Benchmark Parameters Research Articles

On the Feasibility and Benefits of Extensive Evaluation

Benchmark and system parameters often have a significant impact on performance evaluation, which raises a long-lasting question about which settings we should use. This paper studies the feasibility and benefits of extensive evaluation. A full extensive evaluation, which tests all possible settings, is usually too expensive. This work investigates whether it is possible to sample a subset of the settings and, upon them, generate observations that match those from a full extensive evaluation. Towards this goal, we have explored the incremental sampling approach, which starts by measuring a small subset of random settings, builds a prediction model on these samples using the popular ANOVA approach, adds more samples if the model is not accurate enough, and terminates otherwise. To summarize our findings: 1) Enhancing a research prototype to support extensive evaluation mostly involves changing hard-coded configurations, which does not take much effort. 2) Some systems are highly predictable, which means that they can achieve accurate predictions with a low sampling rate, but some systems are less predictable. 3) We have not found a method that can consistently outperform random sampling + ANOVA. Based on these findings, we provide recommendations to improve artifact predictability and strategies for selecting parameter values during evaluation.

Computational influences of convection micropolar fluid influx and permeability on characteristics of heating rate and skin friction over vertical plate

This manuscript merits at examining of an embedded orthogonal plate inside porous domain exposed to uniform heat influx to elaborate on how micro polar fluid factors and permeability characteristic affect the local skin friction, heating rate, and angular velocity inside boundary layer. The plate is subjected to forced convective micro polar fluid influx under steady, incompressible, and viscous circumstances. To facilitate dependable numerical solution, similarity approach is implemented to mutate set of coupled governing equations relevant to the adopted study into a constrained dimensionless differential equations. Computational analysis has been executed hiring Runge-Kutta scheme by Matlab function bvp4c to settle the governing equations. Study's results are highlighted graphically the impact of micro polar fluid factors on the local skin friction, heating rate, and angular velocity curves. High degree of acceptability of present findings compare with prior research results. It is found that the rising of Darcy parameter drives to decrease linearly both heating rate and local skin friction. Among the examined factors, the benchmark parameter of decreasing skin friction is the porosity. Additionally, it is found that an increasing of Prandtl number and micro rotation element lead to enhance Nusselt number. Once curves of micro rotation are interfered at certain distance from the plate due to increase in porosity, Darcy, Forchheimer's, and microelement rotation, the micro rotation curves are inverted.

A novel hybrid genetic algorithm and Nelder-Mead approach and it’s application for parameter estimation

Background Traditional optimization methods often struggle to balance global exploration and local refinement, particularly in complex real-world problems. To address this challenge, we introduce a novel hybrid optimization strategy that integrates the Nelder-Mead (NM) technique and the Genetic Algorithm (GA), named the Genetic and Nelder-Mead Algorithm (GANMA). This hybrid approach aims to enhance performance across various benchmark functions and parameter estimation tasks. Methods GANMA combines the global search capabilities of GA with the local refinement strength of NM. It is first tested on 15 benchmark functions commonly used to evaluate optimization strategies. The effectiveness of GANMA is also demonstrated through its application to parameter estimation problems, showcasing its practical utility in real-world scenarios. Results GANMA outperforms traditional optimization methods in terms of robustness, convergence speed, and solution quality. The hybrid algorithm excels across different function landscapes, including those with high dimensionality and multimodality, which are often encountered in real-world optimization issues. Additionally, GANMA improves model accuracy and interpretability in parameter estimation tasks, enhancing both model fitting and prediction. Conclusions GANMA proves to be a flexible and powerful optimization method suitable for both benchmark optimization and real-world parameter estimation challenges. Its capability to efficiently explore parameter spaces and refine solutions makes it a promising tool for scientific, engineering, and economic applications. GANMA offers a valuable solution for improving model performance and effectively handling complex optimization problems.

