Fuzzy Function Research Articles

Bridging the Semantic Latent Space between Brain and Machine: Similarity Is All You Need

How our brain encodes complex concepts has been a longstanding mystery in neuroscience. The answer to this problem can lead to new understandings about how the brain retrieves information in large-scale data with high efficiency and robustness. Neuroscience studies suggest the brain represents concepts in a locality-sensitive hashing (LSH) strategy, i.e., similar concepts will be represented by similar responses. This finding has inspired the design of similarity-based algorithms, especially in contrastive learning. Here, we hypothesize that the brain and large neural network models, both using similarity-based learning rules, could contain a similar semantic embedding space. To verify that, this paper proposes a functional Magnetic Resonance Imaging (fMRI) semantic learning network named BrainSem, aimed at seeking a joint semantic latent space that bridges the brain and a Contrastive Language-Image Pre-training (CLIP) model. Given that our perception is inherently cross-modal, we introduce a fuzzy (one-to-many) matching loss function to encourage the models to extract high-level semantic components from neural signals. Our results claimed that using only a small set of fMRI recordings for semantic space alignment, we could obtain shared embedding valid for unseen categories out of the training set, which provided potential evidence for the semantic representation similarity between the brain and large neural networks. In a zero-shot classification task, our BrainSem achieves an 11.6% improvement over the state-of-the-art.

Fuzzy neural network adaptive AUV control based on FTHGO

ABSTRACT A fuzzy radial basis function neural network (Fuzzy RBFNN) adaptive control scheme, based on fixed-time high gain state observer (FTHGO), is proposed to address the unpredictability of real-time state and composite interference in the trajectory tracking of the fully driven Autonomous Underwater Vehicle (AUV), ensuring fixed-time system convergence regardless of initial conditions. Firstly, a fixed-time backstepping controller is designed and a first-order fixed-time filter is introduced to tackle the differential explosion issue. Secondly, an FTHGO is developed to observe the real-time states of the AUV without assuming global known state signal. Then, the composite interference in the AUV system is effectively compensated by integrating the Fuzzy RBFNN technique. Finally, the fixed-time stability of the entire closed-loop system is proven utilising the Lyapunov stability theory. The effectiveness of the proposed algorithm is proved by the simulation experiment.

Semi-supervised learning towards automated segmentation of PET images with limited annotations: application to lymphoma patients.

Manual segmentation poses a time-consuming challenge for disease quantification, therapy evaluation, treatment planning, and outcome prediction. Convolutional neural networks (CNNs) hold promise in accurately identifying tumor locations and boundaries in PET scans. However, a major hurdle is the extensive amount of supervised and annotated data necessary for training. To overcome this limitation, this study explores semi-supervised approaches utilizing unlabeled data, specifically focusing on PET images of diffuse large B-cell lymphoma (DLBCL) and primary mediastinal large B-cell lymphoma (PMBCL) obtained from two centers. We considered 2-[18F]FDG PET images of 292 patients PMBCL (n = 104) and DLBCL (n = 188) (n = 232 for training and validation, and n = 60 for external testing). We harnessed classical wisdom embedded in traditional segmentation methods, such as the fuzzy clustering loss function (FCM), to tailor the training strategy for a 3D U-Net model, incorporating both supervised and unsupervised learning approaches. Various supervision levels were explored, including fully supervised methods with labeled FCM and unified focal/Dice loss, unsupervised methods with robust FCM (RFCM) and Mumford-Shah (MS) loss, and semi-supervised methods combining FCM with supervised Dice loss (MS + Dice) or labeled FCM (RFCM + FCM). The unified loss function yielded higher Dice scores (0.73 ± 0.11; 95% CI 0.67-0.8) than Dice loss (p value < 0.01). Among the semi-supervised approaches, RFCM + αFCM (α = 0.3) showed the best performance, with Dice score of 0.68 ± 0.10 (95% CI 0.45-0.77), outperforming MS + αDice for any supervision level (any α) (p < 0.01). Another semi-supervised approach with MS + αDice (α = 0.2) achieved Dice score of 0.59 ± 0.09 (95% CI 0.44-0.76) surpassing other supervision levels (p < 0.01). Given the time-consuming nature of manual delineations and the inconsistencies they may introduce, semi-supervised approaches hold promise for automating medical imaging segmentation workflows.

Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability

Lyapunov stability theory provides a powerful technique for stability analysis of dynamical systems, particularly for the stability of nonlinear dynamical system. This paper deals with the stability of fuzzy dynamical systems using a novel notion called granular fuzzy Lyapunov function. In order to analyze the stability, some new notions are introduced such as fuzzy equilibrium point, the ball of fuzzy state space, granular fuzzy 2-norm and etc. Based on the concept of fuzzy-number-valued function granular differentiability, two theorems are proved for calculation. Moreover, using granular fuzzy Lyapunov function, the granular fuzzy local stability theorem is proposed, and two definitions of exponential stability and like-Lyapunov stability are generalized. Finally, several examples are given to illustrate the proposed theorems.

The problems and countermeasures of private education management based on fuzzy logic system

At present, private education plays an important role in China’s education system, but there are a series of problems and challenges in the management of private education. The purpose of this study is to discuss and solve the problems existing in the management of private education through the method of fuzzy logic system. Firstly, the application of fuzzy logic systems in related fields is reviewed to understand the potential and advantages of fuzzy logic systems. Then, through the analysis of the main problems in the management of private education, the root of these problems and their impact on the education system are revealed. By establishing a private education management model based on fuzzy logic system, the application and function of this model in problem analysis and decision making are demonstrated. In the analysis of the results, the accuracy and effectiveness of the fuzzy logic system in the management of private education are evaluated, and the targeted management strategies and countermeasures are put forward to solve the problems in the management of private education.

A fuzzy rough granular ensemble learning based on the feature selection with chi-square1

Neighborhood granulation is a classical granulation method. Although it is adequate for clustering and classification tasks, its granules are more complex, and the data representation is binary. This paper proposes a new granulation method based on the neighborhood granulation. Firstly, a detailed definition of the granular form is given with fuzzy rough set theory. Then, a modified fuzzy rough discriminant function is proposed based on neighborhood systems. The samples are globally granulated on single features to construct granules and on multiple features to construct granular vectors. Also, a feature selection technique based on the Chi-square, which strikingly reduces the complexity of the fuzzy rough granular vectors, is introduced to address the disadvantage of the fuzzy rough granular vectors. An ensemble model structure is also proposed in the paper for the mixed nature of fuzzy rough granular vectors. The paper makes a detailed comparison between the fuzzy rough granulation and the neighborhood granulation. The results show that fuzzy rough granulation has higher computational efficiency and classification performance. Finally, a detailed comparison is made between the fuzzy rough granular ensemble model and various classical ensemble algorithms. The final results show that the fuzzy rough granular ensemble model has better robustness and generalization.

A novel optimized fractional order system for tuning biological parameters

AbstractIn contemporary biological research and applications, control systems have become indispensable for understanding and managing the intricate dynamics of the human biological system. Given the critical role of components such as the pancreas structure, protein formation, insulin and glucose regulation, and the genetic regulatory network (GRN), any disturbances in these systems can lead to severe health issues. To overcome these issues, to introduced a novel hybrid controller called the fuzzy lion‐based optimized fractional order system (FL‐OFOS) for evaluating the performance of the system. This controller aims to efficiently govern and regulate key components of the human biological system, including insulin dynamics, protein synthesis, pancreas functionality, and GRN management. The controller is specifically tailored to regulate insulin, protein synthesis, pancreas function, and GRN dynamics within the human biological system. The optimization of biological parameter values is achieved through the incorporation of the fuzzy lion function. The results of this study highlight the efficacy of the FL‐OFOS controller in optimizing and regulating various biological parameters. The system demonstrates minimal error rates, rapid response times, reduced overshoot, and high control precision and accuracy. The proposed controller achieves a minimal error rate of 0.98%, with only minor overshoot occurring in the outcomes. As a result, the FL‐OFOS controller offers substantial gains and delivers optimal results in the realm of biological systems.

