Fuzzy Logic Techniques Research Articles

Design AI platform using fuzzy logic technique to diagnose kidney diseases

Artificial intelligence (AI) is an advanced scientific technology that can provide strong ability to assist in analysis and diagnosis of almost every type of data, therefore; AI widely used in medical fields, which is applied in the diagnosis and early detection of diseases. Kidney disease is one of the common diseases that are diagnosed and the necessary treatments are suggested by artificial intelligence. In this research, a logic system was used. The fuzzy logic system (FLS) is one of the artificial intelligence systems for diagnosing kidney diseases, where the fuzzy logic system divided into five variable inputs, namely urea, creatinine, glucose, bun, and uric acid, and they represented laboratory tests of the patients, this variables and also three outputs were identified, which are chronic inflammation and kidney failure, stones and salts, acute inflammation of the kidneys and bladder, which is the result of the medical diagnosis of the disease. Five memberships for inputs and three memberships for outputs are used in FLS. Diseases are concluded based on the values of the inputs, and thus the system proved its effectiveness and accuracy in diagnosis and this system is considered an aid to the specialized doctors in the field of kidney diseases.

Optimization and Reduction of Losses in 330kv Power Systems for Efficient and Optimal Operation

Abstract: This study was undertaken to mitigate against the loss of electrical power in transformers within the 330kv transmission system in Nigeria using Fuzzy logic technique. The objectives included to utilise Newton-Raphson’s technique to perform a load flow analysis to determine line losses, bus voltages, and load angles, and to use a Fuzzy Inference System to determine the points suitable for capacitor placement in order to reduce reactive power losses on the process and increase voltage profile, thereby improving the power system's stability and efficiency. Using the MATLAB toolbox, Newton- Raphson's power flow software was run to yield p.u nodal voltages ranging from 0.8890 to 1.0564, total real power line losses (0.09438 p.u), and total reactive power line losses. The power loss index is assessed and normalized in the range [0, 1] using power loss reduction. These indices, along with the magnitude of the p.u nodal voltage, were fed into the Fuzzy Inference System to produce the Capacitor Suitability Index (CSI). The obtained CSIs vary from additional to 0.897. Most nodes are influenced by the strength of the CSIs. for capacitor establishment. Tentatively, most elevated upsides of CSIs are picked for capacitor establishment. Therefore, 3 transports (3, 8, and 10) with CSI upsides of 0.680, 0.750, and 0.897 separately, are picked. Capacitor sizes of 50MVar, 85MVar, and 60MVar (got from Index Based Method) are introduced on the buses. Voltage profile improved by 3.74%, 3.27%, and 3.33% individually, while absolute genuine power loss in the framework reduced by 17.55% and all out receptive influence infusion to the system diminished by 8.70% separately. By the installation of capacitors at strategic areas in a transmission framework we were able to achieve a more stable network, reliable service delivery and a record of minimal technical losses.

Power Quality Analysis of Fuzzy DVR based Hybrid Solar PV-PEMFC System Under Severe Disturbance

Hybrid Energy System (HES) is becoming popular as it is identified as the most safe, sustainable, and long-term option for energy management. The grid-connected power network is vulnerable to frequent interruptions, which can lead to instability and a huge blackout. Furthermore, the presence of switching devices in industrial and domestic applications causes disturbances such as voltage swell/sag, waveform distortion, interruptions, impulsive voltage, and so on. Dynamic voltage restorer, known as a modern power compensating device, is cost effective, compact in size and can handle more energy capacity than DTSATCOM and UPFC. Hence for addressing the power quality issues in hybrid solar photovoltaic (PV)-proton exchange membrane fuel cells (PEMFC) system, dynamic voltage restorer (DVR) has been designed in this paper. As the fuzzy logic technique can provide flexible solutions in the case of uncertainty, fuzzy logic-based controller has also been employed with DVR to regulate the firing pulses of a PWM generator. Based on the simulation results obtained using fast fourier transform (FFT) analysis in MATLAB/Simulink, the dynamic performance of HES against the most important contingency condition or three phase faults is analyzed in detail. Further, the impact of DVR on power quality improvement under severe fault has also been demonstrated in this research work. On analyzing the total harmonic distortion (THD) values of HES under heavy disturbances, the fuzzy controlled dynamic voltage regulator (FCDVR) is identified as an efficient control mechanism for enhancing power quality in grid-connected HES.