Search for charged excited states of dark matter with KamLAND-Zen

Particle dark matter could belong to a multiplet that includes an electrically charged state. WIMP dark matter (χ0) accompanied by a negatively charged excited state (χ−) with a small mass difference (e.g. < 20 MeV) can form a bound-state with a nucleus such as xenon. This bound-state formation is rare and the released energy is O(1−10) MeV depending on the nucleus, making large liquid scintillator detectors suitable for detection. We searched for bound-state formation events with xenon in two experimental phases of the KamLAND-Zen experiment, a xenon-doped liquid scintillator detector. No statistically significant events were observed. For a benchmark parameter set of WIMP mass mχ0=1 TeV and mass difference Δm=17 MeV, we set the most stringent upper limits on the recombination cross section times velocity 〈σv〉 and the decay-width of χ− to 9.2×10−30cm3/s and 8.7×10−14 GeV, respectively at 90% confidence level.

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Assessing the Intrinsic Activity of Pt‐Group Electrocatalysts for Carbon Monoxide Oxidation: Best Practices and Benchmarking Parameters

AbstractPt‐group elements are the state‐of‐the‐art electrocatalysts for various fuel cells. However, their CO‐poising is a critical hitch for large‐scale applications, so the researchers are exerting huge efforts to solve this issue. The exponentially increasing attention in this field pressures the researchers to publish their findings quickly, leading to unavoidable flawed evaluation parameters for the intrinsic activity of electrocatalysts. The CO oxidation (COOxid) is highly sensitive to various factors. Thus, it is urgent to afford a deeper understanding of the inherent COOxid activity of state‐of‐the‐art electrocatalysts and adopt accurate guidelines for researchers to test, optimize, and compare their electrocatalysts. This review provides exactitude in the evaluation and precise assessment of the key descriptors related to electrocatalysts (i. e., effect of both size, shape, and support) and CO oxidation (i. e., effect of electrolyte, working electrode, and CO surface diffusion). This is besides the fundamental aspects (i. e., COOxid Process, mechanism, measurements, calculations, thermodynamics, and kinetics). Various experimental results from our group and others besides in‐situ analysis were provided to support our deep discussion. Finally, we provide a brief synopsis of the relevant milestones of the up‐to‐date challenges and perspectives.

Innovative drilling fluid containing sand grafted with a cationic surfactant capable of drilling high pressure and high temperature geothermal and petroleum wells

Maintaining the rheology and filtration properties of a drilling fluid plays a vital role during a drilling operation. With the current challenges of high pressure and high temperature environments, there is an urgent need to design thermally stable water-based mud systems (WBM) which are environmentally clean and economically cheap.High pressure and high temperature (HPHT) environments affect drilling fluid systems leading to degradation of additives hence reducing the efficiency of the drilling fluid. Nanotechnology has been widely used to answer questions about additive degradation, and many studies are currently being conducted on how to use nanotechnology to design smart drilling fluids. However, nanotechnology comes at a high cost, resulting in an increase in the overall drilling operation costs and the project as a all. Therefore, the effectiveness of sand particles as a replacement of commercial nanoparticles is investigated in this study as an additive for designing effective-performance water-based drilling fluids. Effective-performance drilling fluids are environmentally friendly, stable at high temperatures, and help to avoid well damage during drilling operations.The research compared sand particles, which are widely available and inexpensive to silica nanoparticles at 0.5 wt% concentration. The samples were tested at different aging temperatures. Rheological properties were measured at room temperature up to 232 °C. The performance of sand and silica nanoparticles was studied by comparing each of the nanoparticle muds with the reference mud sample, taking filtration and rheological properties as the benchmark parameters. Experimental data showed that sand particles enhanced almost all the rheological and filtration properties of the WBM compared to the reference mud. When compared to silica nanoparticles, the results showed neither statistically significant variance in plastic viscosity and yield point among the samples, with muds containing sand particles performing similarly or better. Formulation S2 (35–70 μm) demonstrated the ability to improve the rheology of WBM. At 204 °C and 232 °C, Formulation S2 (35–70 μm) filtrate loss decreased by 16.35% and 29.52%, respectively, compared to 5.66% and 11.32% by mud containing nano silica. The same mud sample decreased the mud cake thickness at the same temperatures conditions by 54.74% and 45.45%, respectively, as opposed to 36.84% and 11.81%. The new innovative mud system can be used to drill in HPHT conditions.