Interval Type-2 Mutual Subsethood Cauchy Fuzzy Neural Inference System (IT2MSCFuNIS)

An interval type-2 (IT2) mutual subsethood Cauchy fuzzy neural inference system has been proposed in this paper. The network architecture consists of 3-layers with all connection weights being IT2 Cauchy fuzzy membership functions (CMFs). The crisp inputs to the system are fuzzified into IT2CMFs with fixed centers and uncertain spreads. The hidden layer represents the rule-based knowledge. The firing degree of the antecedent part of each rule at the hidden layer is computed by aggregating the product of the mutual subsethood similarity measures between the inputs and the connection weights. A volume defuzzification is used to compute the numeric output. A gradient descent back-propagation algorithm is used to train the model. The novelty of the proposed model is threefold. First, is enriching the theory of the mutual subsethood fuzzy neural models by adopting the Cauchy membership function (CMF) as another powerful fuzzy basis function (FBF) rather than the classical choice of Gaussian fuzzy membership functions (GMFs). Second, is the success of computing the mutual subsethood similarity measure between the IT2CMFs and all the model parameters’ updating equations in analytic closed-form formulas, not numerically or approximately. Third, is the ability to extract the type-1 (T1) mutual subsethood Cauchy fuzzy neural inference system (T1MSCFuNIS) with all its analytic closed-form formulas directly as a special case from the general formulas of IT2MSCFuNIS model. Such a novelty makes the proposed model a concrete and effective development of the theory of mutual subsethood fuzzy neural models. Both IT2MSCFuNIS and T1MSCFuNIS models have been tested using different examples from the domains of function approximation, classification, and prediction. The results ensure the efficacy of both models compared with other models reported in the literature.

A novel state transition algorithm with adaptive fuzzy penalty for multi-constraint UAV path planning

Unmanned aerial vehicles (UAVs) require pre-planned flight paths that are energy-efficient, safe and smooth across their wide range of application scenarios. In this study, a novel UAV path planning method is proposed. Firstly, the UAV path planning under numerous obstacles is modeled as a continuous constrained optimization problem. The cost function is formulated as a linear combination of length, height variation, and smoothness, while the constraints include obstacle avoidance, height limitation, and the maneuverability of UAV. Subsequently, a novel constrained state transition algorithm with adaptive fuzzy penalty (AFSTA) is proposed to solve the optimization problem. In AFSTA, a novel adaptive fuzzy penalty function is designed to leverage expert knowledge to establish a reasonable mapping relationship from the fitness value and the degree of constraint violation to the penalty factor for a candidate solution. Meanwhile, the state transition algorithm (STA) is used as the search engine for both global and local search. Experimental results illustrate that the proposed method can find energy-efficient, safe, and maneuverable flight paths successfully with the superiority over other state-of-the-art metaheuristic algorithms.

Bipolar Fuzzy Supra Topology via (Q-) Neighborhood and Its Application in Data Mining Process

The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their neighborhood structure in bipolar fuzzy supra topological spaces. Then, we consider another important structure, “quasi-coincident”, in the case of bipolar fuzzy points and bipolar fuzzy sets. Then, we introduce the corresponding neighborhood structure called “Q-neighborhood system” by using the quasi-coincident relations. Furthermore, we also investigate the characterization of bipolar fuzzy supra topological space in terms of quasi-neighborhoods. Finally, we present a new method to solve medical diagnosis problems by using the bipolar fuzzy score function.

