Search Results (124)

Intuitionistic fuzzy sets (IFSs), proposed in 1983, are one of the most viable and widely explored extensions of Zadeh’s fuzzy sets. In the decade following their introduction, they were extended to interval-valued IFSs (IVIFSs), temporal IFSs, IFSs of the second type (incorrectly called “Pythagorean fuzzy sets” by some authors) IFSs of n-th type, and IFSs over different universes. For each of these extensions, at least one geometrical interpretation has been defined, and for IVIFSs, at least seven different interpretations are known. In the present paper, revisiting some existing results on IVIFSs, some necessary modifications, additions, and corrections to the planar and spatial geometrical interpretations are introduced here for the first time. A new, eighth, geometrical interpretation of IVIFSs is proposed. A basic logic operation and two modal operators are illustrated and a comparison is made between the planar and the new “two-rods” geometrical interpretations of identical IVIFS elements. Finally, a new operator over IVIFSs is proposed for the first time, some of its properties are proven, and its geometrical interpretations are described. Full article

With the growing integration of electronic systems into modern infrastructure, the need for effective electromagnetic interference (EMI) shielding materials has intensified. This study explores the development of electroless Ni-plated fiber composites and systematically investigates the effects of post-heat treatment on their electrical, structural, and interfacial performance. Both carbon fibers (CFs) and glass fibers (GFs) were employed as reinforcing substrates, chosen for their distinct mechanical and thermal characteristics. Ni plating enhanced the electrical conductivity of both fibers, and heat treatment facilitated phase transformations from amorphous to crystalline Ni₃P and Ni₂P, leading to improved EMI shielding effectiveness (EMI-SE). NGF-based composites achieved up to a 169% increase in conductivity and a 116% enhancement in EMI-SE after treatment at 400 °C, while NCF-based composites treated at 800 °C attained superior conductivity and shielding performance. However, thermal degradation and reduced interfacial shear strength (IFSS) were observed, particularly in GF-based systems. The findings highlight the importance of material-specific thermal processing to balance functional performance and structural reliability. This study provides critical insights for designing fiber-reinforced composites with optimized EMI shielding properties for application-driven use in next-generation construction materials and intelligent infrastructure. Full article

This study presents a novel method for altering the surface properties of carbon fiber (CF) to improve the bonding strength at its interface with norbornene–polyimide (PI-NA) resin. Cobaltous sulfide (CoS) nanosheets were successfully synthesized on the CF surface using a solvothermal method combined with a chemical sulfidation process. The modification increased the specific surface area and surface roughness of the CFs, enhancing the interfacial mechanical lock-in effect between the fibers and the resin. This facilitated effective load transfer between the resin and the fibers, thereby significantly improving the interfacial strength of CF-reinforced polymers (CFRPs). The experimental findings showed that after solvothermal treatment with a precursor solution of 0.006 g/mL for 4.5 h, vertical CoS nanosheets were successfully grown on the CF surface. The interlaminar shear strength (ILSS) and interfacial shear strength (IFSS) of the modified CF reached 60.03 MPa and 83.27 MPa, respectively, representing increases of 19.49% and 27.01% compared to untreated fiber composites. This research demonstrates that this method is simple to apply and promising in terms of industrial scalability. Full article

For a self-affine iterated function system (IFS) ${\left\{f_j\right\}}_{j=1}^N$ on ${\mathbb{R}}^d$ defined by $f_j\left(x\right)=A^{-1}(x+d_j)$, where A is an expansive matrix and $d_j\in {\mathbb{R}}^d$, we reveal a novel characterization of the open set and weak separation conditions through the bounded degree of the augmented tree induced by the IFS. Furthermore, the augmented tree is shown to be a Gromov hyperbolic graph, and its hyperbolic boundary is Hölder equivalent to the self-affine set generated by the IFS, establishing a canonical association between self-affine IFSs and Gromov hyperbolic graphs. Full article

