Search results for: fuzzy functions

Authors: Saroj Kumar Pradhan, Dayal Ramakrushna Parhi, Anup Kumar Panda

Abstract:

This paper deals with motion planning of multiple mobile robots. Mobile robots working together to achieve several objectives have many advantages over single robot system. However, the planning and coordination between the mobile robots is extremely difficult. In the present investigation rule-based and rulebased- neuro-fuzzy techniques are analyzed for multiple mobile robots navigation in an unknown or partially known environment. The final aims of the robots are to reach some pre-defined goals. Based upon a reference motion, direction; distances between the robots and obstacles; and distances between the robots and targets; different types of rules are taken heuristically and refined later to find the steering angle. The control system combines a repelling influence related to the distance between robots and nearby obstacles and with an attracting influence between the robots and targets. Then a hybrid rule-based-neuro-fuzzy technique is analysed to find the steering angle of the robots. Simulation results show that the proposed rulebased- neuro-fuzzy technique can improve navigation performance in complex and unknown environments compared to this simple rulebased technique.

Keywords: Mobile robots, Navigation, Neuro-fuzzy, Obstacle avoidance, Rule-based, Target seeking

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Authors: S. Wiriyarattanakun, A. Ruengsiriwatanakun, S. Noimanee

Abstract:

The drainage Estimating is an important factor in dam management. In this paper, we use fuzzy support vector regression (FSVR) to predict the drainage of the Sirikrit Dam at Uttaradit province, Thailand. The results show that the FSVR is a suitable method in drainage estimating.

Keywords: Drainage Estimation, Prediction.

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Authors: Robert O. Abolade, Olumide O. Ajayi, Zacheaus K. Adeyemo, Solomon A. Adeniran

Abstract:

Link adaptation is an important strategy for achieving robust wireless multimedia communications based on quality of service (QoS) demand. Scheme switching in multiple-input multiple-output (MIMO) systems is an aspect of link adaptation, and it involves selecting among different MIMO transmission schemes or modes so as to adapt to the varying radio channel conditions for the purpose of achieving QoS delivery. However, finding the most appropriate switching method in MIMO links is still a challenge as existing methods are either computationally complex or not always accurate. This paper presents an intelligent switching method for the MIMO system consisting of two schemes - transmit diversity (TD) and spatial multiplexing (SM) - using fuzzy logic technique. In this method, two channel quality indicators (CQI) namely average received signal-to-noise ratio (RSNR) and received signal strength indicator (RSSI) are measured and are passed as inputs to the fuzzy logic system which then gives a decision – an inference. The switching decision of the fuzzy logic system is fed back to the transmitter to switch between the TD and SM schemes. Simulation results show that the proposed fuzzy logic – based switching technique outperforms conventional static switching technique in terms of bit error rate and spectral efficiency.

Keywords: Channel quality indicator, fuzzy logic, link adaptation, MIMO, spatial multiplexing, transmit diversity.

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Authors: Shirong Li, Huan Yan

Abstract:

To help the client to select a competent agent construction enterprise (ACE), this study aims to investigate the selection standards by using the Fuzzy Analytic Hierarchy Process (FAHP) and build an evaluation mathematical model with Grey Relational Analysis (GRA). According to the outputs of literature review, four orderly levels are established within the model, taking the consideration of various agent construction models in practice. Then, the process of applying FAHP and GRA is discussed in detailed. Finally, through a case study, this paper illustrates how to apply these methods in getting the weights of each standard and the final assessment result.

Keywords: agent construction enterprise, agent constructionmodel, fuzzy analytic hierarchy process, grey relational analysis

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Authors: H. Iranmanesh, S. Nazari Shirkouhi, M. R. Skandari

Abstract:

Information Technology (IT) projects are always accompanied by various risks and because of high rate of failure in such projects, managing risks in order to neutralize or at least decrease their effects on the success of the project is strongly essential. In this paper, fuzzy analytical hierarchy process (FAHP) is exploited as a means of risk evaluation methodology to prioritize and organize risk factors faced in IT projects. A real case of IT projects, a project of design and implementation of an integrated information system in a vehicle producing company in Iran is studied. Related risk factors are identified and then expert qualitative judgments about these factors are acquired. Translating these judgments to fuzzy numbers and using them as an input to FAHP, risk factors are then ranked and prioritized by FAHP in order to make project managers aware of more important risks and enable them to adopt suitable measures to deal with these highly devastative risks.

