Triangular Membership Research Articles

A Prognostic Based Fuzzy Logic Method to Speculate Yarn Quality Ratio in Jute Spinning Industry

Jute is a bio-degradable, agro-renewable, and widely available lingo cellulosic fiber having high tensile strength and initial modulus, moisture regain, good sound, and heat insulation properties. For these unique properties and eco-friendly nature of jute fibers, jute-based products are now widely used in many sectors such as packaging, home textiles, agro textiles, build textiles, and so forth. The diversified applications of jute products create an excellent opportunity to mitigate the negative environmental effect of petroleum-based products. For producing the best quality jute products, the main prerequisite is to ensure the jute yarn quality that can be defined by the load at break (L.B), strain at break (S.B), tenacity at break (T.B), and tensile modulus (T.M). However, good quality yarn production by considering these parameters is quite difficult because these parameters follow a non-linear relationship. Therefore, it is essential to build up a model that can cover this entire inconsistent pattern and forecast the yarn quality accurately. That is why, in this study, a laboratory-based research work was performed to develop a fuzzy model to predict the quality of jute yarn considering L.B, S.B, T.B, and T.M as input parameters. For this purpose, 173 tex (5 lb/spindle) and 241 tex (7 lb/spindle) were produced, and then L.B, S.B, T.B and T.M values were measured. Using this measured value, a fuzzy model was developed to determine the optimum L.B, S.B, T.B, and T.M to produce the best quality jute yarn. In our proposed fuzzy model, for 173 tex and 241 tex yarn count, the mean relative error was found to be 1.46% (Triangular membership) and 1.48% (Gaussian membership), respectively, and the correlation coefficient was 0.93 for both triangular and gaussian membership function. This result validated the effectiveness of the proposed fuzzy model for an industrial application. The developed fuzzy model may help a spinner to produce the best quality jute yarn.

Open Circuit Fault Diagnosis in Five-Level Cascaded H-Bridge Inverter

The development of power electronic converter, especially multilevel converter, is remarkable for several decades. The complex switching and increased power of semiconductor devices are prime reasons for faults in multilevel inverters and have raised question about reliability. To improve the reliability, a cost-effective solution in terms of fault diagnosis is essential. In this context, this study proposed an open circuit fault (OCF) diagnosis technique for a switching device in a five-level cascaded H-bridge multilevel inverter using fuzzy logic control. The OCF features like output voltage total harmonic distortion (THD) and normalized average output voltage are fuzzed as input variables of the fuzzy logic controller. These input variables are divided into various triangular antecedent membership function (MF). The output produced by the fuzzy controller as consequent MFs is divided into different levels to identify the faulty switch. In order to make a complete fault-tolerant structure, a reduced modulation index-based postfault control is suggested to get a balanced output voltage. The MATLAB/Simulink results and prototype results are the evidence to support the proposed fault diagnosis technique.

Optimization of Inventory Model Cost Parameters, Inventory and Lot Size as Fuzzy Numbers

In general, the demand rate and the unit cost of the items remains constant inspite of lot size in inventory models. But in reality, the demand rate and the unit cost of the items are connected together. In this research, demand dependent unit cost inventory model is considered where different cost parameters, maximum inventory and the lot size of the model are taken under fuzzy environment. First an analytic solution of the crisp model is obtained by the method of calculus where the inventory parameters are exact and deterministic. Later, the problem is developed with fuzzy parameters where inaccuracy has been introduced through triangular membership function.Then the defuzzification of the model is done by using the method of Graded mean integration. An optimal solution is obtained using Karush Kuhn-Tucker conditions approach. An illustrative model is done and an analysis of total cost for different measures of possibility are performed and tabulated.

A Novel Method to Evaluate the Effect of Slope Blasting under Impact Loading

In this paper, the quantitative evaluation of the explosion effect based on the fuzzy comprehensive evaluation method is proposed to describe the qualitative evaluation results. The selected state characteristic parameters are expressed by two kinds of membership functions, fuzzy normal and triangular distribution membership functions, and preliminary evaluation results are obtained. The validity index of the maximum membership principle is used to assess the accuracy of the evaluation results of two algorithms, and a relevant approaching degree is chosen to optimize the results. The entire evaluation process selects eleven indicators to form an evaluation set, including the boulder yield, root rate, flying distance of flyrock, explosive consumption, postcracking distance, detonator unit consumption, vibration velocity, loose coefficient, cast distance, throw rate, and blasted volume per meter of hole. Part of the indicator parameters are derived from field test monitoring, and another part of the indicator parameters are derived from numerical simulation. The simulation process uses the user-defined material interface function provided by LS-DYNA. And the numerical model of slope blasting is established by embedding the evolution relationship of tensile and compressive damage into the elastoplastic constitutive material. The evaluation method proposed in this paper is used to evaluate the postexplosion effect of Zijin Mountain gold-copper mine slope cast blasting. The results demonstrate that the fuzzy normal distribution membership function can correlate the state characteristic information and evaluation index effectively, and the working condition after explosion can be reflected accurately. Additionally, the influencing factors can be ranked by the importance degrees according to the calculated value of the evaluation index.