Electrocatalytic Effects of Au Nanoclusters in Its Electrochemiluminescence Enhanced by Coreactant Tertiary Amines

AbstractAtomically precise metal nanoclusters are increasingly exploited in electrocatalysis such as water electrolysis and CO2 reduction. The catalytic effects are generally evaluated by conventional electrochemical methods or end‐product analysis. Herein, near infrared electrochemiluminescence (ECL) of the nanoclusters is introduced as a new signaling mechanism to complement classical voltammetric analysis for elucidating essential electrocatalytic parameters. Coreactant ECL from an aqueous soluble Au22 nanocluster (NCs) enhanced by a common pH buffer materials 4‐(2‐hydroxyethyl)‐1‐piperazineethanesulfonic acid (HEPES) and by a piperazine drug hydroxyzine (HDZ) is studied under oxidative reduction pathways. Foot of the wave analysis on voltametric features and the kinetics profiles in potential‐step experiments are studied in different nanocluster and coreactant concentrations. Benchmark parameters such as rate constants are determined under EC (Electron‐transfer‐Chemical‐reaction) mechanism as feasibility validations. Because the luminescence properties of AuNCs are sensitive to the surface ligands or adsorbents, ECL is proposed as a new signal readout for operando studies providing insights for governing reaction mechanism and kinetics during catalytic reactions. Retrospectively, mechanistic understanding of the complex multi‐step reactions during ECL generation can provide guidance for the evaluation and optimization of ECL property for better quantitative applications.

Technical evaluation and standardization of the human thyroid microtissue assay.

The success and sustainability of U.S. EPA efforts to reduce, refine, and replace in vivo animal testing depends on the ability to translate toxicokinetic and toxicodynamic data from in vitro and in silico new approach methods (NAMs) to human-relevant exposures and health outcomes. Organotypic culture models employing primary human cells enable consideration of human health effects and inter-individual variability but present significant challenges for test method standardization, transferability, and validation. Increasing confidence in the information provided by these in vitro NAMs requires setting appropriate performance standards and benchmarks, defined by the context of use, to consider human biology and mechanistic relevance without animal data. The human thyroid microtissue (hTMT) assay utilizes primary human thyrocytes to reproduce structural and functional features of the thyroid gland that enable testing for potential thyroid-disrupting chemicals. As a variable-donor assay platform, conventional principles for assay performance standardization need to be balanced with the ability to predict a range of human responses. The objectives of this study were to (1) define the technical parameters for optimal donor procurement, primary thyrocyte qualification, and performance in the hTMT assay, and (2) set benchmark ranges for reference chemical responses. Thyrocytes derived from a cohort of 32 demographically diverse euthyroid donors were characterized across a battery of endpoints to evaluate morphological and functional variability. Reference chemical responses were profiled to evaluate the range and chemical-specific variability of donor-dependent effects within the cohort. The data-informed minimum acceptance criteria for donor qualification and set benchmark parameters for method transfer proficiency testing and validation of assay performance.

A 3D printed plant model for accurate and reliable 3D plant phenotyping.

This study addresses the importance of precise referencing in 3-dimensional (3D) plant phenotyping, which is crucial for advancing plant breeding and improving crop production. Traditionally, reference data in plant phenotyping rely on invasive methods. Recent advancements in 3D sensing technologies offer the possibility to collect parameters that cannot be referenced by manual measurements. This work focuses on evaluating a 3D printed sugar beet plant model as a referencing tool. Fused deposition modeling has turned out to be a suitable 3D printing technique for creating reference objects in 3D plant phenotyping. Production deviations of the created reference model were in a low and acceptable range. We were able to achieve deviations ranging from -10 mm to +5 mm. In parallel, we demonstrated a high-dimensional stability of the reference model, reaching only ±4 mm deformation over the course of 1 year. Detailed print files, assembly descriptions, and benchmark parameters are provided, facilitating replication and benefiting the research community. Consumer-grade 3D printing was utilized to create a stable and reproducible 3D reference model of a sugar beet plant, addressing challenges in referencing morphological parameters in 3D plant phenotyping. The reference model is applicable in 3 demonstrated use cases: evaluating and comparing 3D sensor systems, investigating the potential accuracy of parameter extraction algorithms, and continuously monitoring these algorithms in practical experiments in greenhouse and field experiments. Using this approach, it is possible to monitor the extraction of a nonverifiable parameter and create reference data. The process serves as a model for developing reference models for other agricultural crops.