Keywords: Information technology projects, Risk evaluation, Analytic hierarchal process, fuzzy logic.

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Authors: Peyman Naderi, Ali Farhadi, S. Mohammad Taghi Bathaee

Abstract:

One of the best ways for achievement of conventional vehicle changing to hybrid case is trustworthy simulation result and using of driving realities. For this object, in this paper, at first sevendegree- of-freedom dynamical model of vehicle will be shown. Then by using of statically model of engine, gear box, clutch, differential, electrical machine and battery, the hybrid automobile modeling will be down and forward simulation of vehicle for pedals to wheels power transformation will be obtained. Then by design of a fuzzy controller and using the proper rule base, fuel economy and regenerative braking will be marked. Finally a series of MATLAB/SIMULINK simulation results will be proved the effectiveness of proposed structure.

Keywords: Hybrid, Driving, Fuzzy, Regeneration.

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Authors: Om Prakash Verma, Rajesh Singla, Rajesh Kumar

Abstract:

Conventional controller’s usually required a prior knowledge of mathematical modelling of the process. The inaccuracy of mathematical modelling degrades the performance of the process, especially for non-linear and complex control problem. The process used is Water-Bath system, which is most widely used and nonlinear to some extent. For Water-Bath system, it is necessary to attain desired temperature within a specified period of time to avoid the overshoot and absolute error, with better temperature tracking capability, else the process is disturbed.

To overcome above difficulties intelligent controllers, Fuzzy Logic (FL) and Adaptive Neuro-Fuzzy Inference System (ANFIS), are proposed in this paper. The Fuzzy controller is designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. To design ANFIS, Fuzzy-Inference-System is combined with learning capability of Neural-Network.

It is analyzed that ANFIS is best suitable for adaptive temperature control of above system. As compared to PID and FLC, ANFIS produces a stable control signal. It has much better temperature tracking capability with almost zero overshoot and minimum absolute error.

Keywords: PID Controller, FLC, ANFIS, Non-Linear Control System, Water-Bath System, MATLAB-7.

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Authors: M. Hassani, Y. Hassani, N. Ajudanioskooei, N. N. Benvid

Abstract:

Laser Forming process as a non-contact thermal forming process is widely used to forming and bending of metallic and non-metallic sheets. In this process, according to laser irradiation along a specific path, sheet is bent. One of the most important output parameters in laser forming is bending angle that depends on process parameters such as physical and mechanical properties of materials, laser power, laser travel speed and the number of scan passes. In this paper, Artificial Neural Network and Fuzzy Logic System were used to predict of bending angle in laser forming process. Inputs to these models were laser travel speed and laser power. The comparison between artificial neural network and fuzzy logic models with experimental results has been shown both of these models have high ability to prediction of bending angles with minimum errors.

Keywords: Artificial neural network, bending angle, fuzzy logic, laser forming.

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Authors: K. Kouzi

Abstract:

In order to have stable and high performance of direct torque and flux control (DTFC) of double star induction motor drive (DSIM), proper on-line adaptation of the stator resistance is very important. This is inevitably due to the variation of the stator resistance during operating conditions, which introduces error in estimated flux position and the magnitude of the stator flux. Error in the estimated stator flux deteriorates the performance of the DTFC drive. Also, the effect of error in estimation is very important especially at low speed. Due to this, our aim is to overcome the sensitivity of the DTFC to the stator resistance variation by proposing on-line fuzzy estimation stator resistance. The fuzzy estimation method is based on an on-line stator resistance correction through the variations of the stator current estimation error and its variations. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of the suggested algorithm control is to avoid the drive instability that may occur in certain situations and ensure the tracking of the actual stator resistance. The validity of the technique and the improvement of the whole system performance are proved by the results.

Keywords: Direct torque control, dual stator induction motor, fuzzy logic estimation, stator resistance adaptation.

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Authors: Changzhao Li, Juan Zhang

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In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.

Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.

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Authors: Abbas Al-Refaie

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This paper aims at improving the performance of the tableting process using statistical quality control and fuzzy goal programming. The tableting process was studied. Statistical control tools were used to characterize the existing process for three critical responses including the averages of a tablet’s weight, hardness, and thickness. At initial process factor settings, the estimated process capability index values for the tablet’s averages of weight, hardness, and thickness were 0.58, 3.36, and 0.88, respectively. The L₉ array was utilized to provide experimentation design. Fuzzy goal programming was then employed to find the combination of optimal factor settings. Optimization results showed that the process capability index values for a tablet’s averages of weight, hardness, and thickness were improved to 1.03, 4.42, and 1.42, respectively. Such improvements resulted in significant savings in quality and production costs.

Keywords: Fuzzy goal programming, control charts, process capability, tablet optimization.

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Authors: Daesung Moon, Woo-Yong Choi, Kiyoung Moon

Abstract:

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

Keywords: Fuzzy vault, fingerprint recognition multiple polynomials.

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Authors: Shreyash Sinai Kunde, Siddhang Tendulkar, Shiv Prakash Gupta, Gaurav Kumar, Suresh Mikkili

Abstract:

One of the major power quality concerns in modern times is the problem of current harmonics. The current harmonics is caused due to the increase in non-linear loads which is largely dominated by power electronics devices. The Shunt active filtering is one of the best solutions for mitigating current harmonics. This paper describes a fuzzy logic controller based (FLC) based three Phase Shunt active Filter to achieve low current harmonic distortion (THD) and Reactive power compensation. The performance of fuzzy logic controller is analysed under both balanced sinusoidal and unbalanced sinusoidal source condition. The above controller serves the purpose of maintaining DC Capacitor Voltage constant. The proposed shunt active filter uses hysteresis current controller for current control of IGBT based PWM inverter. The simulation results of model in Simulink MATLAB reveals satisfying results.

Keywords: Shunt active filter, Current harmonics, Fuzzy logic controller, Hysteresis current controller.

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Authors: Bainian Li, Kongsheng Zhang, Jian Xu

Abstract:

In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method.

Keywords: FCM algorithm, Principal Components Analysis, Clustervalidity

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Authors: J. Mehena, M. C. Adhikary

Abstract:

In this paper, a spatial multiple-kernel fuzzy C-means (SMKFCM) algorithm is introduced for segmentation problem. A linear combination of multiples kernels with spatial information is used in the kernel FCM (KFCM) and the updating rules for the linear coefficients of the composite kernels are derived as well. Fuzzy cmeans (FCM) based techniques have been widely used in medical image segmentation problem due to their simplicity and fast convergence. The proposed SMKFCM algorithm provides us a new flexible vehicle to fuse different pixel information in medical image segmentation and detection of MR images. To evaluate the robustness of the proposed segmentation algorithm in noisy environment, we add noise in medical brain tumor MR images and calculated the success rate and segmentation accuracy. From the experimental results it is clear that the proposed algorithm has better performance than those of other FCM based techniques for noisy medical MR images.

Keywords: Clustering, fuzzy C-means, image segmentation, MR images, multiple kernels.

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Authors: S. Suwannasri, R. Sirovetnukul

Abstract:

The effective machine-job assignment of injection molding machines is very important for industry because it is not only directly affects the quality of the product but also the performance and lifetime of the machine as well. The phase of machine selection was mostly done by professionals or experienced planners, so the possibility of matching a job with an inappropriate machine might occur when it was conducted by an inexperienced person. It could lead to an uneconomical plan and defects. This research aimed to develop a machine selection system for plastic injection machines as a tool to help in decision making of the user. This proposed system could be used both in normal times and in times of emergency. Fuzzy logic principle is applied to deal with uncertainty and mechanical factors in the selection of both quantity and quality criteria. The six criteria were obtained from a plastic manufacturer's case study to construct a system based on fuzzy logic theory using MATLAB. The results showed that the system was able to reduce the defects of Short Shot and Sink Mark to 24.0% and 8.0% and the total defects was reduced around 8.7% per month.