Determining weight coefficients for an optimal system of control over electric energy generation in a combined electric power system

This paper reports a solution to a relevant scientific task of determining the weight coefficients for an optimal system of automated control over the level of electric energy generation by renewable energy sources in a combined electric power system. It has been established that existing control systems of electric power generation by renewable sources, based on solving a problem on multicriteria optimization, do not take into consideration a change in the quantitative and qualitative composition of electric consumers over time.It has been proposed, in order to determine those weight coefficients that influence the resulting solution to the problem on multicriterial optimization, to employ a mathematical apparatus of fuzzy logic. This has made it possible, in contrast to existing systems, to better account for a time-dependent change in the quantitative and qualitative composition of electricity consumers. It has been shown that it is expedient to choose, as the input parameters for a fuzzy model, the values for a coefficient of consumer load and a coefficient of load importance that takes into consideration the sensitivity of electric consumers to voltage deviations.A database of rules for a fuzzy system of weight coefficients determination has been constructed, which includes 15 rules of fuzzy production. The Mamdani algorithm has been used as an algorithm of fuzzy logic derivation. To determine the input and output linguistic variables we have used triangular and trapezoidal membership functions. The output parameter was defuzzified by the method of determining the center of gravity (centroid method).We have performed computer simulation of the optimal system of an automated system of control over the level of electric energy generation by renewable energy sources using the designed fuzzy unit for determining weight coefficients. Analysis of the simulation results has shown that the devised system of automated control makes it possible to increase the level of electricity generation to a network, as compared to existing systems

METHOD FOR OBTAINING THE PARAMETERS OF MEMBERSHIP FUNCTIONS OF FUZZY SETS BASED ON REAL DATA FOR AUTOMATED INFORMATION PROCESSING SYSTEMS

Objectives Development of a method for selecting the type of accessory function and obtaining its parameters to allow subjective personal influences in automated information processing to be excluded.Method. Existing methods for constructing membership functions were analysed. The research was based on the methods of fuzzy logic and data analysis.Results. A method for obtaining the parameters of membership functions of fuzzy sets using real data is suggested. It is proposed to use the data obtained from the object under study to determine the kernel of the fuzzy number, as well as derive theoretical information about the object for the carrier. Triangular, trapezoidal, bell-shaped and Gaussian membership functions are considered. The appearance of the membership function can be defined using the criterion of the relations of the kernel to the carrier of a fuzzy set. The results of calculations for obtaining the membership functions based on data on the power consumption of electric motors of different types are given.Conclusion. The developed method can be used both in decision support systems as well as in automated systems for controlling technological processes. If necessary, the values of the criterion proposed in the article can be revised to take the values included in the set of measured real data into account or to simplify the procedure of automated processing. Further research will use the described method to obtain the terms of linguistic variables.

Training High-Order Takagi-Sugeno Fuzzy Systems Using Batch Least Squares and Particle Swarm Optimization

This paper proposes two methods for training Takagi–Sugeno (T-S) fuzzy systems using batch least squares (BLS) and particle swarm optimization (PSO). The T-S system is considered with triangular and Gaussian membership functions in the antecedents and higher-order polynomials in the consequents of fuzzy rules. In the first method, the BLS determines the polynomials in a system in which the fuzzy sets are known. In the second method, the PSO algorithm determines the fuzzy sets, whereas the BLS determines the polynomials. In this paper, the ridge regression is used to stabilize the solution when the problem is close to the singularity. Thanks to this, the proposed methods can be applied when the number of observations is less than the number of predictors. Moreover, the leave-one-out cross-validation is used to avoid overfitting and this way to choose the structure of a fuzzy model. A method of obtaining piecewise linear regression by means of the zero-order T-S system is also presented.