Investigation of Uncertainty Propagation in the Resolved Resonance Range

This paper presents a comparative study using the first-order formula (also called “sandwich”) and the multivariate sampling methodologies for propagating uncertainty in the resolved resonance region. A distinctive aspect of this work is the generation of random cross sections by sampling Resonance Parameters (RPs) taking in consideration their correlations provided in nuclear data libraries via the Resonance Parameter Covariance Matrix (RPCM). SCOOBY (Sampling COvariance OBservatorY), a newly developed sampling tool, is presented in this paper. This tool relies on the GAIA-2 nuclear data processing code to read and correct the RPCM and generate random cross sections. The study compares the sandwich method that relies on sensitivity coefficients and covariance matrices, with the sampling method, which involves numerous Monte Carlo simulations with random cross sections. The comparison is tested on an ICSBEP benchmark, PU-MET-MIXED-002, chosen for its sensitivity to 239Pu cross sections. The results indicate that both methods quantify similar uncertainties, confirming the reliability of both the SCOOBY module and the GAIA-2 code. By using the PU-MET-MIXED-002 benchmark and sampling 239Pu resonance parameters, this work demonstrates the effectiveness of these methodologies in estimating uncertainty in criticality safety calculations. The findings highlight the robustness of these approaches in uncertainty propagation, suggesting the need for further research on additional benchmarks and expanded uncertainty propagation studies.

Optimization and evaluation of the distribution of Fischer-Tropsch products over a cobalt-based catalyst utilising design expert software

Modelling biomass to liquid via the Fischer-Tropsch synthesis (FTS) system allows researchers to investigate the most efficient parameters while running the system under optimal conditions. As part of the design of experiments (DOE) procedure, a special data simulation method based on response surface methodology (RSM) is utilized to thoroughly analyse the impact of operating circumstances. The objective of this study was to examine the factors that affect the production of C1, C2–C4, and C5+ in FTS process, and then optimize the critical factors utilising factorial design and response surface techniques. The parameters evaluated were reaction temperature, reaction pressure and the crystallite size of cobalt. The effects of these factors and their potential for synergy were explored simultaneously using multivariate DOE, with the yield of different hydrocarbon composition selectivity's as the measured responses. In the concept generation phase, optimization was based on the literature consulted, which proved to be an effective method for determining the optimization parameters. The detailed conceptual design included the generation of models using statistical methods and response surface models. Finally, the optimized design was validated using catalysts and parameters obtained during the optimization process, and this were compared to the output recorded in the theoretical modelling. The optimized parameters resulted in performance consistency, with the theoretical model for each group of hydrocarbons being validated by actual experiments. The established models were seen to characterize hydrocarbon distributions accurately and repeatedly over a wide range of reaction conditions (200–270 °C, 5–20 Bar, and 3–26 nm) using a cobalt-based catalyst. According to the detailed quantitative models developed, for higher C5+ production, 220 °C, 10 barg and 11 nm (cobalt crystallite) benchmark parameters were set to produce 19.3 % C1, 11.4 % C2–C4 and 69 % C5+ selectivity's. Comparative analysis showed a 1.9 %, 3.9 % and 0.3 % percentage difference between the theoretical output and the actual output of C1, C2–C4 and C5+, respectively.

