Search results for: Fuzzy neural networks
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3159

Search results for: Fuzzy neural networks

2919 Trajectory Estimation and Control of Vehicle using Neuro-Fuzzy Technique

Authors: B. Selma, S. Chouraqui

Abstract:

Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.

Keywords: Adaptive neuro-fuzzy inference system (ANFIS), Fuzzy logic, neural network, nonlinear system, control

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2918 Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay

Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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2917 A New Fuzzy Mathematical Model in Recycling Collection Networks: A Possibilistic Approach

Authors: B. Vahdani, R. Tavakkoli-Moghaddam, A. Baboli, S. M. Mousavi

Abstract:

Focusing on the environmental issues, including the reduction of scrap and consumer residuals, along with the benefiting from the economic value during the life cycle of goods/products leads the companies to have an important competitive approach. The aim of this paper is to present a new mixed nonlinear facility locationallocation model in recycling collection networks by considering multi-echelon, multi-suppliers, multi-collection centers and multifacilities in the recycling network. To make an appropriate decision in reality, demands, returns, capacities, costs and distances, are regarded uncertain in our model. For this purpose, a fuzzy mathematical programming-based possibilistic approach is introduced as a solution methodology from the recent literature to solve the proposed mixed-nonlinear programming model (MNLP). The computational experiments are provided to illustrate the applicability of the designed model in a supply chain environment and to help the decision makers to facilitate their analysis.

Keywords: Location-allocation model, recycling collection networks, fuzzy mathematical programming.

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2916 Prediction of Slump in Concrete using Artificial Neural Networks

Authors: V. Agrawal, A. Sharma

Abstract:

High Strength Concrete (HSC) is defined as concrete that meets special combination of performance and uniformity requirements that cannot be achieved routinely using conventional constituents and normal mixing, placing, and curing procedures. It is a highly complex material, which makes modeling its behavior a very difficult task. This paper aimed to show possible applicability of Neural Networks (NN) to predict the slump in High Strength Concrete (HSC). Neural Network models is constructed, trained and tested using the available test data of 349 different concrete mix designs of High Strength Concrete (HSC) gathered from a particular Ready Mix Concrete (RMC) batching plant. The most versatile Neural Network model is selected to predict the slump in concrete. The data used in the Neural Network models are arranged in a format of eight input parameters that cover the Cement, Fly Ash, Sand, Coarse Aggregate (10 mm), Coarse Aggregate (20 mm), Water, Super-Plasticizer and Water/Binder ratio. Furthermore, to test the accuracy for predicting slump in concrete, the final selected model is further used to test the data of 40 different concrete mix designs of High Strength Concrete (HSC) taken from the other batching plant. The results are compared on the basis of error function (or performance function).

Keywords: Artificial Neural Networks, Concrete, prediction ofslump, slump in concrete

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2915 Lithofacies Classification from Well Log Data Using Neural Networks, Interval Neutrosophic Sets and Quantification of Uncertainty

Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

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2914 Fuzzy Cost Support Vector Regression

Authors: Hadi Sadoghi Yazdi, Tahereh Royani, Mehri Sadoghi Yazdi, Sohrab Effati

Abstract:

In this paper, a new version of support vector regression (SVR) is presented namely Fuzzy Cost SVR (FCSVR). Individual property of the FCSVR is operation over fuzzy data whereas fuzzy cost (fuzzy margin and fuzzy penalty) are maximized. This idea admits to have uncertainty in the penalty and margin terms jointly. Robustness against noise is shown in the experimental results as a property of the proposed method and superiority relative conventional SVR.

Keywords: Support vector regression, Fuzzy input, Fuzzy cost.

