Search results for: intuitionistic fuzzy cycle

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

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Authors: Drago Jakovčević, Maja Mihelja Žaja

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This paper provides an analysis of the insurance cycle in the Republic of Croatia and whether they are affected by catastrophic losses on a global level. In general, it is considered that insurance cycles are particularly pronounced in periods of financial crisis, but are also affected by the growing number of catastrophic losses. They cause the change of insurance cycle and premium growth and intensification and narrowing of the coverage conditions, so these variables move in the same direction and these phenomena point to a new cycle. The main goal of this paper is to determine the existence of insurance cycle in the Republic of Croatia and investigate whether catastrophic losses have an influence on insurance cycles.

Keywords: catastrophic loss, insurance cycle, premium, Republic of Croatia

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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: 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

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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

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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: 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

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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: Raziyeh Shamsi

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In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

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Authors: Rishabh Srivastav, Divyam Sharma

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We propose an algorithm to cluster categorical data named as ‘Genetic algorithm initialized rough set based fuzzy K-Modes for categorical data’. We propose an amalgamation of the simple K-modes algorithm, the Rough and Fuzzy set based K-modes and the Genetic Algorithm to form a new algorithm,which we hypothesise, will provide better Centroid Model clustering results, than existing standard algorithms. In the proposed algorithm, the initialization and updation of modes is done by the use of genetic algorithms while the membership values are calculated using the rough set and fuzzy logic.

Keywords: categorical data, fuzzy logic, genetic algorithm, K modes clustering, rough sets

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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: Haoshui Yu, Donghoi Kim, Truls Gundersen

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Low-temperature waste heat is abundant in the process industries, and large amounts of Liquefied Natural Gas (LNG) cold energy are discarded without being recovered properly in LNG terminals. Power generation is an effective way to utilize low-temperature waste heat and LNG cold energy simultaneously. Organic Rankine Cycles (ORCs) and CO₂ power cycles are promising technologies to convert low-temperature waste heat and LNG cold energy into electricity. If waste heat and LNG cold energy are utilized simultaneously in one system, the performance may outperform separate systems utilizing low-temperature waste heat and LNG cold energy, respectively. Low-temperature waste heat acts as the heat source and LNG regasification acts as the heat sink in the combined system. Due to the large temperature difference between the heat source and the heat sink, cascaded power cycle configurations are proposed in this paper. Cascaded power cycles can improve the energy efficiency of the system considerably. The cycle operating at a higher temperature to recover waste heat is called top cycle and the cycle operating at a lower temperature to utilize LNG cold energy is called bottom cycle in this study. The top cycle condensation heat is used as the heat source in the bottom cycle. The top cycle can be an ORC, transcritical CO₂ (tCO₂) cycle or supercritical CO₂ (sCO₂) cycle, while the bottom cycle only can be an ORC due to the low-temperature range of the bottom cycle. However, the thermodynamic path of the tCO₂ cycle and sCO₂ cycle are different from that of an ORC. The tCO₂ cycle and the sCO₂ cycle perform better than an ORC for sensible waste heat recovery due to a better temperature match with the waste heat source. Different combinations of the tCO₂ cycle, sCO₂ cycle and ORC are compared to screen the best configurations of the cascaded power cycles. The influence of the working fluid and the operating conditions are also investigated in this study. Each configuration is modeled and optimized in Aspen HYSYS. The results show that cascaded tCO₂/ORC performs better compared with cascaded ORC/ORC and cascaded sCO₂/ORC for the case study.

Keywords: LNG cold energy, low-temperature waste heat, organic Rankine cycle, supercritical CO₂ cycle, transcritical CO₂ cycle

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

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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: John K. Avor, Choong-Koo Chang

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The transfer of electrical loads at power generation stations from Standby Auxiliary Transformer (SAT) to Unit Auxiliary Transformer (UAT) and vice versa is through a fast bus transfer scheme. Fast bus transfer is a time-critical application where the transfer process depends on various parameters, thus transfer schemes apply advance algorithms to ensure power supply reliability and continuity. In a nuclear power generation station, supply continuity is essential, especially for critical class 1E electrical loads. Bus transfers must, therefore, be executed accurately within 4 to 10 cycles in order to achieve safety system requirements. However, the main problem is that there are instances where transfer schemes scrambled due to inaccurate interpretation of key parameters; and consequently, have failed to transfer several critical loads from UAT to the SAT during main generator trip event. Although several techniques have been adopted to develop robust transfer schemes, a combination of Artificial Neural Network and Fuzzy Systems (Neuro-Fuzzy) has not been extensively used. In this paper, we apply the concept of Neuro-Fuzzy to determine plant operating mode and dynamic prediction of the appropriate bus transfer algorithm to be selected based on the first cycle of voltage information. The performance of Sequential Fast Transfer and Residual Bus Transfer schemes was evaluated through simulation and integration of the Neuro-Fuzzy system. The objective for adopting Neuro-Fuzzy approach in the bus transfer scheme is to utilize the signal validation capabilities of artificial neural network, specifically the back-propagation algorithm which is very accurate in learning completely new systems. This research presents a combined effect of artificial neural network and fuzzy systems to accurately interpret key bus transfer parameters such as magnitude of the residual voltage, decay time, and the associated phase angle of the residual voltage in order to determine the possibility of high speed bus transfer for a particular bus and the corresponding transfer algorithm. This demonstrates potential for general applicability to improve reliability of the auxiliary power distribution system. The performance of the scheme is implemented on APR1400 nuclear power plant auxiliary system.