Stabilization control of rotary inverted pendulum using a novel EKF-based fuzzy adaptive sliding-mode controller: design and experimental validation

This article methodically develops an improved self-regulating fuzzy-adaptive Sliding Mode Controller (SMC) that strengthens the disturbance compensation capacity of the nonlinear rotary pendulum systems while effectively attenuating the chattering content and curbing the control energy consumption. The article contributes to augmenting the SMC with online adaptation tools to achieve the said objectives. It employs the conventional Gao’s power-rate reaching law as the baseline. The scaling gain and the power rate of the said reaching law are adaptively modulated via a pre-calibrated two-input state-error-driven fuzzy nonlinear function. Additionally, the sign function in the law is also replaced with an odd-symmetric nonlinear fuzzy function to address the hard limits imposed by the former. Finally, the membership functions of the fuzzy function are self-regulated using the Extended-Kalman-Filter to improve the compensator’s adaptability in handling the system’s rapidly changing control requirements under exogenous disturbances. The aforementioned propositions are verified by performing customized and reliable hardware-in-loop experiments on the Quanser single-link rotary pendulum platform. As compared to baseline SMC law, the proposed control procedure contributes a ∼45.2%, ∼48.5%, and ∼34.8% reduction in position-regulation errors, control energy consumption, and peak overshoots, respectively. The experimental assessment validates the proposed control system’s enhanced robustness and chattering-suppression capability.

A new approach to the fractional Abel k−integral equations and linear fractional differential equations in a fuzzy environment

This paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel k−integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally, a new approach to the linear fuzzy fractional differential equations in the space of generalized fuzzy functions is introduced. Unlike previous approaches with gH-differentiability, this approach avoids making any prior assumptions about the solution's monotonic behavior during the solving process. It also overcomes the problem of multiple solutions for fuzzy fractional differential equations. To demonstrate the benefits of this approach, two initial value problems of linear fuzzy differential equations are compared using two different concepts of fractional derivatives: the Caputo fractional gH-differentiability and the Caputo fractional derivative in the generalized fuzzy space. Furthermore, some applications are provided in a viscoelastic material model and a population growth with harvesting model.

Enhanced Resilient Fuzzy Stabilization of Discrete-Time Takagi-Sugeno Systems Based on Augmented Time-Variant Matrix Approach.

In this technical correspondence, the resilient fuzzy stabilization is enhanced in the direction of elevating the feasible stabilization region as large as possible while the same alert threshold is chosen as the recent one. To do this, the switching-type fuzzy state-feedback controller is designed with a set of switch modes so that more groups of gain matrices can be introduced to enhance the degree of freedom. What is far more important is that a novel augmented time-variant matrix approach is proposed in order to collect the proprietary features of normalized fuzzy weighting functions with regard to each switch mode. Then, all the obtained augmented time-variant matrices are split into a set of positive/negative matrices, which can be elaborately assigned into different monomials of our designing conditions under the framework of homogeneous polynomials. Therefore, less conservative results of resilient fuzzy stabilization are obtained even if some higher alert thresholds are chosen for probably ensuring the establishment of the involved precondition. Finally, the superiority of our approach is validated by giving some detailed comparisons on the benchmark example.

Guaranteed cost extended dissipative stabilization of switched IT2 fuzzy systems via intermittent control and its applications

This paper deals with the guaranteed cost extended dissipative stabilization problem of switched IT-2 fuzzy systems (SFSs) via intermittent control. Firstly, we propose a new class of system performance coefficients, taking both the extended dissipative performance and quadratic cost function performance into account. Then, by using a switched-path-dependent fuzzy Lyapunov functions (SFLFs) approach, the membership-function-shape-dependent (MFSD) existence conditions of a set of intermittent controllers are established. Furthermore, we apply the designed intermittent control scheme to three practical control problems: 1) A controller/actuator-failure-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured in the presence of controller/actuator failures; 2) A switching-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured in the presence of transmission delay of switching signal, and the asynchronous phenomena is eliminated; 3) A hybrid-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured while the control resources are saved. Finally, the effectiveness of the results are demonstrated through a robot arm model.

