Distribution Of Membership Functions Research Articles

Empirical Research on Coordination Degree of 3E System of China

As environmental issues become more and more apparent, the energy, economy and environment system has become the academic focus. This paper established an energy, economy and environment comprehensive development evaluation system proceeding from quantity, structure and quality, selected the factor method to give the weight for indicators and calculate the development standard of subsystems. Finally, it used normal distribution membership function to measure the coordination degree of the 3E system during the China’s eleventh five-year plan. The research found that China's current 3E system is in intermediate coordination state, the contradiction between energy consumption and environmental protection is the biggest obstacle to the overall 3E coordination, the economy-environment coordination degree has been improved and the energy-economy system is in great state. And energy strategies, economic development policies and environmental policies need to be developed to keep the good development trend of the 3E system’s coordination degree.

Analysis of Clustering Algorithms for MR Image Segmentation using IQI

This paper presents the analysis of clustering algorithms for medical MR (magnetic resonance) images using IQI (image quality index). The clustering algorithms used are classical C means, fuzzy C means and rough fuzzy C means. With the assistance of the lower and upper approximation of rough sets, the rough fuzzy C means clustering algorithm improves the objective function and further the distribution of membership function for the traditional fuzzy C means clustering. These algorithms are implemented on various medical MR images to detect diseases. The results of various clustering algorithms are compared using IQI index, and it has been found that rough fuzzy C means (RFCM) clustering algorithm fairs better as compared to classical C means and fuzzy C means algorithm respectively.

Prediction of Water Quality Index Using Neuro Fuzzy Inference System

The groundwater near mines is contaminated heavily as regards acidity, alkalinity, toxicity, heavy mineral, and microbes. During rainy season, the mines are filled with the water which contaminates the groundwater and gradually disperses by percolating through the soil into urban area, making the water unsuitable for use. In addition, fertilizers used for agricultural purpose affect pH and nitrate content of groundwater. Hence, evaluation of WQI of groundwater is extremely important in urban areas close to mines to prepare for make remedial measures. To this end, the present study proposes an efficient methodology such as adaptive network fuzzy inference system (ANFIS) for the prediction of water quality. The parameters used to assess water quality are usually correlated and this makes an assessment unreasonable. Therefore, the parameters are uncorrelated using principal component analysis with varimax rotation. The uncorrelated parameters values are fuzzified to take into account uncertainty and impreciseness during data collection and experimentation. An efficient rule base and optimal distribution of membership function is constructed from the hybrid learning algorithm of ANFIS. The model performed quite satisfactorily with the actual and predicted water quality. The model can also be used for estimating water quality on-line, but the accuracy of the model depends upon the proper training and selection of parameters.

Prediction of entrance length for low Reynolds number flow in pipe using neuro-fuzzy inference system

This paper proposes an adaptive network fuzzy inference system (ANFIS) for the prediction of entrance length in pipe for low Reynolds number flow. After using the computational fluid dynamics (CFD) technique to establish the basic database under various working conditions, an efficient rule database and optimal distribution of membership function is constructed from the hybrid-learning algorithm of ANFIS. An experimental data set is obtained with Reynolds number, diameter of the pipe, and inlet velocity as input parameters and entrance length as output parameter. The input–output data set is used for training and validation of the proposed techniques. After validation, they are forwarded for the prediction of entrance length. The entrance length estimation results obtained by the model are compared with existing predictive models and are presented. The model performed quite satisfactory results with the actual and predicted entrance length values. The model can also be used for estimating entrance length on-line but the accuracy of the model depends upon the proper training and selection of data points.

Multi-Item Multi-Period Dynamic Capacity-Constrained Lot-Sizing Model with Parallel Machines and Fuzzy Demand

Multi-item, multi-period production systems are prevalent in traditional production and distribution settings. A dynamic lot size production scheduling model (DLSPM) for multi-Production/inventory item multi-period production system with parallel machines is proposed in this paper. A mathematical framework that extends the DLSPM to multi-Production/inventory item-multi-period production planning constrained by storage space was built. The criteria of DLSPM explore optimal production schedule with the constraints of inventory, backlogs, production and demand to minimize the total inventory costs over finite planning horizon. Demand analogous to a typical production environment considered includes dynamic deterministic and fuzzy demand. The model was tested with both deterministic and fuzzy demand spread over ten years, for five equal planning periods, with a two Production/inventory item and two parallel machine test bed. From the various demand types, several iterations (sub problems) were generated and optimality condition was then verified. To capture the imprecision that is often inherent in the estimated future demand, demand was specified by fuzzy numbers and modeled using the triangular membership function distribution. Centre of gravity defuzzification scheme was used within finite intervals to obtain defuzzified demand. Tora Operations Research software was used to run the model using a test problem. Computational results vindicate the robustness and flexibility of the approach based on the quality of the solutions obtained.