Application of fuzzy C-means clustering and fuzzy EDAS to assess groundwater irrigation suitability and prioritization for agricultural development in a complex hydrogeological basin.

The current research is focused on detecting a river basin suitable for agriculture and priority for management using a new clustering tool of groundwater quality with fuzzy logic technique in R and Geographical Information System. A new fuzzy clustering-soft computing technique has been executed to determine the different hydrochemical zones considering 13 essential parameters such as electrical conductivity, hardness, chloride, sodium adsorption ratio, residual sodium carbonate, soluble sodium percent, magnesium hazard, permeability index, potential salinity, residual sodium bicarbonate, Kelly's ratio, synthetic harmful coefficient, and exchangeable sodium percentage. The derived fuzzy C-mean clustering (FCM) outperformed other available hard computing techniques like hierarchical clustering, K-means clustering, and agglomerative clustering. It divided the sampling sites into 2 clustering groups (FCM I and FCM II) which has been validated using fuzzy silhouette index (0.85), the partition coefficient (0.76), the partial entropy (0.68), and the modified partition coefficient (0.52). The hydrogeochemical analysis confirmed that the rock-water interaction, chemical weathering, and ion exchange process are predominant in the aquifer system of the study area. According to the correlation plots, the studied groundwater samples largely evolved from [Formula: see text], mixed [Formula: see text] types, and [Formula: see text] types. The spatial distribution map and the hydrochemical analysis also gives a clear depiction of the fluoride (> 1.0mg/l) and high iron (> 0.3mg/l) contamination in groundwater quality, making it unsuitable for both drinking and irrigation. A fuzzy EDAS priority map has been prepared based on all the irrigation suitability parameters which concludes that the groundwater at the upstream and downstream section of the basin requires the most attention. Based on the highest priority for management, five zones have been delineated: very high (5.98%), high (22.31%), medium (16.39%), low (32.30%), and very low (23.02). The findings of this study will be beneficial to planners and policymakers as they can develop schemes to solve similar problems across the country.

Empirical enhancement of EEG classification models for epileptic seizures using a fuzzy statistical perspective

The signals produced by an electrocardiogram (ECG) are made up of intricate pattern se-quences that have a periodic structure. These pattern sequences contain an initial P-wave, which denotes the beginning of an ECG wave, a QRS sequence, which denotes the intensi-ty of the pulse, and a T segment, which denotes the conclusion of the wave. Characteris-tics such as PR interval, QRS interval, QT interval, ST interval, R to R interval, etc. are employed to recognize chronic, ischemic, and other cardiac illnesses. These wave patterns need the simultaneous execution of many high-complexity signal processing operations to be classified into cardiac disorders. Signal pre-processing, feature extraction, feature se-lection, classification into epileptic and non-epileptic seizures, and post-processing are some of these operations. For each of these operations, researchers create a wide range of algorithms. These algorithms' performance differs significantly in terms of the quantity of leads utilized for ECG collection, filtering effectiveness, feature extraction & selection ef-fectiveness, and classifier effectiveness. Thus, researchers and system designers have be-come unclear when choosing the optimum algorithm set for an application. This text of-fers a thorough analysis & design of fuzzy CNN model of a broad range of epileptic & non-epileptic seizure classification techniques to lessen ambiguity. Convolutional neural network (CNN) based models outperform other models in terms of general-purpose per-formance, whereas application-specific deployments need the employment of customized fuzzy CNN models. A significant area of research & development is presented by the ob-servation that fuzzy logic techniques are not observed while constructing ECG classifica-tion models. Based on these findings, a new fuzzy logic-based classification method is provided in this text that employs quantization techniques to transform input ECG signals into fuzzy values. With these parameters and a specially created CNN model, it was pos-sible to achieve an accuracy of 99.5% for diverse ECG datasets. This accuracy was com-pared to a number of cutting-edge models, and it was observed that the suggested model is quite good at categorizing ECG signals. The suggested technique was observed to be quicker than traditional procedures due to the usage of a fuzzy logic model, enhancing its scalability for a broad range of clinical applications.

