Search results for: fuzzy peer group filter
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3031

Search results for: fuzzy peer group filter

2911 Tunable Photonic Microwave Bandpass Filter Based on EOPM and VPBS

Authors: R. Heydari, M. R. Salehi

Abstract:

A tunable photonic microwave bandpass filter with negative coefficient based on an electro-optic phase modulator (EOPM) and a variable polarization beamsplitter (VPBS) is demonstrated. A two-tap microwave bandpass filter with one negative coefficient is presented. The chromatic dispersion and optical coherence are not affected on this filter.

Keywords: Bandpass filter, EOPM, photonic microwave filter, polarization beamsplitter.

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2910 Determinate Fuzzy Set Ranking Analysis for Combat Aircraft Selection with Multiple Criteria Group Decision Making

Authors: C. Ardil

Abstract:

Using the aid of Hausdorff distance function and Minkowski distance function, this study proposes a novel method for selecting combat aircraft for Air Force. In order to do this, the proximity measure method was developed with determinate fuzzy degrees based on the relationship between attributes and combat aircraft alternatives. The combat aircraft selection attributes were identified as payloadability, maneuverability, speedability, stealthability, and survivability. Determinate fuzzy data from the combat aircraft attributes was then aggregated using the determinate fuzzy weighted arithmetic average operator. For the selection of combat aircraft, correlation analysis of the ranking order patterns of options was also examined. A numerical example from military aviation is used to demonstrate the applicability and effectiveness of the proposed method.

Keywords: Combat aircraft selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Hausdorff distance function, Minkowski distance function, PMM, MCDM

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2909 An Innovative Fuzzy Decision Making Based Genetic Algorithm

Authors: M. A. Sharbafi, M. Shakiba Herfeh, Caro Lucas, A. Mohammadi Nejad

Abstract:

Several researchers have proposed methods about combination of Genetic Algorithm (GA) and Fuzzy Logic (the use of GA to obtain fuzzy rules and application of fuzzy logic in optimization of GA). In this paper, we suggest a new method in which fuzzy decision making is used to improve the performance of genetic algorithm. In the suggested method, we determine the alleles that enhance the fitness of chromosomes and try to insert them to the next generation. In this algorithm we try to present an innovative vaccination in the process of reproduction in genetic algorithm, with considering the trade off between exploration and exploitation.

Keywords: Genetic Algorithm, Fuzzy Decision Making.

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2908 Dependent Weighted Aggregation Operators of Hesitant Fuzzy Numbers

Authors: Jing Liu

Abstract:

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.

Keywords: Hesitant fuzzy numbers, hesitant fuzzy dependent weighted averaging(HFDWA) operators, hesitant fuzzy dependent weighted geometric(HFDWG) operators.

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2907 Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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2906 A new Configurable Decimation Filter using Pascal-s Triangle Theorem

Authors: A. Chahardah Cherik, E. Farshidi

Abstract:

This paper presents a new configurable decimation filter for sigma-delta modulators. The filter employs the Pascal-s triangle-s theorem for building the coefficients of non-recursive decimation filters. The filter can be connected to the back-end of various modulators with different output accuracy. In this work two methods are shown and then compared from area occupation viewpoint. First method uses the memory and the second one employs Pascal-s triangle-s method, aiming to reduce required gates. XILINX ISE v10 is used for implementation and confirmation the filter.

Keywords: Decimation filter, sigma delta, Pascal's triangle'stheorem, memory

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2905 Sensitizing Rules for Fuzzy Control Charts

Authors: N. Pekin Alakoç, A. Apaydın

Abstract:

Quality control charts indicate out of control conditions if any nonrandom pattern of the points is observed or any point is plotted beyond the control limits. Nonrandom patterns of Shewhart control charts are tested with sensitizing rules. When the processes are defined with fuzzy set theory, traditional sensitizing rules are insufficient for defining all out of control conditions. This is due to the fact that fuzzy numbers increase the number of out of control conditions. The purpose of the study is to develop a set of fuzzy sensitizing rules, which increase the flexibility and sensitivity of fuzzy control charts. Fuzzy sensitizing rules simplify the identification of out of control situations that results in a decrease in the calculation time and number of evaluations in fuzzy control chart approach.

Keywords: Fuzzy set theory, Quality control charts, Run Rules, Unnatural patterns.

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2904 Auto Regressive Tree Modeling for Parametric Optimization in Fuzzy Logic Control System

Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao

Abstract:

The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.

Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.

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2903 A Note on Characterization of Regular Γ-Semigroups in terms of (∈,∈ ∨q)-Fuzzy Bi-ideal

Authors: S.K.Sardar, B.Davvaz, S.Kayal, S.K.Majumdar

Abstract:

The purpose of this note is to obtain some properties of (∈,∈ ∨q)- fuzzy bi-ideals in a Γ-semigroup in order to characterize regular and intra-regular Γ-semigroups.

Keywords: Regular Γ-semigroup, belong to or quasi-coincident, (∈, ∈ ∨q)-fuzzy subsemigroup, (∈, ∈ ∨q)-fuzzy bi-ideals.

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2902 Some Equalities Connected with Fuzzy Soft Matrices

Authors: D. R. Jain

Abstract:

The aim of this paper is to use matrix representation of Fuzzy soft sets for proving some equalities connected with Fuzzy soft sets based on set-operations.

Keywords: Equality, Fuzzy soft matrix, Fuzzy soft sets, operations.

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2901 Fuzzy Shortest Paths Approximation for Solving the Fuzzy Steiner Tree Problem in Graphs

Authors: Miloš Šeda

Abstract:

In this paper, we deal with the Steiner tree problem (STP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. We propose a modification of the shortest paths approximation based on the fuzzy shortest paths (FSP) evaluations. Since a fuzzy min operation using the extension principle leads to nondominated solutions, we propose another approach to solving the FSP using Cheng's centroid point fuzzy ranking method.

Keywords: Steiner tree, single shortest path problem, fuzzyranking, binary heap, priority queue.

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2900 Ranking Fuzzy Numbers Based On Epsilon-Deviation Degree

Authors: Vincent F. Yu, Ha Thi Xuan Chi

Abstract:

Nejad and Mashinchi (2011) proposed a revision for ranking fuzzy numbers based on the areas of the left and the right sides of a fuzzy number. However, this method still has some shortcomings such as lack of discriminative power to rank similar fuzzy numbers and no guarantee the consistency between the ranking of fuzzy numbers and the ranking of their images. To overcome these drawbacks, we propose an epsilon-deviation degree method based on the left area and the right area of a fuzzy number, and the concept of the centroid point. The main advantage of the new approach is the development of an innovative index value which can be used to consistently evaluate and rank fuzzy numbers. Numerical examples are presented to illustrate the efficiency and superiority of the proposed method.

Keywords: Ranking fuzzy numbers, Centroid, Deviation degree.

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2899 Design of Gain Scheduled Fuzzy PID Controller

Authors: Leehter Yao, Chin-Chin Lin

Abstract:

An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.

Keywords: Gain scheduling, fuzzy PID controller, adaptive control, genetic algorithm.

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2898 Intuitionistic Fuzzy Implicative Ideals with Thresholds (λ,μ) of BCI-Algebras

Authors: Qianqian Li, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the notion of intuitionistic fuzzy implicative ideals with thresholds (λ, μ) of BCI-algebras and to investigate its properties and characterizations.

Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy ideal with thresholds (λ, μ), intuitionistic fuzzy implicative ideal with thresholds (λ, μ).

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2897 Takagi-Sugeno Fuzzy Control of Induction Motor

Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss

Abstract:

This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.

Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)

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2896 Design of Two-Channel Quadrature Mirror Filter Banks Using Digital All-Pass Filters

Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

The paper deals with the minimax design of two-channel linear-phase (LP) quadrature mirror filter (QMF) banks using infinite impulse response (IIR) digital all-pass filters (DAFs). Based on the theory of two-channel QMF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired group delay responses of the IIR DAFs and the magnitude response of the low-pass analysis filter. Through a frequency sampling and iterative approximation method, the design problem can be solved by utilizing a weighted least squares approach. The resulting two-channel QMF banks can possess approximately LP response without magnitude distortion. Simulation results are presented for illustration and comparison.

Keywords: Chebyshev approximation, Digital All-Pass Filter, Quadrature Mirror Filter, Weighted Least Squares.

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2895 Prime(Semiprime) Fuzzy h-ideal in Γ-hemiring

Authors: Sujit Kumar Sardar, Debabrata Mandal

Abstract:

The notions of prime(semiprime) fuzzy h-ideal(h-biideal, h-quasi-ideal) in Γ-hemiring are introduced and some of their characterizations are obtained by using "belongingness(∈)" and "quasi - coincidence(q)". Cartesian product of prime(semiprime) fuzzy h-ideals of Γ-hemirings are also investigated.

Keywords: Γ-hemiring, Fuzzy h-ideals, Prime fuzzy left h-ideal, Prime(semiprime) (∈, ∈ ∨q)-fuzzy left h-bi-ideal(h-ideal, h-quasiideal), Cartesian product

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2894 Peer Corrective Feedback on Written Errors in Computer-Mediated Communication

Authors: S. H. J. Liu

Abstract:

This paper aims to explore the role of peer Corrective Feedback (CF) in improving written productions by English-as-a- foreign-language (EFL) learners who work together via Wikispaces. It attempted to determine the effect of peer CF on form accuracy in English, such as grammar and lexis. Thirty-four EFL learners at the tertiary level were randomly assigned into the experimental (with peer feedback) or the control (without peer feedback) group; each group was subdivided into small groups of two or three. This resulted in six and seven small groups in the experimental and control groups, respectively. In the experimental group, each learner played a role as an assessor (providing feedback to others), as well as an assessee (receiving feedback from others). Each participant was asked to compose his/her written work and revise it based on the feedback. In the control group, on the other hand, learners neither provided nor received feedback but composed and revised their written work on their own. Data collected from learners’ compositions and post-task interviews were analyzed and reported in this study. Following the completeness of three writing tasks, 10 participants were selected and interviewed individually regarding their perception of collaborative learning in the Computer-Mediated Communication (CMC) environment. Language aspects to be analyzed included lexis (e.g., appropriate use of words), verb tenses (e.g., present and past simple), prepositions (e.g., in, on, and between), nouns, and articles (e.g., a/an). Feedback types consisted of CF, affective, suggestive, and didactic. Frequencies of feedback types and the accuracy of the language aspects were calculated. The results first suggested that accurate items were found more in the experimental group than in the control group. Such results entail that those who worked collaboratively outperformed those who worked non-collaboratively on the accuracy of linguistic aspects. Furthermore, the first type of CF (e.g., corrections directly related to linguistic errors) was found to be the most frequently employed type, whereas affective and didactic were the least used by the experimental group. The results further indicated that most participants perceived that peer CF was helpful in improving the language accuracy, and they demonstrated a favorable attitude toward working with others in the CMC environment. Moreover, some participants stated that when they provided feedback to their peers, they tended to pay attention to linguistic errors in their peers’ work but overlook their own errors (e.g., past simple tense) when writing. Finally, L2 or FL teachers or practitioners are encouraged to employ CMC technologies to train their students to give each other feedback in writing to improve the accuracy of the language and to motivate them to attend to the language system.

Keywords: Peer corrective feedback, computer-mediated communication, second or foreign language learning, Wikispaces.

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2893 Adaptive Notch Filter for Harmonic Current Mitigation

Authors: T. Messikh, S. Mekhilef, N. A. Rahim

Abstract:

This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.

Keywords: Adaptive notch filter, Active power filter, harmonic filtering, Time varying frequency.

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2892 On the Fuzzy Difference Equation xn+1 = A +

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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2891 Thermal Properties of Chitosan-Filled Empty Fruit Bunches Filter Media

Authors: Aziatul Niza Sadikin, Norasikin Othman, Mohd Ghazali Mohd Nawawi, Umi Aisah Asli, Roshafima Rasit Ali, Rafiziana Md Kasmani

Abstract:

Non-woven fibrous filter media from empty fruit bunches were fabricated by using chitosan as a binder. Chitosan powder was dissolved in a 1 wt% aqueous acetic acid, and 1 wt% to 4 wt% of chitosan solutions was prepared. Chitosan-filled empty fruit bunches filter media have been prepared via wet-layup method. Thermogravimetric analysis (TGA) was performed to study various thermal properties of the fibrous filter media. It was found that the fibrous filter media have undergone several decomposition stages over a range of temperatures as revealed by TGA thermo-grams, where the temperature for 10% weight loss for chitosan-filled EFB filter media and binder-less filter media was at 150oC and 300oC, respectively.

Keywords: Empty fruit bunches, chitosan, filter media, thermal property.

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2890 Analysis of Complex Quadrature Mirror Filter Banks

Authors: Chimin Tsai

Abstract:

This work consists of three parts. First, the alias-free condition for the conventional two-channel quadrature mirror filter bank is analyzed using complex arithmetic. Second, the approach developed in the first part is applied to the complex quadrature mirror filter bank. Accordingly, the structure is simplified and the theory is easier to follow. Finally, a new class of complex quadrature mirror filter banks is proposed. Interesting properties of this new structure are also discussed.

Keywords: Aliasing cancellation, complex signal processing, polyphase realization, quadrature mirror filter banks.

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2889 Color Image Segmentation Using SVM Pixel Classification Image

Authors: K. Sakthivel, R. Nallusamy, C. Kavitha

Abstract:

The goal of image segmentation is to cluster pixels into salient image regions. Segmentation could be used for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing, or image database lookup. In this paper, we present a color image segmentation using support vector machine (SVM) pixel classification. Firstly, the pixel level color and texture features of the image are extracted and they are used as input to the SVM classifier. These features are extracted using the homogeneity model and Gabor Filter. With the extracted pixel level features, the SVM Classifier is trained by using FCM (Fuzzy C-Means).The image segmentation takes the advantage of both the pixel level information of the image and also the ability of the SVM Classifier. The Experiments show that the proposed method has a very good segmentation result and a better efficiency, increases the quality of the image segmentation compared with the other segmentation methods proposed in the literature.

Keywords: Image Segmentation, Support Vector Machine, Fuzzy C–Means, Pixel Feature, Texture Feature, Homogeneity model, Gabor Filter.

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2888 Comparative Study of Some Adaptive Fuzzy Algorithms for Manipulator Control

Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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2887 On Weakly Prime and Weakly Quasi-Prime Fuzzy Left Ideals in Ordered Semigroups

Authors: Jian Tang

Abstract:

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.

Keywords: Ordered semigroup, ordered fuzzy point, weakly prime fuzzy left ideal, weakly quasi-prime fuzzy left ideal.

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2886 Compromise Ratio Method for Decision Making under Fuzzy Environment using Fuzzy Distance Measure

Authors: Debashree Guha, Debjani Chakraborty

Abstract:

The aim of this paper is to adopt a compromise ratio (CR) methodology for fuzzy multi-attribute single-expert decision making proble. In this paper, the rating of each alternative has been described by linguistic terms, which can be expressed as triangular fuzzy numbers. The compromise ratio method for fuzzy multi-attribute single expert decision making has been considered here by taking the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away as possible from the negative-ideal solution simultaneously. From logical point of view, the distance between two triangular fuzzy numbers also is a fuzzy number, not a crisp value. Therefore a fuzzy distance measure, which is itself a fuzzy number, has been used here to calculate the difference between two triangular fuzzy numbers. Now in this paper, with the help of this fuzzy distance measure, it has been shown that the compromise ratio is a fuzzy number and this eases the problem of the decision maker to take the decision. The computation principle and the procedure of the compromise ratio method have been described in detail in this paper. A comparative analysis of the compromise ratio method previously proposed [1] and the newly adopted method have been illustrated with two numerical examples.

Keywords: Compromise ratio method, Fuzzy multi-attributesingle-expert decision making, Fuzzy number, Linguistic variable

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2885 Fuzzy Scan Method to Detect Clusters

Authors: Laureano Rodríguez, Gladys Casas, Ricardo Grau, Yailen Martínez

Abstract:

The classical temporal scan statistic is often used to identify disease clusters. In recent years, this method has become as a very popular technique and its field of application has been notably increased. Many bioinformatic problems have been solved with this technique. In this paper a new scan fuzzy method is proposed. The behaviors of classic and fuzzy scan techniques are studied with simulated data. ROC curves are calculated, being demonstrated the superiority of the fuzzy scan technique.

Keywords: Scan statistic, fuzzy scan, simulating study

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2884 Frequency Transformation with Pascal Matrix Equations

Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: Frequency transformation, Bilinear z-transformation, Pre-warping frequency, Digital filters, Analog filters, Pascal’s triangle.

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2883 Adaptation of Iterative Methods to Solve Fuzzy Mathematical Programming Problems

Authors: Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami

Abstract:

Based on the fuzzy set theory this work develops two adaptations of iterative methods that solve mathematical programming problems with uncertainties in the objective function and in the set of constraints. The first one uses the approach proposed by Zimmermann to fuzzy linear programming problems as a basis and the second one obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. We outline similarities between the two iterative methods studied. Selected examples from the literature are presented to validate the efficiency of the methods addressed.

Keywords: Fuzzy Theory, Nonlinear Optimization, Fuzzy Mathematics Programming.

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2882 Implementation of Intuitionistic Fuzzy Approach in Maximizing Net Present Value

Authors: Gaurav Kumar, Rakesh Kumar Bajaj

Abstract:

The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented.

Keywords: Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

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