Design of genetic fuzzy system for forward and reverse mapping of green sand mould system

A genetic fuzzy system has been developed to solve the forward and reverse mapping problems of green sand mould systems. The performance of a fuzzy logic (FL) system depends on its knowledge base, which consists of a database and a rule base. A binary coded genetic algorithm (GA) has been used to optimise the knowledge base for the FL based approaches. Two approaches have been developed for each model (i.e. forward and reverse modelling). In the first approach, a manually compiled database and rule base of the FL system are optimised by GA, whereas in the second approach, the GA is used to evolve the optimal FL system automatically. The membership function distributions of the FL system are assumed to be asymmetric triangular. The first approach is found to perform better than the latter in terms of accuracy in prediction of the responses.

Diagnosis of Arthritis Through Fuzzy Inference System

Expert or knowledge-based systems are the most common type of AIM (artificial intelligence in medicine) system in routine clinical use. They contain medical knowledge, usually about a very specifically defined task, and are able to reason with data from individual patients to come up with reasoned conclusion. Although there are many variations, the knowledge within an expert system is typically represented in the form of a set of rules. Arthritis is a chronic disease and about three fourth of the patients are suffering from osteoarthritis and rheumatoid arthritis which are undiagnosed and the delay of detection may cause the severity of the disease at higher risk. Thus, earlier detection of arthritis and treatment of its type of arthritis and related locomotry abnormalities is of vital importance. Thus the work was aimed to design a system for the diagnosis of Arthitis using fuzzy logic controller (FLC) which is, a successful application of Zadeh's fuzzy set theory. It is a potential tool for dealing with uncertainty and imprecision. Thus, the knowledge of a doctor can be modelled using an FLC. The performance of an FLC depends on its knowledge base which consists of a data base and a rule base. It is observed that the performance of an FLC mainly depends on its rule base, and optimizing the membership function distributions stored in the data base is a fine tuning process.

Reinforcement Learning Based Self-Constructing Fuzzy Neural Network Controller for AC Motor Drives

A self-constructing fuzzy neural network (SCFNN) based on reinforcement learning is proposed in this study. In the SCFNN, structure and parameter learning are implemented simultaneously. Structure learning is based on uniform division of the input space and distribution of membership function. The structure and membership parameters are organized as real value chromosomes, and the chromosomes are trained by the reinforcement learning based on genetic algorithm. This paper uses Matlab/Simulink to establish simulation platform and several simulations are provided to demonstrate the effectiveness of the proposed SCFNN control stratagem with the implementation of AC motor speed drive. The simulation results show that the AC drive system with SCFNN has good anti-disturbance performance while the load change randomly.

Forward and reverse mappings of electrical discharge machining process using adaptive network-based fuzzy inference system

Input–output relationships of an electrical discharge machining process have been established both in forward as well as reverse directions using adaptive network-based fuzzy inference system. Three input parameters, such as peak current, pulse-on-time and pulse-duty-factor, and two outputs, namely material removal rate and surface roughness have been considered for the said mappings. A batch mode of training has been adopted with the help of 1000 data for the developed adaptive network-based fuzzy inference system, which has been designed using linear (say triangular) and non-linear (bell-shaped) membership function distributions of the input variables, separately. The performances of the developed models have been tested for both forward and reverse mappings with the help of some test cases collected through the real experiments. Adaptive network-based fuzzy inference system is found to tackle the problems of forward and reverse mappings efficiently. The fuzzy inference system utilizing non-linear membership functions is seen to perform slightly better than that with linear membership functions for the input variables.

A study of drilling performances with minimum quantity of lubricant using fuzzy logic rules

Nowadays the increasing interest to perform machining operations is in dry/near-dry environments. The reason includes health and safety of operator, cost, ease of chip recyclability, etc. However one important process, which is difficult to perform in dry, is drilling. Without coolant, drilling leads to excessive thermal distortion and poor tool life. In order to tackle these conflicting requirements, the essentiality of study on machining performances with minimum quantity lubricant (MQL) becomes important. Fuzzy logic rules, which are derived based on fuzzy set theory, are used to develop fuzzy rule based model (FRBM). The performance of FRBM depends on two different aspects: structures of fuzzy rules and the associated fuzzy sets (membership function distributions, MFDs). The aim of this study is to investigate the performances of FRBMs based on Mamdani and TSK-types of fuzzy logic rules with different shapes of MFDs for prediction and performance analysis of machining with MQL in drilling of aluminum alloy. A comparison of the model predictions with experimental results and those published in the literature shows that FRBM with TSK-type fuzzy rules describes excellent trade-off with experimental measurements.

MULTI-CHANNEL FUZZY QUEUING SYSTEMS AND MEMBERSHIP FUNCTIONS OF RELATED FUZZY SERVICES AND FUZZY INTER-ARRIVAL TIMES

Queuing models need well defined knowledge on arrivals and service times. However, in real applications, because of some measurement errors or some loss of information, it is hard to achieve deterministic knowledge. Non-deterministic knowledge interferes or complicates analysis of the queuing model. Additionally, when the customers are asked about their impressions on waiting times or service times, mostly the answers are linguistic expressions like "I waited too much", "service was fast", and that the responses are. Linguistic statements and ill defined data make the sense of imprecision in the model. In this study, arrivals and service times are defined as fuzzy numbers in order to represent this imprecision. Fuzzy multi-channel queuing systems and membership functions are introduced in defining the arrivals and service times. Besides, a new membership function based on a probability function is studied. Fuzzy queuing characteristics are calculated via different membership functions and the results are compared on simulations. Among models it is found that, Generalized Beta Distribution membership function is the one that minimized the queuing characteristics.

TSK-type FLC using a combined LR and GA: Surface roughness prediction in ultraprecision turning

Due to non-linearity of the cutting parameters, tool–work combination and rigidity of machine tool, it has been proved that a fuzzy logic concept gives a better way to model a complex manufacturing process, such as grinding, ultraprecision turning, etc. In this paper, an Takagi–Sugeno–Kang (TSK)-type fuzzy logic controller (FLC) is designed to model the input–output relationship of ultraprecision turning. The performance of an FLC primarily depends on its knowledge base, which consists of rule base and the membership function distributions (fuzzy subsets) considered for the variables. In TSK-type fuzzy system, the output of a fuzzy rule is a linear combination of the input variables, which is characterized by function coefficients and the variable's exponential parameters. In the present work, two approaches are considered to design the TSK-type FLC: one is based on linear regression (LR) method with constant and same exponential parameters for all the rule, and the other is based on LR with simultaneous optimization of exponential parameter using genetic algorithm (GA). The results of the proposed approaches are compared with the empirical expression, which is not accurate, as well as real experimental data to predict surface roughness in ultraprecision turning.

Study of using ANFIS to the prediction in the bore-expanding process

This paper develops a forward model and inverse model for the adaptive network fuzzy inference system (ANFIS) to the prediction in the sheet bore-expanding process. After using the dynamic finite element method to establish the basic database under various working conditions, an efficient rule database and optimal distribution of membership function will be constructed from the hybrid-learning algorithm of ANFIS. As a verification of this system, the deformed circle hole diameter D is compared between ANFIS, FEM, and experimental results. In the forward model, it is proved that ANFIS can efficiently predict the deformed circle hole diameter D successfully from the database constructed by punch radius RP, die radius RD, and initial circle hole diameter D0. In the inverse model, the initial circle hole diameter D0 is predicted to obtain a desired target deformed circle hole diameter D after forming. From this forward and inverse investigation, the ANFIS is proved to supply a useful optimal soft computing approach in the forming category .

Automatic design of fuzzy logic controller using a genetic algorithm—to predict power requirement and surface finish in grinding

We have developed a method for automatic design of fuzzy logic controller (FLC) using a genetic algorithm (GA). The performance of an FLC depends on its knowledge base (KB), which consists of membership function distributions (also known as data base) and rule base. To design a proper KB of the FLC, the designer should have a thorough knowledge of the process to be controlled. Sometimes, it becomes difficult to gather knowledge of the process beforehand. Thus, designing the proper KB of an FLC is not an easy task. In this paper, a new approach for designing the KB of an FLC (using a GA) is proposed and its effectiveness is compared to a previous approach based on GA-fuzzy combination for making predictions of power requirement and surface finish in grinding (a machining process to obtain smooth surface on the work).

Design of a genetic-fuzzy system to predict surface finish and power requirement in grinding

We have developed, in this paper, a genetic-fuzzy system, in which a genetic algorithm (GA) is used to improve the performance of a fuzzy logic controller (FLC). The performance of an FLC depends on its knowledge base (KB), which consists of both the data base (membership function distributions of the variables) as well as rule base. In the developed genetic-fuzzy system, the KB of the FLC is optimized, off-line, using a GA. Three approaches are developed, in the present work. In the first approach, the membership function distributions of the variables are assumed to be triangular, whereas a second-order polynomial function and a third-order polynomial function are used in the second and third approaches, respectively. The results of these approaches are compared for making prediction of surface finish and power requirement in grinding, a machining process used to generate smooth surface on the job. For some of the test cases, comparisons are also made of the results predicted by the genetic-fuzzy system with those obtained through the real experiments.

Study of ductile fracture and preform design of upsetting process using adaptive network fuzzy inference system

This paper combines adaptive-network-based inference system (ANFIS) and elasto-plastic finite element to predict the ductile fracture initiation and the preform shape of the upsetting process. From the hybrid-learning algorithm in ANFIS, it can efficiently construct rule database and optimal distribution of membership function to solve the punch stroke which causes the ductile fracture, and the preform shape which results a desired cylindrical workpiece after forming in the upsetting process. As a verification of this system, the punch stroke for ductile fracture initiation and the free boundary radius of the billet after forming are compared between ANFIS and FEM simulated results. In the ductile fracture prediction, it is proved that ANFIS can efficiently predict the ductile fracture initiation successfully for arbitrary friction coefficient and aspect ratio. In the preform shape prediction, the simulated cylindrical radius shows good coincidence with the desired radius after forming. From this forward and inverse investigation, the ANFIS is proved to supply a useful optimal soft computing approach in the forming category.

분리된 비선형 시스템의 적응 퍼지 슬라이딩모드 제어

We proposed a decoupled adaptive fuzzy sliding-mode control scheme for a class of fourth-order nonlinear systems. The system is decoupled into two second-order systems such that each subsystem has a separate control target expressed in terms of sliding surface. For these sliding surfaces, we define main and sub target conditions. and, we made intermediate variables which are interconnected both surface conditions from the sub target sliding surface. Then, Two sets of fuzzy rule bases are utilized to represent the equivalent control input with unknown system functions of the main target sliding surface including intermediate variables. The membership functions of the THEN-part, which is used to construct a suitable equivalent control of sliding-mode control, are changed according to the adaptive law. With such a design scheme, we not only maintain the distribution of membership functions over state space but also reduce the computing time considerably. We apply the decoupled adaptive sliding-mode control to a nonlinear Cart-Pole system and confirms the validity of the proposed approach.

Construction of a fuzzy controller through width adaptation

In this paper, a design scheme for the fuzzy controller through width adaptation of the universe of discourse is presented. The proposed adaptation law, which results from the direct adaptive approach, is used to appropriately determine the width of the output variable, and the result of the membership functions in the THEN part will vary with the width adaptation. The main advantage of the proposed method is that the structure of the fuzzy controller does not need to be changed while using a common design procedure. We know that it is not easy to characterize the linguistic control rules and its membership function distribution without expert knowledge, especially in those cases when the input variables of the fuzzy controller are increased. In this study, we first organize a fuzzy controller without any specific experience of the controlled system. An adaptive law is then used to tune the width of the universe of discourse in the THEN part to appropriately determine each membership function's distribution. Finally, a nonlinear system simulation example is applied to verify the effectiveness of the proposed fuzzy controller.

Identification of fuzzy models with the aid of evolutionary data granulation

The identification of fuzzy rule-based systems is considered. By their nature, these fuzzy models are geared toward capturing relationships between information granules — fuzzy sets. The level of granularity of fuzzy sets helps establish a required level of detail that is of interest in the given modelling environment. The form of the information granules themselves (in particular their distribution and type of membership functions) becomes an important design feature of the fuzzy model, contributing to its structural as well as parametric optimisation. This, in turn, calls for a comprehensive and efficient framework of information (data) granulation, and the one introduced in the study involves a hard C-means (HCM) clustering method and genetic algorithms (GAs). HCM produces an initial collection of information granules (clusters) that are afterwards refined in a parametric way with the aid of a genetic algorithm. The rules of the fuzzy model assume the form `if x1 is A and x2 is B and · · · and xn is W then y=phis(x1 , x2 ,…, xn , param) and come in two forms: a simplified one that involves conclusions that are fixed numeric values (that is, phis is a constant function), and a linear one where the conclusion part (phis) is viewed as a linear function of inputs. The parameters of the rules are optimised through a standard method of linear regression (least square error method). An aggregate objective function with weighting factor used in this study helps maintain a balance between the performance of the model for training and testing data. The proposed identification framework is illustrated with the use of two representative numerical examples.

Fuzzy control of nonlinear systems using rule adjustment

A fuzzy controller design using linguistic control rule adjustment is proposed. The proposed adaptive law, which results from the direct adaptive approach, is used to indirectly regulate the output fuzzy variables in the fuzzy controller according to the prelabelled rules. The main advantage of the proposed method is that the determination of rule selection is formed by an analytical parameter equation with multiple input variables of the fuzzy controller. Practically, it is not easy to characterise the linguistic control rules and their membership function distribution without expert knowledge, especially in those cases when the input state variables of the fuzzy controller are increased. The rules are first labelled, then an adaptive law is used to tune the injected parameters in the IF-part to appropriately determine each output fuzzy variable under situations of lack of any knowledge of the plant. The derivation result shows that the proposed adaptive fuzzy controller is stable in the Lyapunov sense. Finally, a nonlinear system simulation example is applied to verify the effectiveness and the ability of the proposed fuzzy controller.