This study seeks to advance group decision-making in project management by introducing a hybrid intuitionistic fuzzy brainstorming (IFBS) method tailored for identifying and assessing earthquake risks in worn-out urban fabrics in Iran. By integrating the collaborative ideation of brainstorming with intuitionistic fuzzy sets (IFSs), the IFBS method effectively addresses uncertainties inherent in expert judgments, providing a robust and systematic framework for risk prioritization. Expert opinions, captured as linguistic variables, were transformed into triangular intuitionistic fuzzy numbers using a 5-point Likert scale measurement, enabling precise numerical analysis of 11 identified earthquake risks. Compared to the PMBOK-based qualitative analysis, the IFBS method demonstrates superior accuracy and granularity in risk assessment, as evidenced by its ability to model complex uncertainties and prioritize risks effectively. This study contributes a novel, scalable decision-making tool that enhances precision in urban risk management, offering practical implications for project managers and researchers tackling natural disaster risks. Its primary novelty lies in the innovative combination of IFSs with brainstorming, creating a scientific guide for managing earthquake vulnerabilities in worn-out urban fabrics. This approach not only improves decision-making outcomes but also sets a foundation for future research in hybrid fuzzy methodologies for disaster resilience. Full article

Carbon fiber-reinforced polymers (CFRP) are widely used composite materials in structural applications, where their mechanical performance is significantly influenced by interfacial shear strength (IFSS). The single fiber fragmentation test (SFFT) is a common technique for characterizing IFSS, but its reliance on optical microscopy makes it time-consuming and impractical for opaque matrices. This study presents an alternative methodology based on acoustic emission (AE) analysis, enabling the estimation of fragment lengths through statistical modeling. The AE technique captures the energy released during fiber fragmentation, represented as AE bursts, whose accurate detection is crucial. A signal-processing approach based on progressive simplification enhances burst detection. To refine the estimation of fragment lengths, a gamma distribution is fitted to experimental data, accounting for observed asymmetry in optical measurements. Results indicate that this approach achieves an IFSS determination error of 14.16% at a 95% confidence level. This study demonstrates the feasibility of using AE for IFSS characterization in SFFT and contributes to future research on AE applications in composite materials. Full article

This study elucidated the synergistic improvement of the interfacial performance and impact resistance of carbon fiber-reinforced epoxy (CF/EP) composites by employing continuous electrochemical oxidation. CFs were electrochemically treated at different current densities, and the surface physicochemical properties, including the surface morphologies, chemical compositions, and wettabilities, were analyzed. After electrochemical oxidation, the IFSS of the CF/EP increased by 48.8%, significantly improving the impact resistance of the composites. The experimental results showed that, when the current density reached 0.15 mA/cm², the damage area after impact reduced by 61%. Concurrently, fiber fracture and resin failure became the primary energy-dissipation modes, maximizing the fiber reinforcement effect and enhancing the impact resistance. However, fiber fracture deteriorated the static mechanical properties of the composites. Subsequently, at a 0.10 mA/cm² current density, the CF/EP composites exhibited an increased compressive strength after an impact of 331 MPa. Full article

Short fiber-reinforced thermoplastic composites (SFRTPs) have excellent recyclability and processability, but their mechanical properties are weak compared to continuous fiber products. Various studies have reported that the addition of GNPs improves the mechanical properties of SFRTPs, but it is unclear what effect different types of reinforcing fibers have on a hybrid composite system. In this study, the effect of adding a small amount (1 wt%) of graphene nanoplatelets (GNPs) to fiber-reinforced polypropylene composites on their mechanical properties was investigated from a crystallinity perspective. GNPs were mixed with polypropylene (PP)/carbon fiber (CF) or PP/glass fiber (GF) using a melt blending process, and composites were molded by injection molding. The results of mechanical property characterization showed no significant effect when GNPs were added to PP/CF, but when GNPs were added to PP/GF, this increased the composite’s tensile strength and Young’s modulus by approximately 20% and 10%, respectively. The interfacial shear strength (IFSS) predicted using the modified Kelly–Tyson equation did not change much before and after the addition of GNPs to PP/CF. On the other hand, the IFSS increased from 10.8 MPa to 19.2 MPa with the addition of GNPs to PP/GF. The increase in IFSS led to an increase in the tensile strength of PP/GF with the incorporation of GNPs. Differential scanning calorimetry (DSC) indicated that GNPs accelerated the crystallization rate, and the X-ray diffraction (XRD) results confirmed that GNPs acted as a crystal nucleating agent. However, CF was also shown to be a nucleating agent, limiting the effect of GNP addition. In other words, it can be said that the addition of GNPs to PP/GF is more effective than their addition to PP/CF due to the differential crystallization effects of each fiber. Full article