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2913 Anomaly Detection with ANN and SVM for Telemedicine Networks

Authors: Edward Guillén, Jeisson Sánchez, Carlos Omar Ramos

Abstract:

In recent years, a wide variety of applications are developed with Support Vector Machines -SVM- methods and Artificial Neural Networks -ANN-. In general, these methods depend on intrusion knowledge databases such as KDD99, ISCX, and CAIDA among others. New classes of detectors are generated by machine learning techniques, trained and tested over network databases. Thereafter, detectors are employed to detect anomalies in network communication scenarios according to user’s connections behavior. The first detector based on training dataset is deployed in different real-world networks with mobile and non-mobile devices to analyze the performance and accuracy over static detection. The vulnerabilities are based on previous work in telemedicine apps that were developed on the research group. This paper presents the differences on detections results between some network scenarios by applying traditional detectors deployed with artificial neural networks and support vector machines.

Keywords: Anomaly detection, back-propagation neural networks, network intrusion detection systems, support vector machines.

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2912 Fuzzy Bi-ideals in Ternary Semirings

Authors: Kavikumar, Azme Khamis, Young Bae Jun,

Abstract:

The purpose of the present paper is to study the concept of fuzzy bi-ideals in ternary semirings. We give some characterizations of fuzzy bi-ideals. Characterizations of regular ternary semirings are provided.

Keywords: Fuzzy ternary subsemiring, fuzzy quasi-ideal, fuzzy bi-ideal, regular ternary semiring

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2911 Forecasting the Istanbul Stock Exchange National 100 Index Using an Artificial Neural Network

Authors: Birol Yildiz, Abdullah Yalama, Metin Coskun

Abstract:

Many studies have shown that Artificial Neural Networks (ANN) have been widely used for forecasting financial markets, because of many financial and economic variables are nonlinear, and an ANN can model flexible linear or non-linear relationship among variables. The purpose of the study was to employ an ANN models to predict the direction of the Istanbul Stock Exchange National 100 Indices (ISE National-100). As a result of this study, the model forecast the direction of the ISE National-100 to an accuracy of 74, 51%.

Keywords: Artificial Neural Networks, Istanbul StockExchange, Non-linear Modeling.

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2910 Existence and Exponential Stability of Almost Periodic Solution for Recurrent Neural Networks on Time Scales

Authors: Lili Wang, Meng Hu

Abstract:

In this paper, a class of recurrent neural networks (RNNs) with variable delays are studied on almost periodic time scales, some sufficient conditions are established for the existence and global exponential stability of the almost periodic solution. These results have important leading significance in designs and applications of RNNs. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

Keywords: Recurrent neural network, Almost periodic solution, Global exponential stability, Time scale.

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2909 The Ability of Forecasting the Term Structure of Interest Rates Based On Nelson-Siegel and Svensson Model

Authors: Tea Poklepović, Zdravka Aljinović, Branka Marasović

Abstract:

Due to the importance of yield curve and its estimation it is inevitable to have valid methods for yield curve forecasting in cases when there are scarce issues of securities and/or week trade on a secondary market. Therefore in this paper, after the estimation of weekly yield curves on Croatian financial market from October 2011 to August 2012 using Nelson-Siegel and Svensson models, yield curves are forecasted using Vector autoregressive model and Neural networks. In general, it can be concluded that both forecasting methods have good prediction abilities where forecasting of yield curves based on Nelson Siegel estimation model give better results in sense of lower Mean Squared Error than forecasting based on Svensson model Also, in this case Neural networks provide slightly better results. Finally, it can be concluded that most appropriate way of yield curve prediction is Neural networks using Nelson-Siegel estimation of yield curves.

Keywords: Nelson-Siegel model, Neural networks, Svensson model, Vector autoregressive model, Yield curve.

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2908 Exploiting Kinetic and Kinematic Data to Plot Cyclograms for Managing the Rehabilitation Process of BKAs by Applying Neural Networks

Authors: L. Parisi

Abstract:

Kinematic data wisely correlate vector quantities in space to scalar parameters in time to assess the degree of symmetry between the intact limb and the amputated limb with respect to a normal model derived from the gait of control group participants. Furthermore, these particular data allow a doctor to preliminarily evaluate the usefulness of a certain rehabilitation therapy. Kinetic curves allow the analysis of ground reaction forces (GRFs) to assess the appropriateness of human motion. Electromyography (EMG) allows the analysis of the fundamental lower limb force contributions to quantify the level of gait asymmetry. However, the use of this technological tool is expensive and requires patient’s hospitalization. This research work suggests overcoming the above limitations by applying artificial neural networks.

