Search results for: Fuzzy logic system

Authors: Muhammad Aqil, Ichiro Kita, Moses Macalinao

Abstract:

Reliable water level forecasts are particularly important for warning against dangerous flood and inundation. The current study aims at investigating the suitability of the adaptive network based fuzzy inference system for continuous water level modeling. A hybrid learning algorithm, which combines the least square method and the back propagation algorithm, is used to identify the parameters of the network. For this study, water levels data are available for a hydrological year of 2002 with a sampling interval of 1-hour. The number of antecedent water level that should be included in the input variables is determined by two statistical methods, i.e. autocorrelation function and partial autocorrelation function between the variables. Forecasting was done for 1-hour until 12-hour ahead in order to compare the models generalization at higher horizons. The results demonstrate that the adaptive networkbased fuzzy inference system model can be applied successfully and provide high accuracy and reliability for river water level estimation. In general, the adaptive network-based fuzzy inference system provides accurate and reliable water level prediction for 1-hour ahead where the MAPE=1.15% and correlation=0.98 was achieved. Up to 12-hour ahead prediction, the model still shows relatively good performance where the error of prediction resulted was less than 9.65%. The information gathered from the preliminary results provide a useful guidance or reference for flood early warning system design in which the magnitude and the timing of a potential extreme flood are indicated.

Keywords: Neural Network, Fuzzy, River, Forecasting

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Authors: F. Khaber, K. Zehar, A. Hamzaoui

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In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

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Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

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In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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Authors: Konstantin Movsovic, Emanuele Stomeo, Tatiana Kalganova

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The evolutionary design of electronic circuits, or evolvable hardware, is a discipline that allows the user to automatically obtain the desired circuit design. The circuit configuration is under the control of evolutionary algorithms. Several researchers have used evolvable hardware to design electrical circuits. Every time that one particular algorithm is selected to carry out the evolution, it is necessary that all its parameters, such as mutation rate, population size, selection mechanisms etc. are tuned in order to achieve the best results during the evolution process. This paper investigates the abilities of evolution strategy to evolve digital logic circuits based on programmable logic array structures when different mutation rates are used. Several mutation rates (fixed and variable) are analyzed and compared with each other to outline the most appropriate choice to be used during the evolution of combinational logic circuits. The experimental results outlined in this paper are important as they could be used by every researcher who might need to use the evolutionary algorithm to design digital logic circuits.

Keywords: Evolvable hardware, evolutionary algorithm, digitallogic circuit, mutation rate.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

Abstract:

Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: J. Menčík

Abstract:

Actual load, material characteristics and other quantities often differ from the design values. This can cause worse function, shorter life or failure of a civil engineering structure, a machine, vehicle or another appliance. The paper shows main causes of the uncertainties and deviations and presents a systematic approach and efficient tools for their elimination or mitigation of consequences. Emphasis is put on the design stage, which is most important for reliability ensuring. Principles of robust design and important tools are explained, including FMEA, sensitivity analysis and probabilistic simulation methods. The lifetime prediction of long-life objects can be improved by long-term monitoring of the load response and damage accumulation in operation. The condition evaluation of engineering structures, such as bridges, is often based on visual inspection and verbal description. Here, methods based on fuzzy logic can reduce the subjective influences.

Keywords: Design, fuzzy methods, Monte Carlo, reliability, robust design, sensitivity analysis, simulation, uncertainties.

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Authors: E. Ansari-Piri, N. Eghbali

Abstract:

Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: Binyamin Yusoff, Imran Taib, Lazim Abdullah, Abd Fatah Wahab

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Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems.

Keywords: Intuitionistic fuzzy sets, similarity measures, multicriteriadecision making.

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Authors: A. Tellaeche, X. P. Burgos-Artizzu, G. Pajares, A. Ribeiro

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One important objective in Precision Agriculture is to minimize the volume of herbicides that are applied to the fields through the use of site-specific weed management systems. In order to reach this goal, two major factors need to be considered: 1) the similar spectral signature, shape and texture between weeds and crops; 2) the irregular distribution of the weeds within the crop's field. This paper outlines an automatic computer vision system for the detection and differential spraying of Avena sterilis, a noxious weed growing in cereal crops. The proposed system involves two processes: image segmentation and decision making. Image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based attributes measuring the relations among the crops and the weeds. From these attributes, a hybrid decision making approach determines if a cell must be or not sprayed. The hybrid approach uses the Support Vector Machines and the Fuzzy k-Means methods, combined through the fuzzy aggregation theory. This makes the main finding of this paper. The method performance is compared against other available strategies.