An integrated optimization and simulation approach for air pollution control under uncertainty in open-pit metal mine

Open-pit metal mines contribute toward air pollution and without effective control techniques manifests the risk of violation of environmental guidelines. This paper establishes a stochastic approach to conceptualize the air pollution control model to attain a sustainable solution. The model is formulated for decision makers to select the least costly treatment method using linear programming with a defined objective function and multi-constraints. Furthermore, an integrated fuzzy based risk assessment approach is applied to examine uncertainties and evaluate an ambient air quality systematically. The applicability of the optimized model is explored through an open-pit metal mine case study, in North America. This method also incorporates the meteorological data as input to accommodate the local conditions. The uncertainties in the inputs, and predicted concentration are accomplished by probabilistic analysis using Monte Carlo simulation method. The output results are obtained to select the cost-effective pollution control technologies for PM25, PM10, NOx, SO2 and greenhouse gases. The risk level is divided into three types (loose, medium and strict) using a triangular fuzzy membership approach based on different environmental guidelines. Fuzzy logic is then used to identify environmental risk through stochastic simulated cumulative distribution functions of pollutant concentration. Thus, an integrated modeling approach can be used as a decision tool for decision makers to select the cost-effective technology to control air pollution.

Segmentation of Articular Cartilage and Early Osteoarthritis based on the Fuzzy Soft Thresholding Approach Driven by Modified Evolutionary ABC Optimization and Local Statistical Aggregation

Articular cartilage assessment, with the aim of the cartilage loss identification, is a crucial task for the clinical practice of orthopedics. Conventional software (SW) instruments allow for just a visualization of the knee structure, without post processing, offering objective cartilage modeling. In this paper, we propose the multiregional segmentation method, having ambitions to bring a mathematical model reflecting the physiological cartilage morphological structure and spots, corresponding with the early cartilage loss, which is poorly recognizable by the naked eye from magnetic resonance imaging (MRI). The proposed segmentation model is composed from two pixel’s classification parts. Firstly, the image histogram is decomposed by using a sequence of the triangular fuzzy membership functions, when their localization is driven by the modified artificial bee colony (ABC) optimization algorithm, utilizing a random sequence of considered solutions based on the real cartilage features. In the second part of the segmentation model, the original pixel’s membership in a respective segmentation class may be modified by using the local statistical aggregation, taking into account the spatial relationships regarding adjacent pixels. By this way, the image noise and artefacts, which are commonly presented in the MR images, may be identified and eliminated. This fact makes the model robust and sensitive with regards to distorting signals. We analyzed the proposed model on the 2D spatial MR image records. We show different MR clinical cases for the articular cartilage segmentation, with identification of the cartilage loss. In the final part of the analysis, we compared our model performance against the selected conventional methods in application on the MR image records being corrupted by additive image noise.

Triangular Fuzzy Membership-Contrast Limited Adaptive Histogram Equalization (TFM-CLAHE) for Enhancement of Multimodal Biometric Images

The research work proposes a novel triangular fuzzy membership (TFM) function-based contrast limited adaptive histogram equalization (CLAHE) for biometric image enhancement. Biometric images have wide applications in the areas of verification and authentication systems. For accurate identification and verification, pre-processing of captured biometric images becomes essential. When the region of interest is smaller than the original image, a variation of histogram equalization called adaptive histogram equalization (AHE) is used. AHE enhances contrast of images by considering local regions. Along with local contrast, noise in those regions also get amplified by using AHE. This amplification of noise can be resolved by applying a contrast limited AHE (CLAHE) which limits the contrast in the enhanced local regions by clipping the histogram at a pre-fixed limit. CLAHE yields good results by limiting the contrast and enhancing local regions, but it is image invariant since it uses pre-determined clip limit for limiting contrast. The proposed research work TFM-CLAHE puts forward the idea of image variant, automatic clip value determinant algorithm for enhancement. The algorithm employs triangular fuzzy membership function to determine clip-limit and limits contrast by clipping the histogram at the computed clip-level. TFM function computes the clipping parameter by considering intensities of pixels. The computed fuzzy clip-limit overrides the pre-defined limit. Consequently, the clipping parameter varies according to the image under consideration and yields better enhancement results. The proposed work is experimented on multimodal biometric images acquired from Chinese Academy of Science, Institute of Automation Iris, Face and Fingerprint databases. TFM-CLAHE computes appropriate clipping limit for each of these heterogenous images. The results of the proposed work are evaluated on the grounds of images’ average information content, mean square error, peak signal noise ratio, natural image quality evaluator, no-reference free energy based robust metric, blind image quality measure of enhanced images and no reference quality metric for contrast distortion. The results show good enhancement and these are compared with existing conventional image enhancement techniques.