Optimal real-time tuning of autonomous distributed power systems using modern techniques

This work considers using a novel heuristic population-based evolutionary algorithm [viz., the moth flame optimization (MFO) algorithm] to regulate the conventional controller installed in an autonomous power system (APS). The moth flame optimization algorithm intends to produce the optimal magnitudes of the proportional-integral-derivative plus second derivative (PIDD2) controller parameters along with its first- and second-order low-pass filter constraints (installed in the investigated autonomous power system). The present task includes a comparison of the voltage response profiles of the investigated system obtained by the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller and those obtained by other algorithms (conveyed in current state-of-the-art literature) based on a proportional-integral controller. A fast-acting Sugeno fuzzy logic (SFL) technique is used to achieve the dynamic online results of the investigated autonomous power system model for online, off-nominal operational circumstances. Under step perturbations, the time-domain transient investigation in reference to voltage and/or mandate of load for the proposed autonomous power system model is inspected. Additionally, the robustness of the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller is investigated to test its behavior. An investigation has been provided by varying the model components of the studied autonomous power system model. It may be reported, as per the results obtained from the simulation, that the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller is an effective control strategy for the autonomous power system. The current research effort indicates that the proposed moth flame optimization algorithm, along with Sugeno fuzzy logic, may be useful for the actual time process of an autonomous power system.

Motivation assessment model for intelligent tutoring system based on mamdani inference system

<span lang="EN-US">Many educators have used the benefit offer by intelligent tutoring system. To become more personalizing and effective tutoring system, student characteristics need to be considered. One of important student characteristic is motivation. Therefore, in this study a motivation assessment model based on self-efficacy theory was proposed. Refer to the theory, effort, choice of activities, performance and persistence were discussed as motivation attributes. Further, time spend, difficulty level, number of correct answers and number of questions skipped are the parameters was defined for each attribute. The model was designed by taking the advantages of Mamdani inference system as fuzzy logic technique to predict students’ motivation level. The model able to inmates like a human tutor does in the traditional classroom to understand students’ motivation level.</span>

Using fuzzy logic to detect thermal variation in the city of Baquba (New Baquba neighborhood) as a model

The research dealt with the employment of fuzzy logic techniques for the thermal variance of the city of Baqubah by using the digital data of the satellite visuals of the Landsat satellite (ETM+8) to obtain the temperatures for the year 2021. Where the thermal state was extracted for each month of the year after it was processed in Arcmap10.3)) After that, the Fuzzy overlay application was used within the weights, which gives a clear picture of the real reality, similar in terms of temperatures, because the chosen area is a multi-use commercial center. the same, so reality will be reversed by fuzzy logic by existence and the gradient of existence (0-1) zero the cold value and one the hot value.

CHICKEN BANDA PERFORMANCE IMPROVEMENT UTILIZING NEURO-FUZZY LOGIC TECHNIQUE

This study is on improvement of performance of the chicken Banda, using indoor change in environmental conditions for temperature control. The differential change in climatic conditions is technically used to put on the fan and the Banda so as to realize the right comfortable indoor conditions.
 The chicken chicks’ Banda Mathematical model is created, prototype designed, temperature controller to depict a two systems simulation of neuro fuzzy logic and fuzzy logic .The performance is analyzed by the use of Matlab Simulink latest edition. To monitor the temperature of the Chicken cage the neural fuzzy logic technique is utilized. As far as the prototype is concerned the chicks’ cage set temperature is fixed at 26.50C.
 The study will show that the reference input can be kept on track by the process controller hence proving the principle that the neural fuzzy control is much superior in optimizing performance compared to the fuzzy only controllers. The Back propagation (BP) and least square estimator (LSE) are the hybrid optimization methods which are used. For data training the gradient descent method (GDM) is used.
 The research reveal that there is drastic performance improvement in the behavior response where result show that there settling time is reduced from 0.75 to 0.48 seconds while the percentage overshoot is also reduced down from 29.9% to 0.9345%.