Keywords: Injection molding machine, machine selection, fuzzy logic, defects in injection molding, matlab.

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Ε. Giovanis

Abstract:

In this paper we apply an Adaptive Network-Based Fuzzy Inference System (ANFIS) with one input, the dependent variable with one lag, for the forecasting of four macroeconomic variables of US economy, the Gross Domestic Product, the inflation rate, six monthly treasury bills interest rates and unemployment rate. We compare the forecasting performance of ANFIS with those of the widely used linear autoregressive and nonlinear smoothing transition autoregressive (STAR) models. The results are greatly in favour of ANFIS indicating that is an effective tool for macroeconomic forecasting used in academic research and in research and application by the governmental and other institutions

Keywords: Linear models, Macroeconomics, Neuro-Fuzzy, Non-Linear models

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Authors: Mehdi Tatari

Abstract:

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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Authors: Mohammad Hasan Raouf, Ebrahim Rasooli Anarmarzi, Hamid Lesani, Javad Olamaei

Abstract:

This paper proposes the application of a hierarchical fuzzy system (HFS) based on multi-input power system stabilizer (MPSS) and also Static Var Compensator (SVC) in multi-machine environment.The number of rules grows exponentially with the number of variables in a conventional fuzzy logic system. The proposed HFS method is developed to solve this problem. To reduce the number of rules the HFS consists of a number of low-dimensional fuzzy systems in a hierarchical structure. In fact, by using HFS the total number of involved rules increases only linearly with the number of input variables. In the MPSS, to have better efficiency an auxiliary signal of reactive power deviation (ΔQ) is added with ΔP+ Δω input type Power system stabilizer (PSS). Phasor model of SVC is described and used in this paper. The performances of MPSS, Conventional power system stabilizer (CPSS), hierarchical Fuzzy Multi-input Power System Stabilizer (HFMPSS) and the proposed method in damping inter-area mode of oscillation are examined in response to disturbances. By using digital simulations the comparative study is illustrated. It can be seen that the proposed PSS is performing satisfactorily within the whole range of disturbances.

Keywords: Power system stabilizer (PSS), hierarchical fuzzysystem (HFS), Static VAR compensator (SVC)

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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Authors: Hirofumi Miyajima, Kazuya Kishida, Noritaka Shigei, Hiromi Miyajima

Abstract:

Most of self-tuning fuzzy systems, which are automatically constructed from learning data, are based on the steepest descent method (SDM). However, this approach often requires a large convergence time and gets stuck into a shallow local minimum. One of its solutions is to use fuzzy rule modules with a small number of inputs such as DIRMs (Double-Input Rule Modules) and SIRMs (Single-Input Rule Modules). In this paper, we consider a (generalized) DIRMs model composed of double and single-input rule modules. Further, in order to reduce the redundant modules for the (generalized) DIRMs model, pruning and generative learning algorithms for the model are suggested. In order to show the effectiveness of them, numerical simulations for function approximation, Box-Jenkins and obstacle avoidance problems are performed.

Keywords: Box-Jenkins’s problem, Double-input rule module, Fuzzy inference model, Obstacle avoidance, Single-input rule module.

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Authors: Radim Farana, Bogdan Walek, Michal Janosek, Jaroslav Zacek

Abstract:

This paper presents the advantages of fuzzy control use in technological processes control. The paper presents a real application of the Linguistic Fuzzy-Logic Control, developed at the University of Ostrava for the control of physical models in the Intelligent Systems Laboratory. The paper presents an example of a sensitive non-linear model, such as a magnetic levitation model and obtained results which show how modern information technologies can help to solve actual technical problems. A special method based on the LFLC controller with partial components is presented in this paper followed by the method of automatic context change, which is very helpful to achieve more accurate control results. The main advantage of the used system is its robustness in changing conditions demonstrated by comparing with conventional PID controller. This technology and real models are also used as a background for problem-oriented teaching, realized at the department for master students and their collaborative as well as individual final projects.

Keywords: Control, fuzzy logic, sensitive system, technological proves.