USE OF ARTIFICAL INTELLIGENCE MODELS IN ACCEPTANCE TESTS

This paper describes the application of fuzzy perсeptron in acceptance testing problems. A study on the use of various fuzzy functions in solving the problem of approximation of probability densities was carried out. Experiments were conducted on time series with preset distribution laws, evaluating approximation quality using standard deviation in the series of 29 tests. As a result of the research, using Gaussian fuzzy function, the mean value of standard deviation equal to 0.00145 determined which confirms good approximative ability of the fuzzy perсeptron. The system was tested on the acceptance test data of the gas compressor engine. In this case, approximation quality was assessed using the Kolmogorov-Smirnov agreement criterion. Analysis results confirm the high approximative ability of the fuzzy perсeptron, emphasizing its applicability in real acceptance tests.

Adaptive robust control of nonaffine nonlinear systems via an improved event‐triggered mechanism

AbstractThis paper aims to address the problem of event‐based adaptive robust control for a class of nonaffine nonlinear systems against actuator faults and unknown deception attacks. Firstly, different from the widely used relative threshold triggering mechanism, an improved event‐triggered mechanism with the time‐varying function threshold is devised for effectively saving more communication costs between controller and actuator. Then, based on a class of modified filter‐based coordinate transformations and the improved event‐triggered mechanism, the intermediate virtual control laws are devised to construct actual controllers, which not only guarantees robust stabilization of the system but also relaxes the universal assumptions on control coefficients and attack weights. Besides, the design challenges resulting from the presence of coupling terms in the nonaffine nonlinear system are successfully overcome by virtue of mean value theorem and the property of fuzzy basis function. Theoretical analysis proves that all signals of the closed‐loop system are semiglobally uniformly ultimately bounded (SUUB) and the Zeno behavior can be averted. Finally, the effectiveness of the proposed strategy is verified via comprehensive simulation results.

Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer

For the problem in which accessing a high proportion of renewable energy results in exceeding the limit in distribution network voltage, the existing regulating method experiences difficulty in considering the two-way voltage regulation and loss reduction optimization function. This study proposes a series-type dual rotary phase-shifting transformer (DRPST) based on the principle of phase volume synthesis. This transformer exhibits bidirectional voltage regulation, high reliability, and low cost. First, the topology, operating principle, and equivalent circuit of DRPST are introduced, and its simplified circuit model is established. On the basis of this model, the causes of voltage exceeding the limits are analyzed and the active distribution network model that contains DRPST is constructed. A real-time rolling two-layer optimization strategy based on DRPST is proposed. The inner layer model is solved using the multi-objective particle swarm optimization algorithm with the objective of minimizing voltage deviation and line loss. The optimal compromise solution of the Pareto solution set of the inner layer model is determined using the fuzzy subordinate degree function method. The outer model is based on the optimal compromise solution of the inner model, and the DRPST output rotor angle is controlled without deviation through double closed-loop proportional–integral regulation. Finally, the correctness and effectiveness of the proposed topology and control method are verified via simulation and experimental analysis.

$\mathbb{T}-$Relative Fuzzy Linear Programming for $\mathbb{T}-$Relative Fuzzy Target Coverage Problems

Optimal set covering problems are commonplace in communication, remote sensing, logistics, image processing, and network fields [3]. Thus, studies on determining optimal covering sets (sensors) of points (targets) in a region have emerged recently. One characteristic of these studies is the consideration of cases where a target is considered fully covered when it falls within a coverage area ("Boolean" coverage). Consequently, optimality solutions/methods/algorithms founded on this coverage scheme are usually too restrictive and (or) precise and so are not suitable for many complex and real life situations, which are most times plagued with ambiguity, vagueness, imprecision and approximate membership of points and (or) covering sets. Fuzzy structures have proven to be suitable for the representation and analysis of such complex systems with many successful applications. Although fuzzy sets generalizes a set, a more recent generalization for both and its related concepts is the Relative fuzzy set [1] which gives a dynamic fuzzy representation to sets. $\mathbb{T}-$Relative Fuzzy fixed points results of $\mathbb{T}-$Relative fuzzy maps were studied in [5] and recently, the concept of $\mathbb{T}-$Relative fuzzy linear programming [6] was introduced as a generalization of fuzzy linear programming. The results were applied to generalize the Boolean set based covering problems in literature to a $\mathbb{T}-$Relative fuzzy Boolean coverage one. Although, Shan et al. in [15] and others [16] - [21] have given a probabilistic coverage consideration but this lacks subjectivity in representing vagueness and imprecision inherent in most systems. In this present article the Linear Programming (LP) formulation of “A Computational Physics-based Algorithm for Target Coverage Problems" by Jordan Barry and Christopher Thron is generalized by considering a fuzzy and relative fuzzy target coverage instead of the crisp set Boolean coverage. Also we introduce the Fuzzy Linear Programming (FLP) and the $\mathbb{T}-$Relative Fuzzy Linear Programming (RFLP) for the set coverage problem which allows for ascertaining dynamic optimality with aspiration levels.

A Method for Assessing the Level of Nonspecific Protection of the Human Body by Indicators Characterizing the Processes of Adaptation

The purpose of the research is to develop a method for assessing the level of nonspecific protection of the human body according to indicators characterizing the adaptation processes, the use of which in the decisive rules of forecasting and diagnosis of diseases ensures an improvement in the quality of decisions made.Methods. Numerous sources have a fairly detailed description of the protective mechanisms of the human body, implemented by non-specific and specific protection systems, which are closely related to such concepts as: adaptive potential, adaptive reserve, functional state and functional reserve. The paper investigates the use of indicators characterizing the adaptive potential and adaptive reserves for quantifying the nonspecific level of protection of the body from the effects of heterogeneous external factors. The methodology of synthesis of hybrid fuzzy decision rules is used as a basic mathematical apparatus.Results. The paper shows that to quantify the level of protection of the body, it is advisable to use an indicator of the activity of regulatory systems, adaptive potential, an indicator characterizing the immune-endocrine component of adaptation and an indicator characterizing the neuropsychic component of adaptation. For this system of indicators, a method has been developed to assess the level of protection based on basic indicators characterizing adaptation processes at the system-wide level, characterized by taking into account components characterizing various mechanisms for the formation of adaptive potential and adaptive reserve, taking into account the specifics of the data structure and ways of processing them for the best results in terms of quality and time of decisions. Fuzzy functions of the level of protection according to the selected system of indicators with an integral assessment of the level of protection of the body are obtained.Conclusion. The paper shows that in order to improve the quality of forecasting and diagnosis of socially significant and occupational diseases, it is advisable to use indicators of the level of protection of the body determined by adaptive mechanisms. It is established that the quality of decision–making using the proposed models increases by 10-15%, depending on the type of tasks being solved, compared with models that do not use indicators of the level of protection of the body.

Beyond Traditional Assessment: A Fuzzy Logic-Infused Hybrid Approach to Equitable Proficiency Evaluation via Online Practice Tests

This article presents a hybrid approach to assessing students’ foreign language proficiency in a cyber–physical educational environment. It focuses on the advantages of the integrated assessment of student knowledge by considering the impact of automatic assessment, learners’ independent work, and their achievements to date. An assessment approach is described using the mathematical theory of fuzzy functions, which are employed to ensure the fair evaluation of students. The largest possible number of students whose reevaluation of test results will not affect the overall performance of the student group is automatically determined. The study also models the assessment process in the cyber–physical educational environment through the formal semantics of calculus of context-aware ambients (CCAs).