Maximizing Regenerative Braking Energy Harnessing in Electric Vehicles Using Machine Learning Techniques

Innovations in electric vehicle technology have led to a need for maximum energy storage in the energy source to provide some extra kilometers. The size of electric vehicles limits the size of the batteries, thus limiting the amount of energy that can be stored. Range anxiety amongst the crowd prevents the entire population from shifting to a completely electric mode of transport. The extra energy harnessed from the kinetic energy produced due to braking during deceleration is sent back to the batteries to charge them, a process known as regenerative braking, providing a longer range to the vehicle. The work proposes efficient machine learning-based methods used to harness maximum braking energy from an electric vehicle to provide longer mileage. The methods are compared to the energy harnessed using fuzzy logic and artificial neural network techniques. These techniques take into consideration the state of charge (SOC) estimation of the battery, or the supercapacitor and the brake demand, to calculate the energy harnessed from the braking power. With the proposed machine learning techniques, there has been a 59% increase in energy extraction compared to fuzzy logic and artificial neural network methods used for regenerative energy extraction.

Optimal Design and Operation of an Off-Grid Hybrid Renewable Energy System in Nigeria’s Rural Residential Area, Using Fuzzy Logic and Optimization Techniques

This study focuses on a technical and economic analysis of designing and operating an off-grid hybrid renewable energy system (HRES) in a rural community called Olooji, situated in Ogun state, Nigeria, as a case study. First, a size optimization model is developed on the basis of the novel metaheuristic particle swarm optimization (PSO) technique to determine the optimal configuration of the proposed off-grid system on the basis of the minimization of the levelized cost of electricity, by factoring in the local meteorological and electricity load data and details on the technical specification of the main components of the HRES. Second, a fuzzy-logic-controlled energy management system (EMS) is developed for the dynamic power control and energy storage of the proposed HRES, ensuring the optimal energy balance between the different multiple energy sources and the load at each hour of operation. The result of the size optimization model showed that an LCOE for implementing an HRES in the community would be 0.48 USD/kWh in a full-battery-capacity scenario and 1.17 USD/kWh in a half-battery-capacity scenario. The result from this study is important for quick decision-making and effective feasibility studies on the optimal technoeconomic synopsis of implementing minigrids in rural communities.

Investigating the Stability of the Hill of the Acropolis of Athens, Greece, Using Fuzzy Logic and Remote Sensing Techniques

The main objective of this study was to investigate the stability of the Acropolis Hill, Greece, by developing a Rock Instability Model (RIM) based on fuzzy logic and remote sensing techniques. RIM aimed to identify locations on the rock formations of the Acropolis Hill that will potentially have instability issues due to the action of geomorphological factors, weathering and erosive processes. Six factors including lithology, slope angle, density of discontinuities, density of faults, density of surface runoff elements, and the orientation of the stratigraphy of the geological formations in relation to the orientation of the slope were considered as the most appropriate for implementing the proposed novel approach, with each variable classified and weighted by a fuzzy simple additive weighting method. Lithology and slope angle were considered the most significant variables that contributed to the overall stability of the Acropolis Hill. The outcomes of the RIM model were verified by remote sensing data and field observation, showing an agreement and high accuracy. From the satellite data analysis, it was concluded that for the entire Acropolis Hill, minor displacement rates were recorded, probably because of the extensive mitigation measures and consolidation works established in the recent past. Overall, the study highlighted the ability of the proposed methodology to be used as an alternative investigation tool in rock instability-related assessments valuable to land use planning and development, helping reduce the anticipated losses in highly susceptible zones.

Intelligent Latency-Aware Tasks Prioritization and Offloading Strategy in Distributed Fog-Cloud of Things

Offloading the dynamic tasks with fog computing is envisioned as a viable option for prolonging resource-limited constraints and improving the computational and communicational latency for delay-sensitive IoT applications. Besides, the priority of tasks and the target layers for offloading them to minimize the incurred service latency is a prime concern in layered computing architecture. To leverage the efficiency of the underlying computing nodes for the tasks’ heterogeneity and computational requirements with deadline constraints, this article presents a fuzzy logic technique to prioritize the tasks based on their resource requirements and associated deadline. For efficient scheduling, an elitism-based multipopulation Jaya is proposed to map these disparate groups of tasks to a cluster amalgamation of computational-rich heterogeneous computing nodes. Moreover, a compatibility-based heuristic offloading strategy is devised to determine compatible computing nodes to offload the computations considering the availability of resources and communicational time from the respective IoT devices. Finally, extensive simulations are carried out with conflicting scheduling parameters appraising the efficacy of the proposed strategy over existing algorithms. The percentages of improvements of the proposed algorithm over the compared algorithms are 35% and 28% for average waiting. time and average service latency, respectively.