Probing electroweak phase transition in the singlet Standard Model via bbγγ and 4l channels

We investigate the prospects for resonant di-Higgs and heavy Higgs production searches at the 14 TeV HL-LHC in the combination of bbγγ and 4l channels, as a probe of a possible first order electroweak phase transition in real singlet scalar extension of the Standard Model. Event selection follows those utilized in the bbγγ and 4l searches by the ATLAS Collaboration, applied to simulation using benchmark parameters that realize a strong first order electroweak phase transition. The output of discriminant analysis is implemented by numerical calculation, optimised by the joint restriction from the two channels. The prospective reach for bbγγ/4l channel could be more competitive in probing the electroweak phase transition at lower/higher resonance masses. With 3 ab−1 integrated luminosity, the combination of the bbγγ and 4l channels can discover/exclude a significant portion of the viable parameter space that realizes a strong first order phase transition when the resonance mass is heavier than 500 GeV.

System design and thermo-economic analysis of a new coal power generation system based on supercritical water gasification with full CO2 capture

To achieve sustainable energy supply and carbon neutral, it is essential to enhance the efficiency and reduce carbon emissions for coal power. In this study, a coal power generation system based on supercritical water gasification (SCWG) with full CO2 capture is proposed. The system achieves autothermal gasification by partial oxidation of coal in the SCWG gasifier. Gasification water is preheated by turbine exhaust, and organic Rankine cycle (ORC) is integrated to recover the waste heat of turbine exhaust. Simulation and thermodynamic analysis models of the system are developed. Results show the energy efficiency and exergy efficiency of system with benchmark parameters reach 52.95 % and 54.11 %, respectively. The largest exergy destruction occurs in gasifier and accounts for 41.36 % of the total exergy loss. Irreversibility of heat transfer mainly occurs in water heat exchanger and ORC, accounting for 4.81 % and 5.59 % of the total loss. Effects of key operating parameters on the system performance are investigated. Results show the optimal turbine exhaust pressure is 0.1 MPa, and higher turbine inlet temperature can enhance the system efficiency. System with reheat configuration shows potential in thermodynamic and economic aspects, and the exergy efficiency of double reheat system is improved from 37.25 % to 45.08 %.

Optimal investment decision for industry 4.0 under uncertainties of capability and competence building for managing supply chain risks

This study analyses a risk-averse firm’s decision to invest in Industry 4.0 (I4.0) in the presence of supply chain risks (SCR). Literature suggests that I4.0 assists the firm in mitigating SCRs by enhancing its capability and competence. However, due to SCRs associated with I4.0, building only capability and competence does not necessarily help the firm to improve its resilience from any uncertain fluctuations in ex-post net profit from the long-term return. Therefore, it is essential to investigate how a risk-averse firm makes an optimal investment decision in implementing I4.0 when SCRs impair capability and competence, where we determine a firm’s optimal investment decision in terms of utility defined over the expected value and variance of its ultimate random profit from investing in I4.0. This study employs a mean-variance decision-theoretic model to examine I4.0 investment risk-return trade-offs under uncertainties stemming from two types of SCRs, namely system and operational risks, influencing the firm’s capability and competence achievements, respectively. The model demonstrates that under certain sufficiency conditions on the relative risk-return trade-offs, higher variation in capability or competence, or greater congruency between the SCRs, may lead to a lower optimal investment decision in I4.0. However, the optimal investment may increase with higher expected capability or competence for a given level of these SCRs. Finally, we conduct a simulation of the theoretical model, using vignette-based experimental data as the benchmark parameter values, to quantify the predictive ability and analytical merits of our model by identifying risk-return trade-offs.

Identification Analysis of Fluid Type in the Low Resistivity Zone of Well Z-2 Field "Z", South Sumatera