Keywords: Kinetics, kinematics, cyclograms, neural networks.

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2907 A New Class χ2 (M, A,) of the Double Difference Sequences of Fuzzy Numbers

Authors: N.Subramanian, U.K.Misra

Abstract:

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

Keywords: Modulus function, fuzzy number, metric space.

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2906 Sensitivity Analysis for Determining Priority of Factors Controlling SOC Content in Semiarid Condition of West of Iran

Authors: Y. Parvizi, M. Gorji, M.H. Mahdian, M. Omid

Abstract:

Soil organic carbon (SOC) plays a key role in soil fertility, hydrology, contaminants control and acts as a sink or source of terrestrial carbon content that can affect the concentration of atmospheric CO2. SOC supports the sustainability and quality of ecosystems, especially in semi-arid region. This study was conducted to determine relative importance of 13 different exploratory climatic, soil and geometric factors on the SOC contents in one of the semiarid watershed zones in Iran. Two methods canonical discriminate analysis (CDA) and feed-forward back propagation neural networks were used to predict SOC. Stepwise regression and sensitivity analysis were performed to identify relative importance of exploratory variables. Results from sensitivity analysis showed that 7-2-1 neural networks and 5 inputs in CDA models output have highest predictive ability that explains %70 and %65 of SOC variability. Since neural network models outperformed CDA model, it should be preferred for estimating SOC.

Keywords: Soil organic carbon, modeling, neural networks, CDA.

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2905 An Investigation into the Application of Artificial Neural Networks to the Prediction of Injuries in Sport

Authors: J. McCullagh, T. Whitfort

Abstract:

Artificial Neural Networks (ANNs) have been used successfully in many scientific, industrial and business domains as a method for extracting knowledge from vast amounts of data. However the use of ANN techniques in the sporting domain has been limited. In professional sport, data is stored on many aspects of teams, games, training and players. Sporting organisations have begun to realise that there is a wealth of untapped knowledge contained in the data and there is great interest in techniques to utilise this data. This study will use player data from the elite Australian Football League (AFL) competition to train and test ANNs with the aim to predict the onset of injuries. The results demonstrate that an accuracy of 82.9% was achieved by the ANNs’ predictions across all examples with 94.5% of all injuries correctly predicted. These initial findings suggest that ANNs may have the potential to assist sporting clubs in the prediction of injuries.

Keywords: Artificial Neural Networks, data, injuries, sport

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2904 Modified Functional Link Artificial Neural Network

Authors: Ashok Kumar Goel, Suresh Chandra Saxena, Surekha Bhanot

Abstract:

In this work, a Modified Functional Link Artificial Neural Network (M-FLANN) is proposed which is simpler than a Multilayer Perceptron (MLP) and improves upon the universal approximation capability of Functional Link Artificial Neural Network (FLANN). MLP and its variants: Direct Linear Feedthrough Artificial Neural Network (DLFANN), FLANN and M-FLANN have been implemented to model a simulated Water Bath System and a Continually Stirred Tank Heater (CSTH). Their convergence speed and generalization ability have been compared. The networks have been tested for their interpolation and extrapolation capability using noise-free and noisy data. The results show that M-FLANN which is computationally cheap, performs better and has greater generalization ability than other networks considered in the work.

Keywords: DLFANN, FLANN, M-FLANN, MLP

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2903 Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces

Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

Keywords: Contraction, Iterated Function System, Hutchinson- Barnsley Operator, Intuitionistic Fuzzy Metric Space, Hausdorff Intuitionistic Fuzzy Metric.

