Decision Making
M. Romaniuk; Abbas Parchami; P. Grzegorzewski
Volume 23, Issue 2 , March and April 2026, Pages 1-16
Abstract
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 ...
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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 describes some theoretical results and simulation algorithms for another useful family of fuzzy numbers, called the LR fuzzy numbers with interval cores. Starting from a simulation perspective on the piecewise linear LR fuzzy numbers with the interval cores, we consider their limiting behavior, which leads to some of their 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 a way of introducing the random fuzzy intervals.
Fuzzy approximation
Priyadarsini Parida; Bidu Bhusan Jena; Susanta Kumar Paikray; M. Mursaleen
Volume 23, Issue 2 , March and April 2026, Pages 17-35
Abstract
This study introduces and investigates the concepts of deferred N\"{o}rlund statistical Riemann integrability and statistical deferred N\"{o}rlund Riemann summability for double sequences of fuzzy number-valued functions of two variables. An inclusion result is first established to clarify the relationship ...
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This study introduces and investigates the concepts of deferred N\"{o}rlund statistical Riemann integrability and statistical deferred N\"{o}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 $x^{2}+y^{2}$ 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.
Computer Science
shayesteh tabatabaei
Volume 23, Issue 2 , March and April 2026, Pages 37-52
Abstract
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 ...
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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.
Fuzzy Math
Juraj Kalafut
Volume 23, Issue 2 , March and April 2026, Pages 53-64
Abstract
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 ...
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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 such a slight change has only a little effect on the continuity and commutativity of the pseudo-uninorm.
Fuzzy Math
fereshteh Forouzesh; Mahta Bedrood; Giacomo Lenzi
Volume 23, Issue 2 , March and April 2026, Pages 65-80
Abstract
In this paper, we introduce new classes of ideals, called S-prime ideals and S-maximal ideals,based on a ∧-closed system S. The connection between these ideals and classical prime idealsis examined, and it is shown that every S-prime ideal constitutes a specific type of prime ideal.Moreover, it is ...
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In this paper, we introduce new classes of ideals, called S-prime ideals and S-maximal ideals,based on a ∧-closed system S. The connection between these ideals and classical prime idealsis 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, andtheir properties under isomorphisms are investigated. In the final part of the study, the complete∧-closed system S is introduced, and a new topology, called the S-spectral topology, is defined usingS and the family of S-ideals. Several topological properties of this space, including the Hausdorff,T0, and T1 separation axioms, are discussed.
Fuzzy Math
Antoni López-Martínez
Volume 23, Issue 2 , March and April 2026, Pages 81-100
Abstract
Given a dynamical system $(X,f)$ we investigate several dynamical properties for its Zadeh extension $(F(X),\hat{f})$ endowed with the endograph metric $d_E$. In particular, we prove that for topological A-transitivity, topological (ℓ,A)-recurrence, Devaney chaos, and the specification property, the ...
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Given a dynamical system $(X,f)$ we investigate several dynamical properties for its Zadeh extension $(F(X),\hat{f})$ endowed with the endograph metric $d_E$. In particular, we prove that for topological A-transitivity, topological (ℓ,A)-recurrence, Devaney chaos, and the specification property, the endograph metric behaves similarly to the supremum metric $d_∞$, the Skorokhod metric $d_0$ and the sendograph metric $d_S$. Our results not only resolve certain open questions in the existing literature, but also yield completely new outcomes in terms of point-A-transitivity.
Decision Making
Asieh Pourhaghani; Hamid Torabi; Mohammad Mazaheri
Volume 23, Issue 2 , March and April 2026, Pages 101-126
Abstract
In this article, we introduce fuzzy geometric spaces as a unified generalization of broad fuzzy set concepts, including q‑rung orthopair, picture, spherical, and multi-fuzzy sets. The primary objective of this study is to develop a comprehensive framework capable of handling all types of variables, ...
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In this article, we introduce fuzzy geometric spaces as a unified generalization of broad fuzzy set concepts, including q‑rung orthopair, picture, spherical, and multi-fuzzy sets. The primary objective of this study is to develop a comprehensive framework capable of handling all types of variables, thereby overcoming the limitations of existing methods that are often restricted to specific categories (e.g., discrete, continuous, qualitative, or quantitative). We define distance and similarity measures within 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, we apply this framework to analyze Mizaj questionnaires in Persian medicine, yielding more accurate results than previously possible.
Fuzzy Math
KeYu Zhang
Volume 23, Issue 2 , March and April 2026, Pages 127-139
Abstract
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.
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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.
Fuzzy Math
Funda Karaçal; Kübra Karacair; Ümit Ertuğrul; Radko Mesiar
Volume 23, Issue 2 , March and April 2026, Pages 141-156
Abstract
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 ...
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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.
Decision Making
Atakan Ozlek; Bilal Ervural; Beyzanur Cayir Ervural
Volume 23, Issue 2 , March and April 2026, Pages 157-175
Abstract
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 ...
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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.
Fuzzy modelling
Amirhamzeh Khammar; S. Mahmoud Taheri; Pierpaolo D'Urso; Mohsen Arefi
Volume 23, Issue 2 , March and April 2026, Pages 177-195
Abstract
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 ...
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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 investigated, too. In the proposed approach, a weighted operation is utilized 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 approaches, based on three well-known goodness of fit indices. Sensitivity analysis of nonlinear SVWFR parameters is examined, too.
