For local nonlinear Takagi-Sugeno fuzzy systems, a distributed fusion interval estimation method based on zonotopic analysis is proposed in this paper. A novel membership function-dependent L∞ performance index based on the P-radius is introduced. It couples the zonotope contraction upper bound with the membership functions and scales the uncertainty bound in dominant operating regions, thereby yielding a smaller bound on the estimation error zonotope. To make this performance analysis applicable to local nonlinear systems, a semi-infinite programming scheme is employed at each sampling instant to compute a tight outer-bounding zonotope for the local nonlinear term. On this basis, a distributed fusion estimator is constructed to fuse sensor-wise interval estimates and obtain a refined and reliable global estimate. Simulation results show that the proposed method reduces conservatism and improves estimation accuracy.
This paper examines a class of fuzzy fractional differential equations with piecewise constant arguments (FFDEs-PCAs) governed by a multi-order Caputo fractional derivative. For the linear setting, explicit solution representations are established under the generalized Hukuhara (gH)-Caputo differentiability. A set of numerical examples is included to illustrate the theoretical results.
By applying implicit Lyapunov function approach, this paper studies the fixed-time synchronization of fuzzy quaternion-valued inertial neural networks (FQVINNs) with time-varying delay. An implicit function equation containing Lyapunov function is proposed, and a simple controller containing the implicit Lyapunov function is designed. According to the fixed-time synchronization lemma based on implicit functions, the fixed-time synchronization for delayed FQVINNs is analyzed. This idea is extended to the preassigned-time synchronization of the addressed model. From the analysis process, FQVINNs are always regarded as an entirety without involving any decomposition. Ultimately, the feasibility of the proposed method is verified by a numerical simulation.
This paper addresses the critical challenge of guaranteeing safe blood glucose regulation in networked artificial pancreas systems (APSs) under sustained sensor deception attacks focusing on maintaining clinical safety within severely constrained cyber-physical environments. First, a genetic algorithm (GA)-optimized interval type-2 Takagi–Sugeno (IT-2 T-S) fuzzy model is developed, where the GA tunes the footprint-of-uncertainty parameters to improve the representation of nonlinear glucose–insulin dynamics and physiological variability. Second, an integral event-triggered mechanism (IETM) uses accumulated state-error energy to reduce redundant transmissions and, under the adopted packet-wise Bernoulli attack model, limits the expected opportunities for newly falsified packets to refresh the controller. Third, actuator saturation is incorporated into the controller synthesis through a dead-zone sector condition, providing nonnegative and bounded insulin commands within the prescribed regional domain. A Lyapunov–Krasovskii functional is constructed to derive LMI-based sufficient conditions for mean-square asymptotic stability and prescribed H∞ performance. Numerical simulations under routine and severe meals and deception attacks illustrate effective blood-glucose regulation, reduced communication demand, and feasible insulin delivery.
This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup-J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.
In real world, a phenomenon is often observed and recorded by multiple institutions. Based on the recorded data, institutions can construct their own predictive models to understand the phenomenon. However, it is often difficult for a single institution to obtain a comprehensive understanding of the complex phenomenon based on its own data. In this study, we select the fuzzy rule-based model as a representative prediction method and introduce how institutions can effectively use multi-source data to construct their own predictive models with full consideration of data privacy. The originality of the study is summarized as that the overlap degree of data sets belonging to different institutions is considered when building collaborative predictive models, and corresponding modeling strategies are designed for scenarios where data sets of different institutions are either with a high (Scenario A) or low (Scenario B) degree of overlap. In Scenario A, the structure of data sets from different sources varies greatly and institutions can take Union-like strategies to achieve collaboration. For different levels of privacy-retention requirements, we propose strategies based on either sharing data structure or sharing local predictive models. In Scenario B, the structure of data sets from different sources is similar, and individual institutions can take Intersection-like strategies to achieve collaboration. For different levels of efficiency requirements, strategies based on either a single-stage collaboration or a two-stage collaboration are proposed to share local predictive models. Through experiments on a series of synthetic and publicly available data sets, we demonstrate the effectiveness of the proposed approach.
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive probabilities and linear convexity, we employ capacities and max-plus integrals to model qualitative and idempotent decision criteria. Two equilibrium notions are investigated: Nash equilibrium in mixed strategies expressed by capacities, and equilibrium under uncertainty in the sense of Dow and Werlang, where players choose pure strategies but evaluate payoffs with respect to non-additive beliefs. For games with compact strategy spaces and continuous payoffs, we establish existence results for both equilibrium concepts using abstract convexity techniques and a Kakutani-type fixed point theorem.
Judgment aggregation is essential whenever multiple experts provide subjective evaluations that must be combined into a single coherent decision. This work adopts the perspective of a meta-expert who forms its final judgment after consulting a group of experts, giving greater weight to opinions closer to its own. Expert assessments are modelled using trapezoidal fuzzy numbers for both criteria weights and ratings, while the aggregation process relies on t-norms and t-conorms to combine fuzzy information coherently. The influence of each expert is determined through a recently introduced distance measure for trapezoidal fuzzy numbers, suitably rescaled to quantify the divergence between the meta-expert’s confidence index and those of the others. The proposed methodology is applied to a classical benchmark concerning the prediction of pressure increase in the containment building of the Sequoyah nuclear power plant, and the results are compared with those obtained through existing approaches.
This paper introduces a measure of poverty persistence based on fuzzy set theory, designed to capture both the different degrees of poverty and the pattern of poverty experienced over time. This approach places increased emphasis on more recent episodes and on patterns characterised by a bunching of poverty experiences, while not restricting such patterns to strictly adjacent periods. In addition, binary relations, specifically a crisp and a fuzzy dominance relation, are defined for poverty trajectories. To illustrate the advantages of this fuzzification, we compare the proposed measure with the persistent-risk-of-poverty rate adopted by EUROSTAT, using EU-SILC data for Spain in 2024. The results reveal that intermediate patterns, often excluded from the EUROSTAT classification, show persistence levels that challenge the dichotomic distinction between persistent and non-persistent poverty. The fuzzy measure captures these intermediate situations and reveals forms of accumulated risk that conventional indicators overlook, offering valuable insights for policy design.
In *-fuzzy Banach spaces equipped with a continuous t-norm *, we construct a *-fuzzy measure of noncompactness, motivated by classical measures of noncompactness and *-fuzzy measures. This approach extends classical noncompactness measures to the fuzzy setting while preserving their essential properties. The proposed measure satisfies eight fundamental axioms (FM1)-(FM8).We establish several key theorems, including the verification that the proposed measure fulfills all axioms. As a main application, we prove the existence of solutions for a class of nonlinear functional integral equations of the formx(γ)=H(γ,x(γ))+∫0γJ(γ,σ,x(σ))dσ,γ∈R+,in the space E=BC(R+;V) (the *-fuzzy Banach space of fuzzy bounded continuous functions).Numerical simulations are presented to support the theoretical results, where the Artificial Small Parameter Method (ASPM) is employed to approximate the solution. The numerical examples confirm the theoretical findings and illustrate the effectiveness of the proposed approach.
The distributivity of fuzzy implications over t-norms and t-conorms is a vital problem in fuzzy logic, with significant impact on fuzzy control and approximate reasoning. However, for the important family of f-generated implications, the t-norm and t-conorm solutions to their distributivity are largely restricted to the minimum t-norm and the maximum t-conorm, respectively. To overcome this limitation, this paper investigates the more general framework of α-conditional distributivity, where the distributivity holds only when the value of the underlying t-norm (t-conorm) is larger (less) than α. We provide a systematic analysis of solutions to four types of α-conditional distributivity equations for f-generated implications over continuous t-norms and t-conorms. Our findings show that t-norm and t-conorm solutions are no longer the trivial ones, but take the form of ordinal sums. These characterizations not only unify and generalize existing results but, more importantly, reveal that the structure of α-conditional distributivity is inherently richer and more complex than its usual counterpart.
In this paper, we first investigate several inherent properties of uninorms with neutral element e in the class Umaxr on bounded lattices L. Based on these properties and under the assumption that [0, e[ has a greatest element, we establish structural representation theorems for uninorms in Umaxr by considering two lower sets contained in Ie × Ie, where Ie denotes the set of all elements of L that are incomparable with e. Moreover, each case is characterized by a t-norm together with an increasing, commutative, and conditionally associative function. As an application of these representation results, we further propose some construction methods for uninorms in Umaxr. Dually, we obtain the corresponding results for uninorms in Uminr.
This paper identifies the exact structural boundary between genuinely nonlinear threshold sensitivity and Choquet-type additive behavior in the dual Choquet–Stieltjes (DCS) framework. The earlier DCS theory shows that affine threshold laws imply comonotonic additivity, but it does not settle the converse direction. We show that, on finite spaces and bounded threshold ranges, the raw nonnegative DCS functional is not the appropriate object for additivity under the standard normalization because it carries a nonzero baseline at the zero function. This leads to the anchored DCS functional obtained by subtracting that baseline. The main theorem proves that, under a mild visibility condition on the dual set-functions, the anchored DCS functional is comonotonically additive on a bounded nonnegative range if and only if the threshold law is affine on the corresponding threshold interval. We further derive an exact additivity-defect factorization on indicator rays, showing that the loss of additivity splits into a dual-set-function visibility coefficient and a pure threshold non-affinity term, and we isolate the degenerate regime in which the threshold layer becomes invisible to the anchored functional. Thus the paper upgrades the forward affine-additivity statement of the DCS framework to an exact rigidity boundary.
This paper investigates the polynomial fuzzy nonfragile hybrid-triggered (PFNFHT) control problem for nonlinear positive networked control systems, where the system is subject to deception attacks and time-varying delays. Deception attacks with sector nonlinearity compromise communication integrity and induce an asynchronous premise, thereby limiting the effectiveness of existing fuzzy security control strategies. First, an interval type-2 (IT2) polynomial fuzzy modeling framework is utilized to precisely represent parameter uncertainties and inherent attack characteristics. Second, a PFNFHT control strategy is designed to reduce the communication burden while ensuring security against deception attacks. Based on this strategy, a novel controller gain design method is proposed to solve non-convex terms and achieve positive stabilization. Furthermore, an IT2 deception-attack-based membership-function-dependent (IT2-DABMFD) method is proposed to relax the stability conditions. This method ensures system positivity and stability by embedding triggering and attack parameters into the mismatched IT2 membership functions. As a result, it expands the stability region and improves the system’s capability to withstand severe attacks. Finally, an application to electric distribution system (EDS) demonstrates the effectiveness of the PFNFHT strategy.
Multivariate time series prediction faces fundamental challenges from complex variable interactions, non-stationary dynamics, and delayed effects. Traditional fuzzy cognitive maps (FCMs) provide transparent causal reasoning but rely on fixed historical step sizes, while existing deep learning methods lack explicit causal structure representation. This paper proposes a novel multivariate prediction model named ASHFCM-LSTM by integrating adaptively-sparsified higher-order fuzzy cognitive maps (ASHFCMs) with long short-term memory (LSTM) to address these limitations. The KL divergence-guided adaptive sparsification mechanism prunes the causal weight matrix of HFCM by quantifying deviations from ideal temporal decay patterns. Specifically, setting the weight at lag q to zero is equivalent to excluding the q-th historical state from the effective causal horizon, thereby realizing an adaptive adjustment of the effective historical window for each variable pair and eliminating over 30% of redundant HFCM module weights on average while preserving critical dependencies. Unlike traditional FCMs that model purely temporal causality, our approach captures contemporaneous cross-variable interactions and embeds the resulting causal structures directly into LSTM’s gating operations, achieving deep integration of interpretable causal reasoning with nonlinear temporal learning. Comprehensive evaluation across seven benchmark datasets demonstrates consistent superiority over sixteen competing methods. Ablation studies confirm that the KL divergence-guided adaptive sparsification, contemporaneous causal modeling, and deep architectural integration each contribute significantly to overall performance. These results indicate that the proposed model can be regarded as a basic framework for robust and interpretable multivariate time series prediction.
How narrowly a news reader’s attention concentrates across latent topics calls for a measure respecting the graded, time-evolving nature of topic membership. We construct a time-decayed fuzzy news profile by aggregating estimated topic-membership scores over a user’s click stream with exponential recency weighting, and define on it three Lorenz-based indices motivated by the Betti–Verma fuzzy-poverty tradition: the Fuzzy Informational Poverty Index (FIPI), the Gini coefficient of the topic-attention distribution; the Fuzzy Filter-Bubble Index (FFBI), a concave peak-dominance measure; and the composite Fuzzy Information Clarity index (FIC). We prove an applicability theorem against eight axioms, two of them temporal, and position FIPI against entropy-, HHI- and max-share measures. We then propose FIDA, a maximal-marginal-relevance re-ranker whose diversity weight adapts to FIPI. On MIND (up to 668, 004 users) and the Norwegian Adressa log (147, 599 users), topic attention is markedly unequal (mean FIPI 0.57–0.67 under NMF), and FIPI has a positive, highly significant marginal association with the held-out topic-escape rate; its coefficient in the joint FIPI + FFBI + log nu specification stays positive across decay rates, topic counts, topic-model families, restarts, a larger split and a cross-lingual replication. We also show that this marginal association is largely attributable to click-history length, which inflates a Gini computed on short streams and accounts for 72% of FIPI’s between-user variance, so that conditional on activity the sign reverses; length-stratified estimates are reported throughout. FIDA raises intra-list diversity from 0.66–0.75 to 0.87–0.88 at an NDCG@10 cost of at most 0.012, with the largest gains for the shortest, most concentrated histories.