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2902 Fuzzy Join Dependency in Fuzzy Relational Databases

Authors: P. C. Saxena, D. K. Tayal

Abstract:

The join dependency provides the basis for obtaining lossless join decomposition in a classical relational schema. The existence of Join dependency shows that that the tables always represent the correct data after being joined. Since the classical relational databases cannot handle imprecise data, they were extended to fuzzy relational databases so that uncertain, ambiguous, imprecise and partially known information can also be stored in databases in a formal way. However like classical databases, the fuzzy relational databases also undergoes decomposition during normalization, the issue of joining the decomposed fuzzy relations remains intact. Our effort in the present paper is to emphasize on this issue. In this paper we define fuzzy join dependency in the framework of type-1 fuzzy relational databases & type-2 fuzzy relational databases using the concept of fuzzy equality which is defined using fuzzy functions. We use the fuzzy equi-join operator for computing the fuzzy equality of two attribute values. We also discuss the dependency preservation property on execution of this fuzzy equi- join and derive the necessary condition for the fuzzy functional dependencies to be preserved on joining the decomposed fuzzy relations. We also derive the conditions for fuzzy join dependency to exist in context of both type-1 and type-2 fuzzy relational databases. We find that unlike the classical relational databases even the existence of a trivial join dependency does not ensure lossless join decomposition in type-2 fuzzy relational databases. Finally we derive the conditions for the fuzzy equality to be non zero and the qualification of an attribute for fuzzy key.

Keywords: Fuzzy - equi join, fuzzy functions, fuzzy join dependency, type-1 fuzzy relational database, type-2 fuzzy relational database.

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2901 A Cognitive Model for Frequency Signal Classification

Authors: Rui Antunes, Fernando V. Coito

Abstract:

This article presents the development of a neural network cognitive model for the classification and detection of different frequency signals. The basic structure of the implemented neural network was inspired on the perception process that humans generally make in order to visually distinguish between high and low frequency signals. It is based on the dynamic neural network concept, with delays. A special two-layer feedforward neural net structure was successfully implemented, trained and validated, to achieve minimum target error. Training confirmed that this neural net structure descents and converges to a human perception classification solution, even when far away from the target.

Keywords: Neural Networks, Signal Classification, Adaptative Filters, Cognitive Neuroscience

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2900 (∈,∈∨q)-Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, (∈, ∈∨q)-fuzzy subalgebras, (∈, ∈∨q)-fuzzy ideals, (∈, ∈∨q)-fuzzy quotient algebras.

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2899 Application and Assessment of Artificial Neural Networks for Biodiesel Iodine Value Prediction

Authors: Raquel M. de Sousa, Sofiane Labidi, Allan Kardec D. Barros, Alex O. Barradas Filho, Aldalea L. B. Marques

Abstract:

Several parameters are established in order to measure biodiesel quality. One of them is the iodine value, which is an important parameter that measures the total unsaturation within a mixture of fatty acids. Limitation of unsaturated fatty acids is necessary since warming of higher quantity of these ones ends in either formation of deposits inside the motor or damage of lubricant. Determination of iodine value by official procedure tends to be very laborious, with high costs and toxicity of the reagents, this study uses artificial neural network (ANN) in order to predict the iodine value property as an alternative to these problems. The methodology of development of networks used 13 esters of fatty acids in the input with convergence algorithms of back propagation of back propagation type were optimized in order to get an architecture of prediction of iodine value. This study allowed us to demonstrate the neural networks’ ability to learn the correlation between biodiesel quality properties, in this caseiodine value, and the molecular structures that make it up. The model developed in the study reached a correlation coefficient (R) of 0.99 for both network validation and network simulation, with Levenberg-Maquardt algorithm.

Keywords: Artificial Neural Networks, Biodiesel, Iodine Value, Prediction.

