shadowed sets, in which the membership loss in fuzzy-rough transformation is weighted by labeled and unlabeled data. We also analyze the influence of labeled data to the shadowed set construction. Experiments validate that the proposed three-way classification method with semi-supervised shadowed sets is effective to utilize partial labeled data to achieve low-risk uncertain data classification.

Aggregation operators on shadowed sets

In this article, we study aggregation operators on shadowed sets. In particular, since shadowed sets can be obtained as approximations of fuzzy sets, we explore the relationships between aggregation operators on fuzzy sets and corresponding operators on shadowed sets. We focus on studying conditions under which the approximations of fuzzy sets into shadowed sets represent an homomorphism with respect to the corresponding aggregation operators, and we propose classes of fuzzy set operators that correspond to (and satisfy the same properties as) specific shadowed set operators.

Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme

Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a (k↔h,n) threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides h−k+1 possible thresholds, k,k+1,…,h. During image reconstruction, each participant can update their shadow according to the current threshold T based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism.