Based on the idea of Support Vector Machine (SVM) methodology, a new robust support vector linear regression modelling known as Support Vector Weighted Fuzzy Regression (SVWFR) is introduced, for the case when the values of response variable are fuzzy rather than crisp. The extension of the proposed method to the nonlinear case is also investigated. In the proposed approach, a weighted operation is employed to improve the robustness of usual support vector fuzzy regression models by assigning weights to the support hyperplanes constraints. While the fuzzy machine learning-based models are typically sensitive to outliers, the advantages of the proposed models are their robustness with respect to outlier data. The efficiency and applicability of the proposed models are investigated by using three data sets: a synthetic dataset including outliers, a textile engineering data set, and a stress-test simulation with artificially introduced anomalies. Across all cases, the introduced models consistently outperformed current fuzzy regression also approaches, based on three well-known goodness of fit indices. Sensitivity analysis of nonlinear SVWFR parameters is examined.
In this paper, we introduce new classes of ideals, called S-prime ideals and S-maximal ideals, based on an boolean AND-closed system S. The connection between these ideals and classical prime ideals is examined, and it is shown that every S-prime ideal constitutes a specific type of prime ideal. Moreover, it is proven that any proper ideal disjoint from S is contained in an S-prime ideal. The behavior of S-prime ideals is further analyzed in the setting of quotient MV-algebras, and their properties under isomorphisms are investigated. In the final part of the study, the complete boolean AND-closed system S is introduced, and a new topology, called the S-spectral topology, is defined using S and the family of S-ideals. Several topological properties of this space, including the Hausdorff, T-0, and T-1 separation axioms, are discussed.
The rapid proliferation of unmanned aerial vehicles (UAVs) across diverse civil and military domains has heightened the need for careful payload selection due to inherent weight and capacity constraints. Among these payloads, electro-optic (EO) systems are of paramount importance, offering capabilities such as real-time imaging, surveillance, reconnaissance, and precision targeting. Given the increasing diversity and complexity of EO systems, selecting the most appropriate system for Medium-Altitude Long-Endurance (MALE) UAVs has emerged as a multi-dimensional decision-making challenge that requires the integration of both technical specifications and expert evaluations. This study proposes a novel decision-making framework that integrates the Fuzzy Best-Worst Method (BWM) and the Complex Proportional Assessment (COPRAS) method under the Interval Rough Number (IRN) theory. The approach addresses the uncertainty and heterogeneity in expert judgments and objective data, thereby providing a more nuanced and robust evaluation mechanism. The proposed hybrid framework offers methodological contributions by extending traditional MCDM techniques to heterogeneous decision environments through the use of IRNs. Empirical results demonstrate the model's reliability and consistency, with sensitivity and comparative analyses validating its robustness across multiple scenarios. The findings provide valuable insights for decision-makers and system developers in the aerospace and defense industries, offering a structured and adaptable tool for selecting EO systems in MALE-class UAV applications.
In this paper, under the inclusion order, we investigate fuzzy implication construction methods on P-S, the poset of closed intervals of a bounded poset P. We first propose some methods for constructing a fuzzy implication on P-S using pre-implications, up-sets, and down-sets on P. Next, we add two new construction methods based only on the relationship between elements of P-S. The methods are supported by propositions, examples, and related results.
Motivated by the study of common measurability in the unsharp observables approach to quantum mechanics, Jenca (2011) introduced the notion of a witness map on a partially ordered Abelian group with unit u. At the 10th International Conference on Fuzzy Set Theory and Applications (FSTA 2010), Jenca and Sarkoci (Open Problem 2.10) asked for a complete characterization of all commutative and associative binary operations on the standard real unit interval [0, 1] that generate such witness maps. In this paper, we completely resolve this special-case problem. By translating the discrete combinatorial inclusion-exclusion inequality of the witness map definition into the continuous evaluation of an n-dimensional volume, we prove that the witness map condition is algebraically identical to the n-increasing property. Consequently, an operation generates a witness map if and only if its n-ary extension is a valid n-dimensional copula for all n >= 2. Applying Kimberling's Theorem (1974), we establish that a binary operation generates a witness map if and only if it is the minimum t-norm, a strict Archimedean t-norm with a completely monotonic inverse generator, or an ordinal sum of such operations. Several illustrative families, including the product, Clayton, and Gumbel-Hougaard copulas, are discussed in detail, and the explicit form of the corresponding set functions beta O on n-element subsets is given.
In the context of developing a robust multi-objective optimization framework for designing sustainable supply chain networks for perishable items under uncertainty, this paper provides an overview of a possibilistic framework. Using the three pillars of sustainability (i.e., economic, environmental, and social), the proposed framework seeks to minimize overall supply chain costs, minimize CO2 emissions, and maximize regional employment opportunities. The proposed framework addresses the uncertainties associated with product demand (sales), shelf life, and shipping/transportation conditions. To accomplish this, the proposed framework employs fuzzy trapezoidal numbers (which can model how much variation a number might have) in combination with a robust possibilistic programming structure. The objective of the proposed framework is twofold: 1) to solve for and balance each of the objectives and 2) to use GAMS to implement the LP-Metric method. Validation of the model has been conducted through extensive utilization of numerical experiments to create a variety of examples (small, medium, and large-sized), which support the proposed approach's ability to produce stable (balanced) solutions, regardless of the size of the example. Additionally, results indicate that the cost of the system (i.e., total supply chain cost) increases with the size of the network, while the number of employment opportunities created is directly related to network size; the amount of environmental impact is not increased by network size. Finally, results from the model establish that the proposed robust possibilistic approach exhibits superior performance to traditional models based solely upon determinism by producing consistently higher levels of reliability and resiliency within supply chain configurations, thereby providing an invaluable source of potential inputs for the management of perishable goods.
The modularity equation, viewed as a specialized form of restricted general associative equations, holds important theoretical implications in fuzzy logic and fuzzy theory. In this work, we concentrate on examining the structural properties of two bi-uninorms that satisfy the modularity equation.
In this article, we introduce fuzzy geometric spaces as a generalization of broader concepts of fuzzy sets, such as q-rung orthopair, picture, spherical, and multi-fuzzy sets. The primary objective of this study is to develop a comprehensive framework capable of handling diverse variable types, thereby overcoming the limitations of existing methods that are typically restricted to specific categories (e.g., discrete, continuous, qualitative, or quantitative). We define distance and similarity measures for these spaces and present an algorithm for their application in multicriteria decision-making problems. A key advantage of this framework is its ability to accommodate diverse fuzzification methods within a single problem, a capability absent in conventional fuzzy methodologies. Finally, this framework is applied to to analyze Mizaj questionnaires in Persian medicine, yielding more accurate and reliable results.
Extracting meaningful information from high-volatility data and uncovering multi-scale knowledge from stable-state data remain key challenges in complex multi-attribute decision-making (MADM) problems. To address these challenges, a novel methodology that integrates stochastic empirical mode decomposition (EMD) with the Choquet integral is proposed. The resulting three-stage framework first decomposes the original data into trend terms, reflecting objective laws, and deviation terms, capturing subjective cognition. These components are then aggregated using Choquet integrals with Shapley values to explicitly model interactions among attributes. Finally, the framework is extended to accommodate four decision scenarios involving known or unknown attribute sets and complete or incomplete attribute values, with regularization introduced to mitigate potential bias. Case studies in investment decision-making demonstrate the effectiveness of the proposed method in integrating objective trends with subjective deviations, highlighting its advantages in multi-attribute information fusion and adaptability to complex decision environments.
This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsets of prime ideals within an MV-algebra. We investigate a particular class of Zariski-closed sets and demonstrate that they form a lattice under set inclusion. A distinguished filter within this lattice is then examined, and its algebraic properties are analyzed in detail. Building on this framework, we introduce the concept of v(X)-ideals, a new type of ideal defined in terms of these closed sets. We explore their algebraic behavior, including interactions with minimal prime ideals and their stability under homomorphisms. The study reveals new structural insights into Zariski-closed sets and their connections to broader ideal-theoretic constructs. The final diagram synthesizes these findings, offering a unified perspective and laying the foundation for further exploration of topological and algebraic properties in MV-algebras.
Fuzzy data analysis presents significant computational challenges due to its inherent ambiguity and uncertainty. Traditional statistical methods do not have the capability to effectively capture and model the uncertainty in fuzzy observations. A novel approach is proposed in this paper to model unknown bivariate densities between variables with fuzzy observations and incorporating the dependency. By employing this copula-based approach, we have effectively managed the computational complexity associated with the analysis of fuzzy data. The proposed approach has been applied to model groundwater aquifers distribution.
This paper proposes a hybrid approach that integrates an Improved Shark Smell Optimization (ISSO) algorithm with a Fuzzy Ant Colony System (FACS) to enhance the parameter tuning of a fuzzy hierarchical controller for the inverted pendulum and cart system. The standard Shark Smell Optimization (SSO) algorithm suffers from premature convergence and limited exploration capability. The proposed ISSO addresses these limitations by introducing dynamic adaptive coefficients for the gradient and inertia phases, along with a linearly decreasing velocity limit factor. This enhanced global search is then synergistically combined with FACS, which performs fuzzy-guided local exploitation in promising regions of the parameter space. The ISSO-FACS hybrid is applied to determine the optimal sliding surface parameters and scaling factors of a Fuzzy Hierarchical Swing-up and Sliding Controller (FHSSC). Simulation results demonstrate that the proposed approach significantly outperforms the previous FACS method, reducing the total stabilization error by 11.59%,the pendulum angle error by 15.23%,and the cart position error by 26.72%, while achieving 1.27 times faster settling time. The proposed controller also exhibits superior robustness under perturbed initial conditions where the previous method fails, and demonstrates enhanced disturbance rejection capabilities. Convergence analysis confirms the stability properties of the hybrid approach, and computational complexity analysis validates its suitability for offline controller design.
The existing strength of connectedness in fuzzy graph theory is a max-min quantity. According to this definition, the strength of a path is the membership of its weakest edge, and the connectedness between two vertices is the maximum such bottleneck over all paths. That definition is exact for systems in which the weakest edge is the only controlling factor, but it is too rigid when cumulative route quality matters as well. In this paper we adopt a new notion in which the strength of a simple path is a convex combination of its bottleneck and its average edge membership. The new framework defined in this paper for the strength of connectedness is successfully applicable to systems where the classical bottleneck constraint is significant, as well as to systems where the cumulative effects of all edge constraints are more significant than just the bottleneck constraint. Capacity or bandwidth constraints in a network rely only on the weakest (bottleneck) edge, whereas speed, latency, or smoothness constraints have cumulative effects on the entire path from the source to the destination hub in a network. We develop the corresponding theory for fuzzy bunch graphs and fuzzy bunch hypergraphs, that is, grouped fuzzy structures in which vertices are partitioned into bunches and higher-order relations may occur across bunches.
This study introduces a novel Two-Layer Type-II Adaptive Fuzzy Logic Controller (2LT2-FLC) to enhance seismic resilience in structural engineering. The innovative dual-layer approach integrates an inner adaptive fuzzy layer, which dynamically adjusts input scaling gains in real-time based on the instantaneous range of structural response, with a core fuzzy layer that employs interpretable IF-THEN rules to compute control forces. This design overcomes the limitations of controllers with static parameters by providing continuous self-adaptation to varying seismic excitation levels. The controller's performance was evaluated on a nonlinear four-story steel frame benchmark model, with parameters validated against established structural dynamics literature, under historical earthquake records (Kobe and Northridge). The proposed 2LT2-FLC significantly reduced peak inter-story drift-by 50.18% on the second floor and 47.69% on the fourth floor during the Kobe earthquake-outperforming both Type-II Fuzzy-PID and ANFIS-PID controllers. The controller operates with an average computation time of approximately 0.2 milliseconds per time step, confirming its suitability for real-time applications. By simplifying real-time adaptation for nonlinear systems, the 2LT2-FLC ensures robust, interpretable, and computationally efficient control, presenting a significant advancement for practical seismic mitigation.
This study introduces and investigates the concepts of deferred No & uml;rlund statistical Riemann integrability and statistical deferred No & uml;rlund Riemann summability for double sequences of fuzzy number-valued functions of two variables. An inclusion result is first established to clarify the relationship between these newly proposed notions in the bivariate setting. Building on this framework, new fuzzy Korovkin-type approximation theorems are developed using the four fundamental algebraic test functions 1, x, y and x2+y2 under the proposed means. To highlight the applicability of the results, an example is provided involving a fuzzy positive linear operator associated with bivariate Bernstein polynomials. Furthermore, the convergence behavior of these operators is illustrated graphically with the aid of MATLAB.
A wireless sensor network (WSN) consists of a collection of sensor nodes that collaboratively perform monitoring and data acquisition tasks. Considering the strict resource limitations of sensor nodes, achieving high energy efficiency is a critical requirement. In WSNs, it is essential to minimize data collection delay to ensure that sensed information remains current, while simultaneously maximizing the number of collected data samples to enhance accuracy and reliability. To address these conflicting objectives, this paper proposes a clustering-based routing protocol that simultaneously maximizes packet delivery, minimizes energy consumption, and reduces end-to-end delay. The proposed protocol integrates extremal optimization with fuzzy logic to dynamically form clusters, selecting cluster heads based on two primary criteria: residual energy and distance to the sink. The elected cluster heads then construct a minimum spanning tree (MST) to serve as an efficient multi-hop communication backbone toward the sink. The proposed method, termed the Extremal Optimization Fuzzy-Based Clustering Algorithm (EOFBCA), was implemented and evaluated using the OPNET 11.5 simulation platform. Performance is compared against three state-of-the-art protocols: AFSRP, BFOABMS, and NODIC. Simulation results demonstrate that EOFBCA achieves superior performance across multiple metrics, including energy consumption, end-to-end delay, throughput, packet delivery ratio, and signal-to-noise ratio.
Uninorms are a common generalization of t-norms and t-conorms, which are mutually dual aggregation functions. However, no uninorm is self-dual. In this paper, we show that dropping the axiom of commutativity allows a construction for self-dual pseudo-uninorms. We characterize three important classes of self-dual pseudo-uninorms, namely the representable pseudo-uninorms, pseudo-uninorms with all elements idempotent and those pseudo-uninorms that have both underlying functions continuous. Finally, it is proven that each self-dual pseudo-uninorm has continuous underlying functions. Note that such a slight change has only a little effect on the continuity and commutativity of the pseudo-uninorm.
Fuzzy random variables combine the modeling of imprecision (fuzzy component) and unpredictability (caused by random effects) into a single entity. Statistical samples of such units are widely used; therefore, their direct, numerically efficient generation is necessary. Typically, these samples consist of triangular or trapezoidal fuzzy numbers. This paper presents theoretical results and simulation algorithms for another useful family of fuzzy numbers, known as LR fuzzy numbers with interval cores. Starting from a simulation perspective on piecewise linear LR fuzzy numbers with interval cores, we consider their limiting behavior, which reveals some interesting properties and provides a numerically efficient algorithm for simulating a sample consisting of such fuzzy values. As a result, we obtain a new perspective on how to introduce random fuzzy intervals.
Quality control charts with fuzzy data have been successfully used in many real-world applications in recent years. These methods have been extended to estimate the fuzzy population means based on simple random sampling techniques. In this study, a different strategy is used to develop Shewhart control charts with fuzzy means based on fuzzy data. For this purpose, the conventional rank set sampling is first extended to a well-established fuzzy random variable. Then, based on the concept of fuzzy mean and exact variance, the lower, mean, and upper fuzzy control charts are introduced. Additionally, an estimation procedure is presented that can be used to evaluate the proposed fuzzy control limits in cases where the fuzzy mean and exact variance of the population are unknown. An inclusion degree for monitoring process variability is also introduced and discussed. A real case study from photolithography is presented to demonstrate the efficiency of the proposed method for monitoring control charts with fuzzy data based on fuzzy rank set sampling.
The objective of this paper is to provide advanced multi-expert decision-making techniques using N-soft sets as a referential framework. For the first time, the primary analytical tool for achieving this goal is the Choquet integral. First, the application of this aggregation operator within the context of a set {0, 1, 2, ... , N}, representing the available ratings, is investigated. A straightforward formulation of the Choquet integral tailored to this specific set, followed by a detailed presentation of its computational implementation, is presented. Then, the practical implications of these constructions in the realm of N-soft set theory are shown. They encompass the computation of new scores for the assessment of alternatives in N-soft sets (both in individual and multi-agent cases), and aggregation of data that comes in the form of N-soft sets. Ultimately, we demonstrate how these innovative tools enhance multi-expert decision-making methodologies within the framework of N-soft sets. Three different approaches are discussed. Examples and comparisons with existing methodologies are provided too.