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2898 Modeling and Simulation of Position Estimation of Switched Reluctance Motor with Artificial Neural Networks

Authors: Oguz Ustun, Erdal Bekiroglu

Abstract:

In the present study, position estimation of switched reluctance motor (SRM) has been achieved on the basis of the artificial neural networks (ANNs). The ANNs can estimate the rotor position without using an extra rotor position sensor by measuring the phase flux linkages and phase currents. Flux linkage-phase current-rotor position data set and supervised backpropagation learning algorithm are used in training of the ANN based position estimator. A 4-phase SRM have been used to verify the accuracy and feasibility of the proposed position estimator. Simulation results show that the proposed position estimator gives precise and accurate position estimations for both under the low and high level reference speeds of the SRM

Keywords: Artificial neural networks, modeling andsimulation, position observer, switched reluctance motor.

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2897 Local Linear Model Tree (LOLIMOT) Reconfigurable Parallel Hardware

Authors: A. Pedram, M. R. Jamali, T. Pedram, S. M. Fakhraie, C. Lucas

Abstract:

Local Linear Neuro-Fuzzy Models (LLNFM) like other neuro- fuzzy systems are adaptive networks and provide robust learning capabilities and are widely utilized in various applications such as pattern recognition, system identification, image processing and prediction. Local linear model tree (LOLIMOT) is a type of Takagi-Sugeno-Kang neuro fuzzy algorithm which has proven its efficiency compared with other neuro fuzzy networks in learning the nonlinear systems and pattern recognition. In this paper, a dedicated reconfigurable and parallel processing hardware for LOLIMOT algorithm and its applications are presented. This hardware realizes on-chip learning which gives it the capability to work as a standalone device in a system. The synthesis results on FPGA platforms show its potential to improve the speed at least 250 of times faster than software implemented algorithms.

Keywords: LOLIMOT, hardware, neurofuzzy systems, reconfigurable, parallel.

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2896 Interpolation of Geofield Parameters

Authors: A. Pashayev, C. Ardil, R. Sadiqov

Abstract:

Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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2895 Hybrid Machine Learning Approach for Text Categorization

Authors: Nerijus Remeikis, Ignas Skucas, Vida Melninkaite

Abstract:

Text categorization - the assignment of natural language documents to one or more predefined categories based on their semantic content - is an important component in many information organization and management tasks. Performance of neural networks learning is known to be sensitive to the initial weights and architecture. This paper discusses the use multilayer neural network initialization with decision tree classifier for improving text categorization accuracy. An adaptation of the algorithm is proposed in which a decision tree from root node until a final leave is used for initialization of multilayer neural network. The experimental evaluation demonstrates this approach provides better classification accuracy with Reuters-21578 corpus, one of the standard benchmarks for text categorization tasks. We present results comparing the accuracy of this approach with multilayer neural network initialized with traditional random method and decision tree classifiers.

Keywords: Text categorization, decision trees, neural networks, machine learning.

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2894 2D Structured Non-Cyclic Fuzzy Graphs

Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: Double layered fuzzy graph, double layered non-cyclic fuzzy graph, strong, order, degree and size.

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2893 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

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2892 Applying Half-Circle Fuzzy Numbers to Control System: A Preliminary Study on Development of Intelligent System on Marine Environment and Engineering

Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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2891 Intuitionistic Fuzzy Multisets And Its Application in Medical Diagnosis

Authors: Shinoj T. K, Sunil Jacob John

Abstract:

In this paper a new concept named Intuitionistic Fuzzy Multiset is introduced. The basic operations on Intuitionistic Fuzzy Multisets such as union, intersection, addition, multiplication etc. are discussed. An application of Intuitionistic Fuzzy Multiset in Medical diagnosis problem using a distance function is discussed in detail.

Keywords: Intuitionistic Fuzzy set, Multiset, Intuitionistic Fuzzy Multiset

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2890 Regularization of the Trajectories of Dynamical Systems by Adjusting Parameters

Authors: Helle Hein, Ülo Lepik

Abstract:

A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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