Managing privacy of sensitive attributes using fuzzy-based data transformation methods in privacy preserving data mining environment

When we extract personal, sensitive and business information in data mining applications, then certain problems occurs. Privacy attack occurs due to the misuse of individual information. In centralised database environment, data transformation methods in fuzzy-based data in the field of privacy preserving clustering are proposed in this paper. In first case, a fuzzy data transformation method is proposed and different experiments are conducted by changing the fuzzy membership functions such as Z-shaped fuzzy membership function, Triangular fuzzy membership function, Gaussian fuzzy membership function to transform the original dataset. In second case, a hybrid method is proposed as a combination of fuzzy data transformation approach which is specified in first case and random rotation perturbation (RRP). The experimental outcome verified that the hybrid approach permits finest results for every member functions.

Optimization of Hazardous Chemical Waste Location-Routing Logistics Based on Uncertain Conditions

In order to effectively solve the hazardous chemical waste location-routing problem, based on the existing literatures, this paper considers chemical waste production and uncertainties in the processing technology, and establishes a multi-objective optimization calculation model involving transportation and location risks, costs and risk equity. It uses an example to verify the proposed model, and then establishes a measurement method with location-routing risk equity based on the fuzzy description of the chemical waste production by the triangular fuzzy membership function. The calculation model takes into account the variable cost and location risk of the waste disposal centre, reducing the error from single-objective calculation. Through the inverse fuzzy algorithm, the multi-objective fuzzy model is converted into a multi-objective linear model. The verification results of the example show that: if the variable cost is not considered, the total risk is increased by 110.68%; if the location risk is not considered, the cost is increased by 21.35%; if the risk equity is not considered, the total cost is decreased by 8.71%, while the risk is increased by 48.32%, which proves that the combinatorial optimization of multi-objective function model established will lead to a slight increase in cost, but a significant reduction of related risks, thus making the location-routing scheme more in line with the actual situation and needs.

Damage identification of composite beam structure using fuzzy logic-based model

Damage identification of beam structures has been in practice for last few decades. The methodologies adopted were upgraded over the time depending upon the complexities of the damage or crack and the desired accuracy. The utilisation of artificial intelligence (AI) techniques has also been considered by many researchers. In the current research, damage detection of a glass fibre-reinforced composite cantilever beam subjected to vibration has been carried out. A fuzzy-based model using triangular, trapezoidal and Gaussian membership functions has been developed separately to predict the damage characteristics, i.e., relative damage position (RDP) and relative damage severity (RDS). The inputs required for the fuzzy-based model, i.e., first three relative natural frequencies and first three mode shape differences have been determined by finite element analysis of the damaged cantilever beam subjected to the natural vibration. An experimental setup has been used to justify the robustness of the proposed technique for damage identification.

A PSO based virtual sample generation method for small sample sets: Applications to regression datasets

In the early period of process industries, it is an intractable challenge to build an accurate and robust forecasting model using the collected scared samples. The information derived from small sample sets is unreliable and weak. Thus, the models established based on the small sample sets are inefficient. Virtual sample generation (VSG) is a promising technology which can be used to generate plenty of new virtual samples by the information acquired from small sample sets, aiming at improving the accuracy of forecasting models. To capture the tendency of the raw sample set and reduce information gaps among individuals, an information-expanded function based on triangular membership (TMIE) is developed to asymmetrically expand the domain range in each attribute in this paper. A novel particle swarm optimization based VSG (PSOVSG) approach is proposed to iteratively generate the most feasible virtual samples over the search-space. The effectiveness of PSOVSG is tested against other three methods of VSG over two real cases: multi-layer ceramic capacitors (MLCC) and purified Terephthalic acid (PTA). The simulation results show the proposed PSOVSG achieves better performance than other methods.

Fuzzy bi-criteria decision making approach for supplier selection and distribution network planning in supply chain management

Supply chain management (SCM) is to coordinate and integrate material and information within and across organizations. Supplier selection is evaluated as a critical factor for the firms desiring improved and successful supply chain in the process of product realization that starts from the purchasing of raw or sub-assembly material till the end of delivering the final product. With the scope of this paper, a fuzzy bi-objective optimization model is discussed; who coordinates and minimizes the procurement & distribution cost of Convenience stores company and selects the best supplier. Supplier selection process is carried out on the bases of multi factors therefore it is considered as a multi criteria decision problem. The model presented in the paper is using the analytic network process (ANP), a multi criteria decision making technique for supplier selection. To obtain the best coordination, the model is converted into crisp using triangular fuzzy numbers and fuzzy membership functions and solved using fuzzy goal programming technique.

Design of Fuzzy Logic based Plasma Position Control in Aditya Tokamak

Plasma position control is a major concern in Tokamak machines. Radial position and plasma current are the input parameters that affect the plasma stabilization current which in turn affects the plasma position. As the relationship between the input and output parameters are non linear in nature, intelligent controllers are to be developed. In this paper, FIS based plasma position controller is developed. Also the optimization of linguistic variables and membership functions is performed based on the accuracy of the results. It is found that triangular membership with 9 linguistic variable provide better results for stabilization current prediction.

Fuzzy bi-criteria scheduling on parallel machines involving weighted flow time and maximum tardiness

AbstractThis paper considers a bi-criteria scheduling on parallel machines in fuzzy environment which optimizes the weighted flow time and maximum tardiness. The fuzziness, vagueness or uncertainty in processing time of jobs is represented by triangular fuzzy membership function. The bi-criteria problem with weighted flow time and maximum tardiness as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. So, a heuristic algorithm is proposed to find the optimal sequence of jobs processing on parallel machines so as to minimize the secondary criterion of maximum tardiness without violating the primary criterion of weighted flow time. A numerical illustration is also given in support of the algorithm proposed.

An Efficient Approach for Removal of Impulse Noise from Highly Corrupted Images

In this paper, a method based on adaptive fuzzy filter is used to denoise image corrupted by impulse noise. The algorithm is proposed for restoration of grayscale as well as color images which are highly corrupted by salt and pepper noise. The algorithm detects level of corruption for each pixel using triangular fuzzy membership function to ensure the replacement of noisy pixels based on degree of corruption. Besides providing ease of computation here we use fully adaptive and automatically adjustable threshold value. Final result shows better performance in the impulse noise reduction over standard images relative to the conventional median filtering approach in terms of both noise reduction and fine detail preservation.

Applying 2-Tuple Linguistic Representation and a Mamdani Fuzzy Inference System to Fuzzy Time Series

This study applies 2-tuple linguistic representation and a Mamdani fuzzy inference system to fuzzy time series. Mamdani [12] proposed a max-min inference method and applied it to fuzzy logical control problem. The Mamdani fuzzy inference system is a useful tool in fuzzy modeling process, but it is rarely applied to fuzzy time series problems. By integrating 2-tuple linguistic representation, which was proposed by Herra and Martínez [16], the connection between fuzzy modeling inference and fuzzy time series can be established. With the 2-tuple concept, historical data can be fuzzified to a fuzzy set with triangular membership and the loss of information is reduced. The fuzzy if-then rule can be established by two consecutive data and a Mamdani fuzzy inference system can be applied in the inference process. Two examples are investigated. First, the proposed method is applied to forecast enrollments at the University of Alabama. Compared with six different methods, the average MAPE value shown by the proposed method is relatively small. Next, the proposed method is used to forecast the number of Taiwanese tourists traveling to Malaysia. A set of data from 1993 to 2006 is used to establish the forecasting model, and a set of data from 2007 to 2011 is used to test the model. Chen's method [4] is also presented for comparison with the proposed method. Chen's method fails forecast the number of tourists in 2009 and 2010. The proposed method succeeds in forecasting all the testing data from 2007 to 2011. In forecasting unknown future data, the proposed method provides more rules than other methods do.

Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness

Due to the inherent uncertainty associated with various factors in the designing stage, considering uncertainty is important in system designs. In this article, a redundancy allocation problem with active strategy and choice of component type is studied where the system engineer faces with insufficient knowledge about exact values of some characteristics of components such as reliability and cost. The impreciseness is considered in terms of fuzzy numbers with triangular and trapezoidal membership functions. To achieve a robust design under different realizations of uncertain parameters, robust models are developed, which is the first attempt in the area of redundancy allocation problems under fuzziness. In worst case, extreme values of uncertain parameters are considered. In the realistic case, the uncertain parameters are dealt with the help of the credibilistic approach of fuzzy programming and the expected value of fuzzy numbers. In other words, the robust model makes a trade-off between the expected value of system reliability as a performance measure, the deviation of system reliability, and the constraint violation where the penultimate one assures the optimality robustness and the last one preserves the feasibility robustness. The proposed models can help system/product designers and managers who are risk-averse to easily deal with the inherent uncertainty in the designing stage. At the end, numerical examples are presented and the results are analyzed.