Keywords: auxiliary power system, bus transfer scheme, fuzzy logic, neural networks, reliability

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Authors: Youn-Sung Kim, Mi-Sung Kim, Jae-Kun Lee

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This paper deals with the accelerated life cycle test method of the motor for home appliances that demand high reliability. Life Cycle of parts in home appliances also should be 10 years because life cycle of the home appliances such as washing machine, refrigerator, TV is at least 10 years. In case of washing machine, the life cycle test method of motor is advanced for 3000 cycle test (1cycle = 2hours). However, 3000 cycle test incurs loss for the time and cost. Objectives of this study are to reduce the life cycle test time and the number of test samples, which could be realized by using acceleration factor for the test time and reduction factor for the number of sample.

Keywords: accelerated life cycle test, motor reliability test, motor for washing machine, BLDC motor

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Authors: M. M. M. Jaradat

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For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated.

Keywords: cycle space, minimum cycle basis, basis number, wreath product

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Authors: Nazanin Pilevari, Kamyar Mahmoodi

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The purpose of this research is to provide a model based on fuzzy inference system for evaluating empowerment of Knowledge management. The first prototype of the research was developed based on the study of literature. In the next step, experts were provided with these models and after implementing consensus-based reform, the views of Fuzzy Delphi experts and techniques, components and Index research model were finalized. Culture, structure, IT and leadership were considered as dimensions of empowerment. Then, In order to collect and extract data for fuzzy inference system based on knowledge and Experience, the experts were interviewed. The values obtained from designed fuzzy inference system, made review and assessment of the organization's empowerment of Knowledge management possible. After the design and validation of systems to measure indexes ,empowerment of Knowledge management and inputs into fuzzy inference) in the AYANDEH Bank, a questionnaire was used. In the case of this bank, the system output indicates that the status of empowerment of Knowledge management, culture, organizational structure and leadership are at the moderate level and information technology empowerment are relatively high. Based on these results, the status of knowledge management empowerment in AYANDE Bank, was moderate. Eventually, some suggestions for improving the current situation of banks were provided. According to studies of research history, the use of powerful tools in Fuzzy Inference System for assessment of Knowledge management and knowledge management empowerment such an assessment in the field of banking, are the innovation of this Research.

Keywords: knowledge management, knowledge management empowerment, fuzzy inference system, fuzzy Delphi

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

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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

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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: Joseph C. Chen, Venkata Mohan Kudapa

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Development of two real-time surface roughness (Ra) prediction systems for milling operations was attempted. The systems used not only cutting parameters, such as feed rate and spindle speed, but also the cutting current generated and corrected by a clamp type energy sensor. Two different approaches were developed. First, a fuzzy inference system (FIS), in which the fuzzy logic rules are generated by experts in the milling processes, was used to conduct prediction modeling using current cutting data. Second, a neuro-fuzzy system (ANFIS) was explored. Neuro-fuzzy systems are adaptive techniques in which data are collected on the network, processed, and rules are generated by the system. The inference system then uses these rules to predict Ra as the output. Experimental results showed that the parameters of spindle speed, feed rate, depth of cut, and input current variation could predict Ra. These two systems enable the prediction of Ra during the milling operation with an average of 91.83% and 94.48% accuracy by FIS and ANFIS systems, respectively. Statistically, the ANFIS system provided better prediction accuracy than that of the FIS system.

Keywords: surface roughness, input current, fuzzy logic, neuro-fuzzy, milling operations

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Authors: Jeugert Kujtila, Kristi Hoxhalli, Ramazan Dalipi, Erjon Cota, Ardit Murati, Erind Bedalli

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Clustering is a versatile instrument in the analysis of collections of data providing insights of the underlying structures of the dataset and enhancing the modeling capabilities. The fuzzy approach to the clustering problem increases the flexibility involving the concept of partial memberships (some value in the continuous interval [0, 1]) of the instances in the clusters. Several fuzzy clustering algorithms have been devised like FCM, Gustafson-Kessel, Gath-Geva, kernel-based FCM, PCM etc. Each of these algorithms has its own advantages and drawbacks, so none of these algorithms would be able to perform superiorly in all datasets. In this paper we will experimentally compare FCM, GK, GG algorithm and a hybrid two-stage fuzzy clustering model combining the FCM and Gath-Geva algorithms. Firstly we will theoretically dis-cuss the advantages and drawbacks for each of these algorithms and we will describe the hybrid clustering model exploiting the advantages and diminishing the drawbacks of each algorithm. Secondly we will experimentally compare the accuracy of the hybrid model by applying it on several benchmark and synthetic datasets.

Keywords: fuzzy clustering, fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm, hybrid clustering model

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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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