Supplier selection in the shipbuilding industry is a typical multicriteria group decision-making (MCGDM) problem, often characterized by significant uncertainty and fuzziness. To address this issue effectively, this paper proposes a novel integrated approach for supplier selection in shipbuilding enterprises by combining intuitionistic fuzzy sets (IFSs) with the weighted aggregated sum product assessment (WASPAS) method. The proposed method utilizes IFS operators alongside an innovative process for evaluating indicator weights. Initially, an intuitionistic fuzzy number approach is employed to obtain indicator data, which effectively captures the uncertainty of linguistic variables and ensures accurate reflection of real-world conditions. Subsequently, the indicator weights are evaluated by integrating subjective weights, derived through the best–worst method, with objective weights, calculated using an entropy-based approach, resulting in more balanced and realistic weight assignments. Subsequently, the WASPAS method is used to prioritize alternative suppliers, and a shipbuilding enterprise in Shanghai is taken as an example to verify the effectiveness of the model. In addition, to evaluate the stability of the proposed method, sensitivity analyses were performed for varying attribute values. The results demonstrate that the combination of subjective and objective weights enhances the stability of the method under varying attribute weights. Finally, a comparison with various existing methods based on intuitionistic fuzzy information proves that the proposed method exhibits certain advantages in solving the MCGDM problem under uncertain environments. Full article

This study investigated the effect of phosphoric acid treatment on carbon fibers to enhance their flame retardancy, the impact of carbon fiber surface treatment conditions on the interfacial adhesion between carbon fibers and PA6, and the chemical reaction mechanisms on the carbon fiber surface. Phosphoric acid treatment resulted in a flame-retardant effect, with a limited oxygen index of over 52.8%, and V0 level flame retardancy characteristics in the UL-94 test when the concentration exceeded 0.5 vol.%. When the treatment time was fixed at 30 min, the tensile strength increased by approximately 2%, and the interfacial shear strength (IFSS) increased by approximately 11% at 0.5 vol.% phosphoric acid, accompanied by an increase in hydroxyl (C–O), carbonyl (C=O), phosphate (P–O), and phosphoryl (P=O) groups. However, at concentrations higher than 0.5 vol.%, the tensile strength decreased by approximately 90%, and the IFSS decreased by approximately 12%, compared to the untreated nonwoven fabric. When the treatment time was varied at 0.5 vol.% phosphoric acid, both the tensile strength and IFSS increased continuously up to 10 min, with a 31% increase in tensile strength and a 17% increase in IFSS, along with an increase in O=C–O, P–O, and P=O groups, as well as surface energy. After 10 min, the tensile strength decreased by approximately 20%, while the IFSS and surface energy remained relatively unchanged. Full article

We propose a novel approach to fractals by leveraging the approximation of fixed points, emphasizing the deep connections between fractal theory and fixed-point theory. We include a condition of isomorphism, which not only generates traditional fractals but also introduces the concept of generating two fractals simultaneously, using the framework of the best proximity point: one as the original and the other as its best proximity counterpart. We present a notion of the Proximal $\mathcal{F}-$Iterated Function System ($\mathcal{F}-$PIFS), which is constructed using a finite set of ${\mathcal{F}}^{*}-$weak proximal contractions. This extends the classical notions of Iterated Function Systems (IFSs) and Proximal Iterated Function Systems (PIFSs), which are commonly used to create fractals. Our findings show that under specific conditions in a metric space, the $\mathcal{F}-$PIFS has a unique best attractor. In order to illustrate our findings, we provide an example showing how these fractals are generated together. Furthermore, we intend to investigate the possible domains in which our findings may be used. Full article

Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) and similarity (BP-similarity) until now. In this work, we propose a novel framework for the belief and plausibility of intuitionistic fuzzy sets (BP-IFSs) and their BP-distance and BP-similarity measures. We modified steps 4 and 5 of the classical TOPSIS method, utilizing both distance and similarity measures to rank the alternatives that satisfy all necessary axioms of distance and similarity. We present numerical examples involving pattern recognition, linguistic variables, and clustering to illustrate the efficiency of these measures, and we develop belief and plausibility TOPSIS (BP-TOPSIS) using the proposed criteria and apply it to complex multicriteria decision-making (MCDM) challenges. The results demonstrate the practicality and effectiveness of our approach. Full article

Carbon fiber (CF)-reinforced polyimide (PI) resin matrix composites have great application potential in areas such as rail transport, medical devices, and aerospace due to their excellent thermal stability, dielectric properties, solvent resistance, and mechanical properties. However, the epoxy sizing agent used for traditional carbon fiber cannot withstand the processing temperature of polyimide resin, of up to 350 °C, resulting in the formation of pores or defects at the interface between the fiber and the resin matrix, leading to the degradation of the overall composite properties. To overcome this problem, in this study, a low-molecular-weight thermosetting polyimide sizing agent was prepared and the processability of the sized carbon fiber was optimized by a thermoplastic polyimide. Compared with the unsized carbon fiber polyimide composites, the interfacial properties of the composites after the polyimide sizing treatment were significantly improved, with the interfacial shear strength (IFSS) increasing from 82.08 MPa to 136.27 MPa, the interlaminar shear strength (ILSS) increasing from 103.7 to 124.9 MPa, and the bending strength increasing from 2262.2 MPa to 2562.1 MPa. The sizing agent acts as a bridge between the carbon fiber and polyimide resin, with anchorage and bonding at the interface between the fiber and resin, which are beneficial for enhancing the interface performance of composites. Full article

The weakness of the fiber–matrix interface restricts the practical application of basalt fiber (BF) as a reinforcing material. In order to improve the interfacial adhesion between the BF and epoxy matrix, surface activation of the BF was carried out using low-pressure O₂ and H₂-Ar plasma under various conditions. The interfacial shear strength (IFSS), evaluated by a micro-droplet de-bonding test, was adopted to demonstrate the bonding effects at the BF/epoxy interphase. Compared to bare BF, the IFSS between the modified fibers and epoxy matrix was efficiently improved with an increment of 38.4% and 14.4% for O₂ plasma and H₂-Ar plasma treatment, respectively. Scanning Electron Microscope (SEM) and Atomic Force Microscopy (AFM) analysis indicated that H₂-Ar plasma-treated BF had a much rougher and more rugged surface than O₂ plasma-treated samples. X-ray Photoelectron Spectroscopy (XPS) and surface energy results revealed that O₂ plasma activation could effectively increase the content of oxygenous groups on the BF surface, thus resulting in a higher total surface energy value. Based on the results, O₂ plasma modification at a power of 200 W and pressure of 80 Pa for 0.5 min was considered to be the most favorable condition for the surface activation of BF. Full article

In the process of product design decision-making (PDDM), decision-makers (DMs) conventionally engage in discussions to evaluate design alternatives. Achieving a consistent result is essential for selecting optimal product design schemes, as it helps eliminate preference conflicts. However, uncertainties and ambiguities, along with the interrelationships among DMs, make it challenging to attain an acceptable consensus level in PDDM. To address this issue, intuitionistic fuzzy sets (IFSs) are introduced to capture DMs’ preferences regarding product design schemes, and a trust network is integrated to analyze DMs’ interrelationships. A double hierarchy linguistic term set (LTS) is employed to assess DMs’ relationships, and an incomplete trust network is supplemented by leveraging the transitivity principle, thereby determining DMs’ weights. By establishing a consensus measurement model, DMs contributing less to consensus are identified, and consensus optimization is achieved through the modification of DMs’ preferences or the calibration of their trust relationships. A consensus reaching process (CRP) for PDDM is proposed, and the technique for order preference by similarity to ideal solution (TOPSIS) is utilized to rank product design schemes after consensus is reached. A case study involving the decision-making process for a specific household disinfection machine design illustrates the efficacy of our method in achieving consensus by integrating vague PDDM data. Full article