Search results for: fuzzy crisp data

Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

Abstract:

This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

Procedia PDF Downloads 238

Authors: Kishore K. Pochampally

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The success of a supply chain heavily relies on the efficiency of the suppliers involved. In this paper, we propose a neural network approach to evaluate the efficiency of a supplier, which is being considered for inclusion in a supply chain, using the available linguistic (fuzzy) data of suppliers that already exist in the supply chain. The approach is carried out in three phases, as follows: In phase one, we identify criteria for evaluation of the supplier of interest. Then, in phase two, we use performance measures of already existing suppliers to construct a neural network that gives weights (importance values) of criteria identified in phase one. Finally, in phase three, we calculate the overall rating of the supplier of interest. The following are the major findings of the research conducted for this paper: (i) linguistic (fuzzy) ratings of suppliers such as 'good', 'bad', etc., can be converted (defuzzified) to numerical ratings (1 – 10 scale) using fuzzy logic so that those ratings can be used for further quantitative analysis; (ii) it is possible to construct and train a multi-level neural network in order to determine the weights of the criteria that are used to evaluate a supplier; and (iii) Borda’s rule can be used to group the weighted ratings and calculate the overall efficiency of the supplier.

Keywords: fuzzy data, neural network, supplier, supply chain

Procedia PDF Downloads 85

Authors: David G. Maxinez, Andrés Ferreyra Ramírez, Liliana Castillo Sánchez, Nancy Adán Mendoza, Carlos Aviles Cruz

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This research describes the use of fuzzy logic in detection, assessment, analysis and evaluation of children with behavioral disorders. It shows how to acquire and analyze ambiguous, vague and full of uncertainty data coming from the input variables to get an accurate assessment result for each of the typologies presented by children with behavior problems. Behavior disorders analyzed in this paper are: hyperactivity (H), attention deficit with hyperactivity (DAH), conduct disorder (TD) and attention deficit (AD).

Keywords: alteration, behavior, centroid, detection, disorders, economic, fuzzy logic, hyperactivity, impulsivity, social

Procedia PDF Downloads 526

Authors: Mounir Bekaik, Messaoud Ramdani

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We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: Brahim Ferdi, Samira Dib

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The unified power quality conditioner (UPQC), a combination of shunt and series active power filter, is one of the best solutions towards the mitigation of voltage and current harmonics problems in distribution power system. PI controller is very common in the control of UPQC. However, one disadvantage of this conventional controller is the difficulty in tuning its gains (Kp and Ki). To overcome this problem, an adaptive fuzzy logic PI controller is proposed. The controller is composed of fuzzy controller and PI controller. According to the error and error rate of the control system and fuzzy control rules, the fuzzy controller can online adjust the two gains of the PI controller to get better performance of UPQC. Simulations using MATLAB/SIMULINK are carried out to verify the performance of the proposed controller. The results show that the proposed controller has fast dynamic response and high accuracy of tracking the current and voltage references.

Keywords: adaptive fuzzy PI controller, current harmonics, PI controller, voltage harmonics, UPQC

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Jalal Abdulkareem Sultan, Abdulhakeem Luqman Hasan

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With the development of health care systems competition, hospitals face more and more pressures. Meanwhile, resource allocation has a vital effect on achieving competitive advantages in hospitals. Selecting the appropriate number of beds is one of the most important sections in hospital management. However, in real situation, bed allocation selection is a multiple objective problem about different items with vagueness and randomness of the data. It is very complex. Hence, research about bed allocation problem is relatively scarce under considering multiple departments, nursing hours, and stochastic information about arrival and service of patients. In this paper, we develop a fuzzy multiobjective bed allocation model for overcoming uncertainty and multiple departments. Fuzzy objectives and weights are simultaneously applied to help the managers to select the suitable beds about different departments. The proposed model is solved by using Artificial Bee Colony (ABC), which is a very effective algorithm. The paper describes an application of the model, dealing with a public hospital in Iraq. The results related that fuzzy multi-objective model was presented suitable framework for bed allocation and optimum use.

Keywords: bed allocation problem, fuzzy logic, artificial bee colony, multi-objective optimization

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Authors: Tomáš Vyčítal

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In a simulation model of a railway system it is important, besides other crucial algorithms, to have correct behaviour of train overtaking in stochastic conditions. This problem is being addressed in many simulation tools focused on railway traffic, however these are not very human-realistic. The goal of this paper is to create a more human-realistic overtaking decision support system for the use in railway traffic simulations. A fuzzy system has been chosen for this task as fuzzy systems are well-suited for human-like decision making. The fuzzy system designed takes into account timetables, train positions, delays and buffer times as inputs and provides an instruction to overtake or not overtake.

Keywords: decision-making support, fuzzy systems, simulation, railway, transport

Procedia PDF Downloads 104

Authors: Bandreddy Anand Babu, Mandadi Srinivasa Rao, Chintala Pradeep Reddy

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The main theme of this paper is to design fuzzy logic Proportional Integral Derivative controller for controlling of Pulse Width Modulator (PWM) based DCDC buck converter in continuous conduction mode of operation and comparing the results of FPID and ANFIS. Simulation is done to fuzzy the given input variables and membership functions of input values, creating the interference rules linking the input and output variables and after then defuzzfies the output variables. Fuzzy logic is simple for nonlinear models like buck converter. Fuzzy logic based PID controller technique is to control, nonlinear plants like buck converters in switching variables of power electronics. The characteristics of FPID are in terms of rise time, settling time, rise time, steady state errors for different inputs and load disturbances.

Keywords: fuzzy logic, PID controller, DC-DC buck converter, pulse width modulation

Procedia PDF Downloads 974

Authors: Anna Sikharulidze, Gia Sirbiladze

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For the evaluation of unreliability levels of movement on the closed routes in the vehicle routing problem, the fuzzy operators family is constructed. The interactions between routing factors in extreme conditions on the roads are considered. A multi-criteria decision-making model (MCDM) is constructed. Constructed aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are proved. Connections between the operators and the compositions of dual triangular norms are described. The conjugate connections between the constructed operators are shown. Operators reflect interactions among all the combinations of the factors in the fuzzy MCDM process. Several variants of constructed operators are used in the decision-making problem regarding the assessment of unreliability and possibility levels of movement on closed routes.

Keywords: vehicle routing problem, associated probabilities of a fuzzy measure, choquet integral, fuzzy aggregation operator

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Authors: Mafarja Majdi, Salwani Abdullah, Najmeh S. Jaddi

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One of the global combinatorial optimization problems in machine learning is feature selection. It concerned with removing the irrelevant, noisy, and redundant data, along with keeping the original meaning of the original data. Attribute reduction in rough set theory is an important feature selection method. Since attribute reduction is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, we proposed two feature selection mechanisms based on memetic algorithms (MAs) which combine the genetic algorithm with a fuzzy record to record travel algorithm and a fuzzy controlled great deluge algorithm to identify a good balance between local search and genetic search. In order to verify the proposed approaches, numerical experiments are carried out on thirteen datasets. The results show that the MAs approaches are efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.

Keywords: rough set theory, attribute reduction, fuzzy logic, memetic algorithms, record to record algorithm, great deluge algorithm

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Authors: S. Gherbi, F. Bouchareb

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This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: delayed systems, fuzzy immune PID, optimization, Smith predictor

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

Abstract:

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: fuzzy random variables, distance measure, expected value, descriptive parameters

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Authors: Aliasghar Baziar, Hassan Masoumi, Alireza Ale Saadi

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The control of the response of electric motors plays a significant role in the damping of transient responses. In this regard, this paper presents a static VAR compensator (SVC) based on a fuzzy logic which is applied to an industrial power network consisting of three phase synchronous, asynchronous and DC motor loads. The speed and acceleration variations of a specific machine are the inputs of the proposed fuzzy logic controller (FLC). In order to verify the effectiveness and proficiency of the proposed Fuzzy Logic based SVC (FLSVC), several non-linear time-domain digital simulation tests are performed. The proposed fuzzy model can properly control the response of electric motors. The results show that the FLSVC is successful to improve the voltage profile significantly over a wide range of operating conditions and disturbances thus improving the overall dynamic performance of the network.

Keywords: fuzzy logic controller, VAR compensator, single cage asynchronous motor, DC motor

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Authors: U. Chattaraj, D. Meena

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Growth of traffic brings various negative effects, such as road accidents. To avoid such problems, a model is developed for the purpose of highway safety. In such areas, fuzzy logic is the most well-known simulation in the larger field. A model is accomplished for hilly and steep terrain based on Fuzzy Inference System (FIS), for which output is super elevation and input data is horizontal radius, vertical gradient, accident rate (AR). This result shows that the system can be efficaciously applied as for highway safety tool distinguishing hazards components correlated to the characteristics of the highway and has a great influence to the making of decision for accident precaution in transportation models. From this model, a positive relationship between geometric elements, accident rate, and super elevation is also identified.

Keywords: accident rate, fuzzy inference system, fuzzy logic, gradient, radius, super elevation

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Authors: Hajara Abdulkarim Aliyu, Abdulbasid Ismail Isa

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This research paper studies electrohydraulic system for its role in position and motion control system and develops as mathematical model describing the behaviour of the system. The research further proposes Fuzzy logic and conventional PID controllers in order to achieve both accurate positioning of the payload and overall improvement of the system performance. The simulation result shows Fuzzy logic controller has a superior tracking performance and high disturbance rejection efficiency for its shorter settling time, less overshoot, smaller values of integral of absolute and deviation errors over the conventional PID controller at all the testing conditions.

Keywords: electrohydraulic, fuzzy logic, modelling, NZ-PID

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Zeynep Sener, Mehtap Dursun

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Supplier evaluation and selection is one of the most important components of an effective supply chain management system. Due to the expanding competition in healthcare, selecting the right medical device suppliers offers great potential for increasing quality while decreasing costs. This paper proposes a fuzzy decision making approach for medical supplier selection. A real-world medical device supplier selection problem is presented to illustrate the application of the proposed decision methodology.

Keywords: fuzzy decision making, fuzzy multiple objective programming, medical supply chain, supplier selection

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Authors: Syed Talib Abbas Raza, Tahseen Ahmed Jilani, Saleem Abdullah

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This paper presents interval-valued intuitionistic fuzzy soft sets based TOPSIS method for group decision making. The interval-valued intuitionistic fuzzy soft set is a mutation of an interval-valued intuitionistic fuzzy set and soft set. In group decision making problems IVIFSS makes the process much more algebraically elegant. We have used weighted arithmetic averaging operator for aggregating the information and define a new Hybrid Score Function as metric tool for comparison between interval-valued intuitionistic fuzzy values. In an illustrative example we have applied the developed method to a criminological problem. We have developed a group decision making model for integrating the imprecise and hesitant evaluations of multiple law enforcement agencies working on target killing cases in the country.

Keywords: group decision making, interval-valued intuitionistic fuzzy soft set, TOPSIS, score function, criminology

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Authors: Azam Salimi, Majid Delshad

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This paper presents a modified design of a sliding mode controller based on fuzzy logic for a New ZVThigh step up DC-DC Converter . Here a proportional - integral (PI)-type current mode control is employed and a sliding mode controller is designed utilizing fuzzy algorithm. Sliding mode controller guarantees robustness against all variations and fuzzy logic helps to reduce chattering phenomenon due to sliding controller, in that way efficiency increases and error, voltage and current ripples decreases. The proposed system is simulated using MATLAB / SIMULINK. This model is tested under variations of input and reference voltages and it was found that in comparison with conventional sliding mode controllers they perform better.

Keywords: switching mode power supplies, DC-DC converters, sliding mode control, robustness, fuzzy control, current mode control, non-linear behavior

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Authors: Javeria Arain, Saad Malik

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The management of solid waste is a crucial and essential aspect of urban environmental management especially in a city with an ever increasing population such as Karachi. The total amount of municipal solid waste generated from Gulshan e Iqbal town on average is 444.48 tons per day and landfill sites are a widely accepted solution for final disposal of this waste. However, an improperly selected site can have immense environmental, economical and ecological impacts. To select an appropriate landfill site a number of factors should be kept into consideration to minimize the potential hazards of solid waste. The purpose of this research is to analyse the study area for the construction of an appropriate landfill site for disposal of municipal solid waste generated from Gulshan e-Iqbal Town by using geospatial techniques considering hydrological, geological, social and geomorphological factors. This was achieved using analytical hierarchy process and fuzzy analysis as a decision support tool with integration of geographic information sciences techniques. Eight most critical parameters, relevant to the study area, were selected. After generation of thematic layers for each parameter, overlay analysis was performed in ArcGIS 10.0 software. The results produced by both methods were then compared with each other and the final suitability map using AHP shows that 19% of the total area is Least Suitable, 6% is Suitable but avoided, 46% is Moderately Suitable, 26% is Suitable, 2% is Most Suitable and 1% is Restricted. In comparison the output map of fuzzy set theory is not in crisp logic rather it provides an output map with a range of 0-1, where 0 indicates least suitable and 1 indicates most suitable site. Considering the results it is deduced that the northern part of the city is appropriate for constructing the landfill site though a final decision for an optimal site could be made after field survey and considering economical and political factors.

Keywords: Analytical Hierarchy Process (AHP), fuzzy set theory, Geographic Information Sciences (GIS), Multi-Criteria Decision Analysis (MCDA)

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Authors: Pin-Ju Juan, Peng-Yu Juan, Yi-Shan Chen

Abstract:

The main purpose of this paper is to present a fuzzy Analytic Network Process (ANP) model for the hostel organizational performance selection. In this article, we created 39 criteria for selecting hostel organizational performance acquired from literature's review and experts method practical investigations, and the methods of fuzzy analytic network process are used to consolidate decision-makers’ assessments about criteria weightings. Finally, we selected organizational performance of a hostel in Taiwan to determine the effectiveness of the proposed evaluation model in this paper.

Keywords: Fuzzy ANP, hostel, organizational performance, strategy management

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Authors: Roland Lachmayer, Mahtab Afsari

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Research is the cornerstone for advancement of human communities. So that it is one of the indexes for evaluating advancement of countries. Research projects are usually cost and time-consuming and do not end in result in short term. Project scheduling is one of the integral parts of project management. The present article offers a new method by using C# and Matlab software to solve Fuzzy GERT networks for Exclusive-OR kind of nodes to schedule the network. In this article we concentrate on flowcharts that we used in Matlab to show how we apply Matlab to schedule Exclusive-OR nodes.

Keywords: research projects, fuzzy GERT, fuzzy CPM, CPM, α-cuts, scheduling

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Authors: Manish Pandey, Gurinderjit Kaur, Meenu Talwar, Sachin Chauhan, Jagbir Gill

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Health-care management systems are a unit of nice connection as a result of the supply a straightforward and fast management of all aspects relating to a patient, not essentially medical. What is more, there are unit additional and additional cases of pathologies during which diagnosing and treatment may be solely allotted by victimization medical imaging techniques. With associate ever-increasing prevalence, medical pictures area unit directly acquired in or regenerate into digital type, for his or her storage additionally as sequent retrieval and process. Data Mining is the process of extracting information from large data sets through using algorithms and Techniques drawn from the field of Statistics, Machine Learning and Data Base Management Systems. Forecasting may be a prediction of what's going to occur within the future, associated it's an unsure method. Owing to the uncertainty, the accuracy of a forecast is as vital because the outcome foretold by foretelling the freelance variables. A forecast management should be wont to establish if the accuracy of the forecast is within satisfactory limits. Fuzzy regression strategies have normally been wont to develop shopper preferences models that correlate the engineering characteristics with shopper preferences relating to a replacement product; the patron preference models offer a platform, wherever by product developers will decide the engineering characteristics so as to satisfy shopper preferences before developing the merchandise. Recent analysis shows that these fuzzy regression strategies area units normally will not to model client preferences. We tend to propose a Testing the strength of Exponential Regression Model over regression toward the mean Model.

Keywords: health-care management systems, fuzzy regression, data mining, forecasting, fuzzy membership function

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Authors: M. Bouferhane, A. Boukhebza, L. Hatab

Abstract:

In this paper, the position control of linear induction motor using fuzzy sliding mode controller design is proposed. First, the indirect field oriented control LIM is derived. Then, a designed sliding mode control system with an integral-operation switching surface is investigated, in which a simple adaptive algorithm is utilized for generalised soft-switching parameter. Finally, a fuzzy sliding mode controller is derived to compensate the uncertainties which occur in the control, in which the fuzzy logic system is used to dynamically control parameter settings of the SMC control law. The effectiveness of the proposed control scheme is verified by numerical simulation. The experimental results of the proposed scheme have presented good performances compared to the conventional sliding mode controller.

Keywords: linear induction motor, vector control, backstepping, fuzzy-sliding mode control

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Authors: Ruchi Makani, B. V. R. Reddy

Abstract:

Mobile Adhoc Networks (MANETs) are gaining popularity due to their potential of providing low-cost mobile connectivity solutions to real-world communication problems. Integrating Intrusion Detection Systems (IDS) in MANETs is a tedious task by reason of its distinctive features such as dynamic topology, de-centralized authority and highly controlled/limited resource environment. IDS primarily use automated soft-computing techniques to monitor the inflow/outflow of traffic packets in a given network to detect intrusion. Use of machine learning techniques in IDS enables system to make decisions on intrusion while continuous keep learning about their dynamic environment. An appropriate IDS model is essential to be selected to expedite this application challenges. Thus, this paper focused on fuzzy-logic based machine learning IDS technique for MANETs and presented their applicability for achieving effectiveness in identifying the intrusions. Further, the selection of appropriate protocol attributes and fuzzy rules generation plays significant role for accuracy of the fuzzy-logic based IDS, have been discussed. This paper also presents the critical attributes of MANET’s routing protocol and its applicability in fuzzy logic based IDS.

Keywords: AODV, mobile adhoc networks, intrusion detection, anomaly detection, fuzzy logic, fuzzy membership function, fuzzy inference system

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Authors: Jui-Chen Huang, Shou-Hsiung Cheng

Abstract:

This study examined their willingness to use telecare for people who have had experience falling in the last three months in Taiwan. This study adopted convenience sampling and a structural questionnaire to collect data. It was based on the definition and the constructs related to the Health Belief Model (HBM). HBM is comprised of seven constructs: perceived benefits (PBs), perceived disease threat (PDT), perceived barriers of taking action (PBTA), external cues to action (ECUE), internal cues to action (ICUE), attitude toward using (ATT), and behavioral intention to use (BI). This study adopted Fuzzy Neural Network (FNN) to put forward an effective method. It shows the dependence of ATT on PB, PDT, PBTA, ECUE, and ICUE. The training and testing data RMSE (root mean square error) are 0.028 and 0.166 in the FNN, respectively. The training and testing data RMSE are 0.828 and 0.578 in the regression model, respectively. On the other hand, as to the dependence of ATT on BI, as presented in the FNN, the training and testing data RMSE are 0.050 and 0.109, respectively. The training and testing data RMSE are 0.529 and 0.571 in the regression model, respectively. The results show that the FNN method is better than the regression analysis. It is an effective and viable good way.

Keywords: fall, fuzzy neural network, health belief model, telecare, willingness

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Authors: Rosy Joseph

Abstract:

From an algebraic point of view, Semirings provide the most natural generalization of group theory and ring theory. In the absence of additive inverse in a semiring, one had to impose a weaker condition on the semiring, i.e., the additive cancellative law to study interesting structural properties. In many practical situations, fuzzy numbers are used to model imprecise observations derived from uncertain measurements or linguistic assessments. In this connection, a special class of fuzzy numbers whose shape is symmetric with respect to a vertical line called the symmetric fuzzy numbers i.e., for α ∈ (0, 1] the α − cuts will have a constant mid-point and the upper end of the interval will be a non-increasing function of α, the lower end will be the image of this function, is suitable. Based on this description, arithmetic operations and a ranking technique to order the symmetric fuzzy numbers were dealt with in detail. Wherein it was observed that the structure of the class of symmetric fuzzy numbers forms a commutative semigroup with cancellative property. Also, it forms a multiplicative monoid satisfying sub-distributive property.In this paper, we introduce the algebraic structure, sub-distributive semiring and discuss its various properties viz., ideals and prime ideals of sub-distributive semiring, sub-distributive ring of difference etc. in detail. Symmetric fuzzy numbers are visualized as an illustration.

Keywords: semirings, subdistributive ring of difference, subdistributive semiring, symmetric fuzzy numbers

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Authors: František Včelař, Zuzana Pátíková

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Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity

Procedia PDF Downloads 255