Hydrocarbon reserves are one of the main points that are very important in the sustainability of the productivity of an oil and gas field. This important point is greatly influenced by several parameters that can be obtained by various measurements and analysis. One of the most influential parameters in the analyses of the amount of hydrocarbon reserves in a reservoir is the water saturation value. The water saturation parameter will also be greatly influenced by the electrical parameters of the fluid-containing rock in the reservoir. Sometimes the electrical parameters of this rock, in this case resistivity becomes one of the benchmark parameters, whether the zone or reservoir has potential or is interesting to be developed or produced. However, there are several reservoirs or zones that experience low resistivity effects which will give an initial indication that the zones or reservoirs are not attractive or have no effect on development. In this Z field, there is a zone that experiences low resistivity effects, making this zone unattractive for production. So to be able to make these zones attractive for production, an identification analysis was carried out on Zones A and B in this Z field to determine the type or type of fluid from the two zones. The initial analysis was carried out petrographically from rock sample incisions at certain depths in Zones A and B so that it is known that the cause of the low resistivity effect in the two zones is the presence of pyrite minerals and illite clay which are the main causes of the low resistivity effect. Furthermore, an analysis of the identification of fluid types was carried out using the double apparent resistivity method with the results obtained that in Zones A and B there are 2 types of fluids, namely hydrocarbons and water with a depth limit of 3650 ft in Zone A and 4558 ft in Zone B. By knowing the type of fluid, the hydrocarbons contained in these two zones should be able to increase interest in the production of these zones as a potential zone for production, but it is necessary to perforate at a depth range indicated by the hydrocarbon fluid and carry out initial production tests to prove the results of the analysis in this study.

Investigation of wheel squeal noise under mode coupling using two-disk testrig experiments

Wheel squeal noise is a common problem that occurs in railway systems especially on curved tracks. These tonal noises are usually found at high frequency, typically over 1 kHz. The cause of the squeal noise remains unclear and could be different under varied conditions. Several mechanisms that could cause wheel squeal, including falling friction and mode coupling, have been proposed in literature. Most existing lab experimental investigations were focused on the squeal noise caused by falling friction with vertical contacts. As a result, the squeal noise generated by mode coupling could be missed due to the absence of a non-vertical contact angle. In this work, a two-wheel test rig has been designed with curved wheel profiles to achieve adjustable contact angles with lateral components. Experimental and numerical modal analysis of the two-disk system was conducted to determine the dynamic characteristics for exploration of mode coupling effects. Using a set of benchmark parameters predicted to be the cause of significant mode-coupled instability, squeal noise was found at frequencies higher than the existing falling friction experimental tests as reported in the literature. The frequency and amplitude measured in the experiments agreed with the predictions of the analytical mode coupling model. Further experiments varying control parameters, contact angle, angle of attack and direction of rotation were performed, confirming that the new squeal noise was caused by mode coupling.

The Invisible Beauty of the Zeiss-Dywidag Domes: Topology Optimization of the Triangulated Rebar Grids

ABSTRACT The Zeiss-Dywidag system was a pioneer in the history of thin concrete shells, which impacted and advanced theory and praxis worldwide. This study explains its relevance for the history of gridshells: the first ever built Zeiss-Dywidag dome started out as a geodesic gridshell, sprayed over by concrete. Walther Bauersfeld abandoned his own ingenious design for the first Planetarium in Jena in favour of a lamella-type topology for the equally self-bearing reinforcing grid of the later Zeiss-Dywidag domes. We reconstruct the optimization of the geometry and tessellation of the first built example of the latter, the Schott dome, and suggest possible motivations for the change. Bauersfeld’s strikingly advanced theory of equivalent membrane shells, which played an essential role in the process, is published here for the first time. The significance of a unique benchmarking parameter, the so-called bar density (D-value), introduced by Bauersfeld is investigated. Its applicability to assess geometric fitness is assessed by a comparative study of selected grid topologies and geometries.

Performance simulation of water turbines by using 6-DoF UDF and sliding mesh methods

In this work, a comparison between the six degrees of freedom (6-DoF) method and the sliding mesh approach in computational fluid dynamics simulations of an Archimedes screw turbine for hydrokinetic applications was performed using ANSYs Fluent software. The numerical curves obtained by representing the power coefficient () values versus the tip speed ratio ( or ) were compared based on the experimental data available in the literature. Therefore, by considering the values as the comparison benchmark parameter between the numerical and experimental data, the error obtained when using the 6-DoF method and the sliding mesh approach was 13% and 40%, respectively. Both methods allowed the simulation of the rotor rotation, although the 6-DoF method was more accurate in the prediction of the turbine performance, higher computational resources were consumed in comparison with the sliding mesh method, which allows to obtain a computational solution in affordable times.

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored.