Search results for: Fuzzy logic power systemstabilizer

Authors: Myung-Won Lee, Keun-Chang Kwak

Abstract:

This paper is concerned with knowledge representation and extraction of fuzzy if-then rules using Interval Type-2 Context-based Fuzzy C-Means clustering (IT2-CFCM) with the aid of fuzzy granulation. This proposed clustering algorithm is based on information granulation in the form of IT2 based Fuzzy C-Means (IT2-FCM) clustering and estimates the cluster centers by preserving the homogeneity between the clustered patterns from the IT2 contexts produced in the output space. Furthermore, we can obtain the automatic knowledge representation in the design of Radial Basis Function Networks (RBFN), Linguistic Model (LM), and Adaptive Neuro-Fuzzy Networks (ANFN) from the numerical input-output data pairs. We shall focus on a design of ANFN in this paper. The experimental results on an estimation problem of energy performance reveal that the proposed method showed a good knowledge representation and performance in comparison with the previous works.

Keywords: IT2-FCM, IT2-CFCM, context-based fuzzy clustering, adaptive neuro-fuzzy network, knowledge representation.

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Authors: Abder-Rahman Ali, Adélaïde Albouy-Kissi, Manuel Grand-Brochier, Viviane Ladan-Marcus, Christine Hoeffl, Claude Marcus, Antoine Vacavant, Jean-Yves Boire

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In this paper, we present a new segmentation approach for focal liver lesions in contrast enhanced ultrasound imaging. This approach, based on a two-cluster Fuzzy C-Means methodology, considers type-II fuzzy sets to handle uncertainty due to the image modality (presence of speckle noise, low contrast, etc.), and to calculate the optimum inter-cluster threshold. Fine boundaries are detected by a local recursive merging of ambiguous pixels. The method has been tested on a representative database. Compared to both Otsu and type-I Fuzzy C-Means techniques, the proposed method significantly reduces the segmentation errors.

Keywords: Defuzzification, fuzzy clustering, image segmentation, type-II fuzzy sets.

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Authors: Da-kuan Wei, Xian-zhong Zhou, Dong-jun Xin, Zhi-wei Chen

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The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is the generalization of the variable precision rough set model for incomplete information system and that of rough set model for incomplete and fuzzy decision information system. The knowledge reduction and heuristic algorithm, built on the method and theory of precision reduction, are proposed.

Keywords: Rough set, Incomplete and fuzzy decision information system, Limited valued tolerance relation, Knowledge reduction, Variable rough set model

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Authors: Melike Şah, Konstantin Y.Degtiarev

Abstract:

This paper proposes a novel improvement of forecasting approach based on using time-invariant fuzzy time series. In contrast to traditional forecasting methods, fuzzy time series can be also applied to problems, in which historical data are linguistic values. It is shown that proposed time-invariant method improves the performance of forecasting process. Further, the effect of using different number of fuzzy sets is tested as well. As with the most of cited papers, historical enrollment of the University of Alabama is used in this study to illustrate the forecasting process. Subsequently, the performance of the proposed method is compared with existing fuzzy time series time-invariant models based on forecasting accuracy. It reveals a certain performance superiority of the proposed method over methods described in the literature.

Keywords: Forecasting, fuzzy time series, linguistic values, student enrollment, time-invariant model.

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Authors: Sukhveer Singh, Sandeep Singh

Abstract:

A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: Transportation problem, efficient solution, ranking function, fuzzy transportation problem.

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Authors: Amarunnishad T.M., Govindan V.K., Abraham T. Mathew

Abstract:

An image compression method has been developed using fuzzy edge image utilizing the basic Block Truncation Coding (BTC) algorithm. The fuzzy edge image has been validated with classical edge detectors on the basis of the results of the well-known Canny edge detector prior to applying to the proposed method. The bit plane generated by the conventional BTC method is replaced with the fuzzy bit plane generated by the logical OR operation between the fuzzy edge image and the corresponding conventional BTC bit plane. The input image is encoded with the block mean and standard deviation and the fuzzy bit plane. The proposed method has been tested with test images of 8 bits/pixel and size 512×512 and found to be superior with better Peak Signal to Noise Ratio (PSNR) when compared to the conventional BTC, and adaptive bit plane selection BTC (ABTC) methods. The raggedness and jagged appearance, and the ringing artifacts at sharp edges are greatly reduced in reconstructed images by the proposed method with the fuzzy bit plane.

Keywords: Image compression, Edge detection, Ground truth image, Peak signal to noise ratio

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Authors: Noura Boudiaf, Abdelhamid Djebbar

Abstract:

Colored Petri Nets (CPN) are very known kind of high level Petri nets. With sound and complete semantics, rewriting logic is one of very powerful logics in description and verification of non-deterministic concurrent systems. Recently, CPN semantics are defined in terms of rewriting logic, allowing us to built models by formal reasoning. In this paper, we propose an automatic translation of CPN to the rewriting logic language Maude. This tool allows graphical editing and simulating CPN. The tool allows the user drawing a CPN graphically and automatic translating the graphical representation of the drawn CPN to Maude specification. Then, Maude language is used to perform the simulation of the resulted Maude specification. It is the first rewriting logic based environment for this category of Petri Nets.

Keywords: Colored Petri Nets, Rewriting Logic, Maude, Graphical Edition, Automatic Translation, Simulation.

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Authors: S. Panda, S. C. Swain, A. K. Baliarsingh, A. K. Mohanty, C. Ardil

Abstract:

Many real-world optimization problems involve multiple conflicting objectives and the use of evolutionary algorithms to solve the problems has attracted much attention recently. This paper investigates the application of multi-objective optimization technique for the design of a Thyristor Controlled Series Compensator (TCSC)-based controller to enhance the performance of a power system. The design objective is to improve both rotor angle stability and system voltage profile. A Genetic Algorithm (GA) based solution technique is applied to generate a Pareto set of global optimal solutions to the given multi-objective optimisation problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Simulation results are presented to show the effectiveness and robustness of the proposed approach.

Keywords: Multi-objective optimisation, thyristor controlled series compensator, power system stability, genetic algorithm, pareto solution set, fuzzy ranking.

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Authors: Ahmed A.D. Sarhan, Lim Siew Fen, Mum Wai Yip, M. Sayuti

Abstract:

Ti6Al4V alloy is highly used in the automotive and aerospace industry due to its good machining characteristics. Micro EDM drilling is commonly used to drill micro hole on extremely hard material with very high depth to diameter ratio. In this study, the parameters of micro-electrical discharge machining (EDM) in drilling of Ti6Al4V alloy is optimized for higher machining accuracy with less hole-dilation and hole taper ratio. The micro-EDM machining parameters includes, peak current and pulse on time. Fuzzy analysis was developed to evaluate the machining accuracy. The analysis shows that hole-dilation and hole-taper ratio are increased with the increasing of peak current and pulse on time. However, the surface quality deteriorates as the peak current and pulse on time increase. The combination that gives the optimum result for hole dilation is medium peak current and short pulse on time. Meanwhile, the optimum result for hole taper ratio is low peak current and short pulse on time.

Keywords: Micro EDM, Ti-6Al-4V alloy, fuzzy logic based analysis, optimization, machining accuracy.

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Authors: Sufian Ashraf Mazhari, Surendra Kumar

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In this paper performance of Puma 560 manipulator is being compared for hybrid gradient descent and least square method learning based ANFIS controller with hybrid Genetic Algorithm and Generalized Pattern Search tuned radial basis function based Neuro-Fuzzy controller. ANFIS which is based on Takagi Sugeno type Fuzzy controller needs prior knowledge of rule base while in radial basis function based Neuro-Fuzzy rule base knowledge is not required. Hybrid Genetic Algorithm with generalized Pattern Search is used for tuning weights of radial basis function based Neuro- fuzzy controller. All the controllers are checked for butterfly trajectory tracking and results in the form of Cartesian and joint space errors are being compared. ANFIS based controller is showing better performance compared to Radial Basis Function based Neuro-Fuzzy Controller but rule base independency of RBF based Neuro-Fuzzy gives it an edge over ANFIS

Keywords: Neuro-Fuzzy, Robotic Control, RBFNF, ANFIS, Hybrid GA.

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Authors: Nurnadiah Z., Lazim A.

Abstract:

The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making yet to be explored, this paper proposes a new objective weight method by using entropy weight method for multiple attribute decision making (MADM). This paper utilizes the nature of IT2FS concept in the evaluation process to assess the attribute weight based on the credibility of data. An example was presented to demonstrate the feasibility of the new method in decision making. The entropy measure of interval type-2 fuzzy sets yield flexible judgment and could be applied in decision making environment.

Keywords: Objective weight, entropy weight, multiple attributedecision making, type-2 fuzzy sets, interval type-2 fuzzy sets

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Authors: Banaja Mohanty, Prakash Kumar Hota

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This paper demonstrates dynamic performance evaluation of load frequency control (LFC) with different intelligent techniques. All non-linearities and physical constraints have been considered in simulation studies such as governor dead band (GDB), generation rate constraint (GRC) and boiler dynamics. The conventional integral time absolute error has been considered as objective function. The design problem is formulated as an optimisation problem and particle swarm optimisation (PSO), bacterial foraging optimisation algorithm (BFOA) and differential evolution (DE) are employed to search optimal controller parameters. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic control (FLC) for the same interconnected power system. The comparison is done using various performance measures like overshoot, undershoot, settling time and standard error criteria of frequency and tie-line power deviation following a step load perturbation (SLP). It is noticed that, the dynamic performance of proposed controller is better than FLC. Further, robustness analysis is carried out by varying the time constants of speed governor, turbine, tie-line power in the range of +40% to -40% to demonstrate the robustness of the proposed DE optimized PID controller.

Keywords: Automatic generation control, governor dead band, generation rate constraint, differential evolution.

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Authors: Mohanad Alata, Mohammad Molhim, Abdullah Ramini

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Fuzzy C-means Clustering algorithm (FCM) is a method that is frequently used in pattern recognition. It has the advantage of giving good modeling results in many cases, although, it is not capable of specifying the number of clusters by itself. In FCM algorithm most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. Consequently, the main objective of this paper is to use the subtractive clustering algorithm to provide the optimal number of clusters needed by FCM algorithm by optimizing the parameters of the subtractive clustering algorithm by an iterative search approach and then to find an optimal weighting exponent (m) for the FCM algorithm. In order to get an optimal number of clusters, the iterative search approach is used to find the optimal single-output Sugenotype Fuzzy Inference System (FIS) model by optimizing the parameters of the subtractive clustering algorithm that give minimum least square error between the actual data and the Sugeno fuzzy model. Once the number of clusters is optimized, then two approaches are proposed to optimize the weighting exponent (m) in the FCM algorithm, namely, the iterative search approach and the genetic algorithms. The above mentioned approach is tested on the generated data from the original function and optimal fuzzy models are obtained with minimum error between the real data and the obtained fuzzy models.

Keywords: Fuzzy clustering, Fuzzy C-Means, Genetic Algorithm, Sugeno fuzzy systems.

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Authors: J. Kavikumar, N. S. Manian, M. B. K. Moorthy

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The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. 

Keywords: Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best coapproximation, orthogonality

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Authors: Mahdi Taheri, Mehrana Niroumand

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In this paper a new definition of adjacency matrix in the simple graphs is presented that is called fuzzy adjacency matrix, so that elements of it are in the form of 0 and n N n 1 , ∈ that are in the interval [0, 1], and then some charactristics of this matrix are presented with the related examples . This form matrix has complete of information of a graph.

Keywords: Graph, adjacency matrix, fuzzy numbers

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Authors: Anuja Vyas, Aikel Indurkhya, Hari Krishna Garg

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Nearly 25 years have passed since the landmark publication of the Human Genome Project, yet scientists have only begun to scratch the surface of its potential benefits. To bridge this gap, a personalized genomic application has been envisioned as a transformative tool accessible to people worldwide. This innovative solution proposes an integrated framework combining blockchain technology, genome-specific applications, and data compression techniques, ensuring operations to be swift, secure, transparent, and space-efficient. The software harnesses advanced Artificial Intelligence and Machine Learning methodologies, such as neural networks, evaluation matrices, fuzzy logic, and expert systems, to analyze individual genomic data. It generates personalized reports by comparing a user's genome with a reference genome, highlighting significant differences. Blockchain technology, with its inherent security, encryption, and immutability features, is leveraged for robust data transport and storage. In addition, a 'Data Abbreviation' technique ensures that genetic data and reports occupy minimal space. This integrated approach promises to be a significant leap forward, potentially transforming human health and well-being on a global scale.

Keywords: Artificial intelligence in genomics, blockchain technology, data abbreviation, data compression, data security in genomics, data storage, expert systems, fuzzy logic, genome applications, genomic data analysis, human genome project, neural networks, personalized genomics.

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Authors: R. Amandi, A. Shahbazi, A. Mohebi, M. Bazargan, Y. Jaberi, P. Emadi, A. Valizade

Abstract:

The application of Neural Network for disease diagnosis has made great progress and is widely used by physicians. An Electrocardiogram carries vital information about heart activity and physicians use this signal for cardiac disease diagnosis which was the great motivation towards our study. In our work, tachycardia features obtained are used for the training and testing of a Neural Network. In this study we are using Fuzzy Probabilistic Neural Networks as an automatic technique for ECG signal analysis. As every real signal recorded by the equipment can have different artifacts, we needed to do some preprocessing steps before feeding it to our system. Wavelet transform is used for extracting the morphological parameters of the ECG signal. The outcome of the approach for the variety of arrhythmias shows the represented approach is superior than prior presented algorithms with an average accuracy of about %95 for more than 7 tachy arrhythmias.

Keywords: Fuzzy Logic, Probabilistic Neural Network, Tachycardia, Wavelet Transform.

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Authors: Shu-Xin Miao

Abstract:

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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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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Authors: Daniel Stamate

Abstract:

We introduce a logic-based framework for database updating under constraints. In our framework, the constraints are represented as an instantiated extended logic program. When performing an update, database consistency may be violated. We provide an approach of maintaining database consistency, and study the conditions under which the maintenance process is deterministic. We show that the complexity of the computations and decision problems presented in our framework is in each case polynomial time.

Keywords: Databases, knowledge bases, constraints, updates, minimal change, consistency.

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Authors: Serafettin Ekinci, Kursat Zuhtuogullari

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This paper proposes a Fuzzy Expert System design to determine the wearing properties of nitrided and non nitrided steel. The proposed Fuzzy Expert System approach helps the user and the manufacturer to forecast the wearing properties of nitrided and non nitrided steel under specified laboratory conditions. Surfaces of the engineering components are often nitrided for improving wear, corosion, fatigue specifications. A major property of nitriding process is reducing distortion and wearing of the metalic alloys. A Fuzzy Expert System was developed for determining the wearing and durability properties of nitrided and non nitrided steels that were tested under different loads and different sliding speeds in the laboratory conditions.

Keywords: Fuzzy Expert System Design, Rule Based Systems, Fatigue, Corrosion

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Authors: Hataitep Wongsuwarn, Djitt Laowattana

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This paper summaries basic principles and concepts of intelligent controls, implemented in humanoid robotics as well as recent algorithms being devised for advanced control of humanoid robots. Secondly, this paper presents a new approach neuro-fuzzy system. We have included some simulating results from our computational intelligence technique that will be applied to our humanoid robot. Subsequently, we determine a relationship between joint trajectories and located forces on robot-s foot through a proposed neuro-fuzzy technique.

Keywords: Biped Robot, Computational Intelligence, Static and Dynamic Walking, Gait Synthesis, Neuro-Fuzzy System.

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Authors: A. Pashayev, R. Sadiqov, C. Ardil, F. Ildiz , H. Karabork

Abstract:

The new technology of fuzzy neural networks for identification of parameters for mathematical models of geofields is proposed and checked. The effectiveness of that soft computing technology is demonstrated, especially in the early stage of modeling, when the information is uncertain and limited.

Keywords: Identification, interpolation methods, neuro-fuzzy networks, geofield.

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Authors: Engin Yesil, Leon Urbas

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Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and can handle only relatively simple fuzzy cognitive maps; therefore, there is a need of developing new approaches for an automated generation of fuzzy cognitive maps using historical data. In this study, a new learning algorithm, which is called Big Bang-Big Crunch, is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from data. Two real-world examples; namely a process control system and radiation therapy process, and one synthetic model are used to emphasize the effectiveness and usefulness of the proposed methodology.

Keywords: Big Bang-Big Crunch optimization, Dynamic Systems, Fuzzy Cognitive Maps, Learning.

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Authors: Yuanyuan Chai, Limin Jia, Zundong Zhang

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Hybrid algorithm is the hot issue in Computational Intelligence (CI) study. From in-depth discussion on Simulation Mechanism Based (SMB) classification method and composite patterns, this paper presents the Mamdani model based Adaptive Neural Fuzzy Inference System (M-ANFIS) and weight updating formula in consideration with qualitative representation of inference consequent parts in fuzzy neural networks. M-ANFIS model adopts Mamdani fuzzy inference system which has advantages in consequent part. Experiment results of applying M-ANFIS to evaluate traffic Level of service show that M-ANFIS, as a new hybrid algorithm in computational intelligence, has great advantages in non-linear modeling, membership functions in consequent parts, scale of training data and amount of adjusted parameters.

Keywords: Fuzzy neural networks, Mamdani fuzzy inference, M-ANFIS

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Authors: Meredith Stevenson, John E. Porter

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Since the pioneering work of Zadeh, fuzzy set theory has been applied to a myriad of areas. Song and Chissom introduced the concept of fuzzy time series and applied some methods to the enrollments of the University of Alabama. In recent years, a number of techniques have been proposed for forecasting based on fuzzy set theory methods. These methods have either used enrollment numbers or differences of enrollments as the universe of discourse. We propose using the year to year percentage change as the universe of discourse. In this communication, the approach of Jilani, Burney, and Ardil is modified by using the year to year percentage change as the universe of discourse. We use enrollment figures for the University of Alabama to illustrate our proposed method. The proposed method results in better forecasting accuracy than existing models.

Keywords: Fuzzy forecasting, fuzzy time series, fuzzified enrollments, time-invariant model

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Authors: Padmanabhan Balasubramanian, Karthik Anantha

Abstract:

Structural representation and technology mapping of a Boolean function is an important problem in the design of nonregenerative digital logic circuits (also called combinational logic circuits). Library aware function manipulation offers a solution to this problem. Compact multi-level representation of binary networks, based on simple circuit structures, such as AND-Inverter Graphs (AIG) [1] [5], NAND Graphs, OR-Inverter Graphs (OIG), AND-OR Graphs (AOG), AND-OR-Inverter Graphs (AOIG), AND-XORInverter Graphs, Reduced Boolean Circuits [8] does exist in literature. In this work, we discuss a novel and efficient graph realization for combinational logic circuits, represented using a NAND-NOR-Inverter Graph (NNIG), which is composed of only two-input NAND (NAND2), NOR (NOR2) and inverter (INV) cells. The networks are constructed on the basis of irredundant disjunctive and conjunctive normal forms, after factoring, comprising terms with minimum support. Construction of a NNIG for a non-regenerative function in normal form would be straightforward, whereas for the complementary phase, it would be developed by considering a virtual instance of the function. However, the choice of best NNIG for a given function would be based upon literal count, cell count and DAG node count of the implementation at the technology independent stage. In case of a tie, the final decision would be made after extracting the physical design parameters. We have considered AIG representation for reduced disjunctive normal form and the best of OIG/AOG/AOIG for the minimized conjunctive normal forms. This is necessitated due to the nature of certain functions, such as Achilles- heel functions. NNIGs are found to exhibit 3.97% lesser node count compared to AIGs and OIG/AOG/AOIGs; consume 23.74% and 10.79% lesser library cells than AIGs and OIG/AOG/AOIGs for the various samples considered. We compare the power efficiency and delay improvement achieved by optimal NNIGs over minimal AIGs and OIG/AOG/AOIGs for various case studies. In comparison with functionally equivalent, irredundant and compact AIGs, NNIGs report mean savings in power and delay of 43.71% and 25.85% respectively, after technology mapping with a 0.35 micron TSMC CMOS process. For a comparison with OIG/AOG/AOIGs, NNIGs demonstrate average savings in power and delay by 47.51% and 24.83%. With respect to device count needed for implementation with static CMOS logic style, NNIGs utilize 37.85% and 33.95% lesser transistors than their AIG and OIG/AOG/AOIG counterparts.

Keywords: AND-Inverter Graph, OR-Inverter Graph, DirectedAcyclic Graph, Low power design, Delay optimization.

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Authors: Chien-Hua Wang, Meng-Ying Chou, Chin-Tzong Pang

Abstract:

This paper applies fuzzy AHP to evaluate the service quality of online auction. Service quality is a composition of various criteria. Among them many intangible attributes are difficult to measure. This characteristic introduces the obstacles for respondents on reply in the survey. So as to overcome this problem, we invite fuzzy set theory into the measurement of performance and use AHP in obtaining criteria. We found the most concerned dimension of service quality is Transaction Safety Mechanism and the least is Charge Item. Other criteria such as information security, accuracy and information are too vital.

Keywords: Fuzzy set theory, AHP, Online auction, Service quality

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

Abstract:

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

Keywords: Fuzzy random variables, Distance measure, Expected value.

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