Adaptive Neuro-Fuzzy Inference System (ANFIS) Method for Developing a Decision Support System for Determining Landslide Susceptibility

Landslide catastrophes are one of the disasters that frequently occur in Indonesia owing to the weather and climatic features, regional terrain, and geological formations that make this nation prone to landslides. The primary goal of this research is to compare the application of the fuzzy logic technique and the adaptive neuro-fuzzy inference system (ANFIS) approach to landslide detection sensors based on prior research in order to identify landslide-prone locations more easily. The Adaptive Neuro-Fuzzy Inference System (ANFIS) technique analyzes the landslide area using three factors. Rainfall, land slope, and soil moisture are examples of these factors. This variable is used to assess the area's level of vulnerability to landslides: very safe, relatively safe, relatively potential, potential, and very potential. In the study, each piece of data is subjected to a training and testing procedure to identify landslide vulnerability, with the factors and weighting methods aligned with current government standards. This study compares the rules outcomes to those of past studies as well as the system results. Based on the studies findings, it can be stated that the decision support system for the degree of landslide vulnerability utilizing the ANFIS approach is superior to the fuzzy logic method, with an accuracy rate of 86.21%.

A Cloud-Based Software Defect Prediction System Using Data and Decision-Level Machine Learning Fusion

This research contributes an intelligent cloud-based software defect prediction system using data and decision-level machine learning fusion techniques. The proposed system detects the defective modules using a two-step prediction method. In the first step, the prediction is performed using three supervised machine learning techniques, including naïve Bayes, artificial neural network, and decision tree. These classification techniques are iteratively tuned until the maximum accuracy is achieved. In the second step, the final prediction is performed by fusing the accuracy of the used classifiers with a fuzzy logic-based system. The proposed fuzzy logic technique integrates the predictive accuracy of the used classifiers using eight if–then fuzzy rules in order to achieve a higher performance. In the study, to implement the proposed fusion-based defect prediction system, five datasets were fused, which were collected from the NASA repository, including CM1, MW1, PC1, PC3, and PC4. It was observed that the proposed intelligent system achieved a 91.05% accuracy for the fused dataset and outperformed other defect prediction techniques, including base classifiers and state-of-the-art ensemble techniques.

Mathematical Modification to the Classical Volumetric Method for Estimating Oil Reserves

Using fuzzy logic technique, this work proposes a mathematical adjustment to the classical volumetric method for estimating oil reserves to manage the level of uncertainty associated with oil reserves estimation. This technique introduces a risk factor (α) into the volumetric method equation to account for the uncertainty associated with estimating the parameters that are used in the volumetric method equation. Risk types that may affect oil reserves estimation can be considered using the risk factor (α) in the modified equation. Results showed that the amount of proven oil reserves decreases exponentially as the value of risk factor (α) increases. It also showed that the ratio of the expected proven oil reserves with respect to proven oil reserves (N*/N) goes to zero when the value of risk factor (α) reaches a value of (5). Three cases were proposed to categorize uncertainty in proven oil reserves estimation: high risk estimate, middle risk estimate and risk-free estimate. Results showed that, for the case of high-risk estimate, expected proven oil reserves (N*) was appreciably lower than the proven oil reserves (N) due to the inclusion of risk. Sources of risk may include, but not limited to, lack of expertise of the evaluator, level of integrity of the evaluator, engineering errors during measurement and calculation and governmental laws. Results also showed that the calculated amount of proven oil reserves (N*), for the middle risk estimate case, is much higher than that for high risk estimate case. As for the riskfree estimate case, the calculated proven oil reserves (N*) using the modified formula equals to the proven oil reserves (N) calculated by the classical volumetric formula. This case reflects 100% confidence and reliability in the parameters’ estimation which also places great trust in the evaluator’s integrity and expertise.