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Authors: Thi T. Nguyen, Lee N. Gordon-Brown

Abstract:

A new deployment of the multiple criteria decision making (MCDM) techniques: the Simple Additive Weighting (SAW), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for portfolio allocation, is demonstrated in this paper. Rather than exclusive reference to mean and variance as in the traditional mean-variance method, the criteria used in this demonstration are the first four moments of the portfolio distribution. Each asset is evaluated based on its marginal impacts to portfolio higher moments that are characterized by trapezoidal fuzzy numbers. Then centroid-based defuzzification is applied to convert fuzzy numbers to the crisp numbers by which SAW and TOPSIS can be deployed. Experimental results suggest the similar efficiency of these MCDM approaches to selecting dominant assets for an optimal portfolio under higher moments. The proposed approaches allow investors flexibly adjust their risk preferences regarding higher moments via different schemes adapting to various (from conservative to risky) kinds of investors. The other significant advantage is that, compared to the mean-variance analysis, the portfolio weights obtained by SAW and TOPSIS are consistently well-diversified.

Keywords: Fuzzy numbers, SAW, TOPSIS, portfolio optimization, higher moments, risk management.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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Authors: Tao Zhao, Xin Wang

Abstract:

With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: G. M. Arun Prasath, N. Arthi

Abstract:

This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.

Keywords: Fuzzy inventory model, warehouse location model, triangular fuzzy number, secondary warehouse, LINGO software.

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Authors: H. Zarei, M. H. Fazel Zarandi, M. Karbasian

Abstract:

A Decision Support System/Expert System for stock portfolio selection presented where at first step, both technical and fundamental data used to estimate technical and fundamental return and risk (1st phase); Then, the estimated values are aggregated with the investor preferences (2nd phase) to produce convenient stock portfolio. In the 1st phase, there are two expert systems, each of which is responsible for technical or fundamental estimation. In the technical expert system, for each stock, twenty seven candidates are identified and with using rough sets-based clustering method (RC) the effective variables have been selected. Next, for each stock two fuzzy rulebases are developed with fuzzy C-Mean method and Takai-Sugeno- Kang (TSK) approach; one for return estimation and the other for risk. Thereafter, the parameters of the rule-bases are tuned with backpropagation method. In parallel, for fundamental expert systems, fuzzy rule-bases have been identified in the form of “IF-THEN" rules through brainstorming with the stock market experts and the input data have been derived from financial statements; as a result two fuzzy rule-bases have been generated for all the stocks, one for return and the other for risk. In the 2nd phase, user preferences represented by four criteria and are obtained by questionnaire. Using an expert system, four estimated values of return and risk have been aggregated with the respective values of user preference. At last, a fuzzy rule base having four rules, treats these values and produce a ranking score for each stock which will lead to a satisfactory portfolio for the user. The stocks of six manufacturing companies and the period of 2003-2006 selected for data gathering.

Keywords: Stock Portfolio Selection, Fuzzy Rule-Base ExpertSystems, Financial Decision Support Systems, Technical Analysis, Fundamental Analysis.

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Authors: C. Selvaraj, K. R. Karthikeyan

Abstract:

We obtain several interesting subordination results for a class of analytic functions defined by using a generalized integral operator.

Keywords: Analytic functions, Hadamard product, Subordinating factor sequence

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Authors: C. Ardil

Abstract:

The decision to select an unmanned combat aircraft is complicated since several options and conflicting criteria must be considered at simultaneously. When making multiple criteria decision, it is important to consider the selected evaluation criteria, including priceability, payloadability, stealthability, speedability , and survivability. The fundamental goal of the study is to select the best unmanned combat aircraft by taking these evaluation criteria into account. The optimal aircraft was chosen using the fuzzy proximity measure method, which enables decision-makers to designate preferences as standard fuzzy set numbers during the multiple criteria decision-making process. To assess the applicability of the proposed approach, a numerical example is provided. Finally, by comparing determined unmanned combat aircraft, the proposed method produced a successful application, and the best aircraft was selected.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), multiple criteria group decision making (MCGDM), proximity measure method (PMM)

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