A Fuzzy Logic Control for Maximum Power Point Tracking Algorithm Validated in a Commercial PV System

Photovoltaic (PV) panels are devices capable of transforming solar energy into electricity without emissions. They are still a trending technology in the market not only because of the renewable features but also due to the avoidance of movable parts, which makes them an option with low maintenance. If the output voltage is insufficient or needs to be regulated, a boost converter is commonly connected to a PV panel. In this article, a commercial PV with a boost converter is controlled through a dSPACE platform for a maximum power point tracking (MPPT) task. Due to previous related experience, a fuzzy logic technique is designed and tested in real-time. The results are compared with an incremental conductance (IncCond) algorithm because it is a feasible and reliable tool for MPPT purposes. The outcomes show enhancement (in comparison with IncCond) in the steady-state oscillation, response time and overshoot values, which are 73.2%, 81.5% and 52.9%, respectively.

A fuzzy sustainable model for drug supply chain networks during a pandemic

This research focuses on developing a fuzzy sustainable model for drug supply chain networks during a pandemic. The outbreak of a pandemic introduces unprecedented uncertainties and complexities to the drug supply chain, necessitating the integration of sustainability considerations and fuzzy logic techniques into decision-making processes. The proposed model aims to optimize decision variables, such as inventory levels, production capacities, transportation routes, and allocation strategies, while balancing conflicting objectives and addressing sustainability criteria. The model incorporates fuzzy logic to handle imprecise and uncertain inputs, allowing decision-makers to capture qualitative information and expert knowledge. The research emphasizes the importance of sustainability in drug supply chains, encompassing environmental impact, social welfare, and economic viability. Through the use of an optimization framework and a decision support system, stakeholders can make informed decisions considering sustainability criteria and dynamic pandemic conditions. The research contributes to enhancing the resilience, efficiency, and sustainability of drug supply chains during pandemics, facilitating better patient care and community well-being.

Data and Ensemble Machine Learning Fusion Based Intelligent Software Defect Prediction System

The software engineering field has long focused on creating high-quality software despite limited resources. Detecting defects before the testing stage of software development can enable quality assurance engineers to concentrate on problematic modules rather than all the modules. This approach can enhance the quality of the final product while lowering development costs. Identifying defective modules early on can allow for early corrections and ensure the timely delivery of a high-quality product that satisfies customers and instills greater confidence in the development team. This process is known as software defect prediction, and it can improve end-product quality while reducing the cost of testing and maintenance. This study proposes a software defect prediction system that utilizes data fusion, feature selection, and ensemble machine learning fusion techniques. A novel filter-based metric selection technique is proposed in the framework to select the optimum features. A three-step nested approach is presented for predicting defective modules to achieve high accuracy. In the first step, three supervised machine learning techniques, including Decision Tree, Support Vector Machines, and Naïve Bayes, are used to detect faulty modules. The second step involves integrating the predictive accuracy of these classification techniques through three ensemble machine-learning methods: Bagging, Voting, and Stacking. Finally, in the third step, a fuzzy logic technique is employed to integrate the predictive accuracy of the ensemble machine learning techniques. The experiments are performed on a fused software defect dataset to ensure that the developed fused ensemble model can perform effectively on diverse datasets. Five NASA datasets are integrated to create the fused dataset: MW1, PC1, PC3, PC4, and CM1. According to the results, the proposed system exhibited superior performance to other advanced techniques for predicting software defects, achieving a remarkable accuracy rate of 92.08%.

Dynamic Programming Approach in Aggregate Production Planning Model under Uncertainty

In order to achieve a competitive edge in the market, one of the most essential components of effective operations management is aggregate production planning, abbreviated as APP. The sources of uncertainty discussed in the APP model include uncertainty in demand, uncertainty of production costs, and uncertainty of storage costs. The problem of APP usually involves many imprecise, conflicting and incommensurable objective functions. The application of APP in real conditions is often inaccurate, because some information is incomplete or cannot be obtained. The aim of this study is to develop APP model under uncertainty with a dynamic programming (DP) approach to meet consumer demand and minimize total costs during the planning period. The APP model includes several parameters including market demand, production costs, inventory costs, production levels and production capacity. After describing the problem, the optimal APP model is formulated using artificial neural network (ANN) techniques in the demand forecasting process and fuzzy logic (FL) in the DP framework. The ANN technique is used to forecast the input demand for APP and minimize the total cost during the planning period using the FL technique in the DP framework to accommodate uncertainties. The model input is historical data obtained through interviews. A case study was conducted on the the need for aluminum plates for the automotive industry. The results show that the ANN technique proposed for demand projection has a low error value in forecasting demand and FL in the DP framework is able to find minimal production costs in the APP model.