Keywords: Fuzzy k-Means, Precision agriculture, SupportVectors Machines, Weed detection.

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Authors: Ajay Shekhar Pandey, D. Singh, S. K. Sinha

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A clustering based technique has been developed and implemented for Short Term Load Forecasting, in this article. Formulation has been done using Mean Absolute Percentage Error (MAPE) as an objective function. Data Matrix and cluster size are optimization variables. Model designed, uses two temperature variables. This is compared with six input Radial Basis Function Neural Network (RBFNN) and Fuzzy Inference Neural Network (FINN) for the data of the same system, for same time period. The fuzzy inference system has the network structure and the training procedure of a neural network which initially creates a rule base from existing historical load data. It is observed that the proposed clustering based model is giving better forecasting accuracy as compared to the other two methods. Test results also indicate that the RBFNN can forecast future loads with accuracy comparable to that of proposed method, where as the training time required in the case of FINN is much less.

Keywords: Load forecasting, clustering, fuzzy inference.

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Authors: D. Krishnaveni, M. Geetha Priya

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Applications of reversible logic gates in the design of complex integrated circuits provide power optimization.  This technique finds a great use in low power CMOS design, optical computing, quantum computing and nanotechnology. This paper proposes a reversible signed division circuit that can divide an n-bit signed dividend with an n-bit signed divisor using non-restoration division logic. The proposed design adequately addresses the ‘delay’ there by improving the efficiency of the circuit. An attempt is made to design a reversible signed division circuit. This paper provides a threshold to build more complex arithmetic systems using reversible logic, thus increasing the performance of computing systems.

Keywords: Low power CMOS, quantum computing, reversible logic gates, shift register, signed division.

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Authors: Shih-Ching Lo, Hsieh-Chu Huang

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Mostly, pedestrian-car accidents occurred at a signalized interaction is because pedestrians cannot across the intersection safely within the green light. From the viewpoint of pedestrian, there might have two reasons. The first one is pedestrians cannot speed up to across the intersection, such as the elders. The other reason is pedestrians do not sense that the signal phase is going to change and their right-of-way is going to lose. Developing signal logic to protect pedestrian, who is crossing an intersection is the first purpose of this study. Another purpose of this study is improving the reliability and reduce delay of public transportation service. Therefore, bus preemption is also considered in the designed signal logic. In this study, the traffic data of the intersection of Chong-Qing North Road and Min-Zu West Road, Taipei, Taiwan, is employed to calibrate and validate the signal logic by simulation. VISSIM 5.20, which is a microscopic traffic simulation software, is employed to simulate the signal logic. From the simulated results, the signal logic presented in this study can protect pedestrians crossing the intersection successfully. The design of bus preemption can reduce the average delay. However, the pedestrian safety and bus preemptive signal will influence the average delay of cars largely. Thus, whether applying the pedestrian safety and bus preemption signal logic to an isolated intersection or not should be evaluated carefully.

Keywords: vulnerable road user, bus preemption, signal design.

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Authors: Jonqlan Lin, C. Y. Tasi, K. H. Lin

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This paper addresses the issue of the autonomous mobile robot (AMR) navigation task based on the hybrid control modes. The novel hybrid control mode, based on multi-sensors information by using the fuzzy approach, has been presented in this research. The system operates in real time, is robust, enables the robot to operate with imprecise knowledge, and takes into account the physical limitations of the environment in which the robot moves, obtaining satisfactory responses for a large number of different situations. An experiment is simulated and carried out with a pioneer mobile robot. From the experimental results, the effectiveness and usefulness of the proposed AMR obstacle avoidance and navigation scheme are confirmed. The experimental results show the feasibility, and the control system has improved the navigation accuracy. The implementation of the controller is robust, has a low execution time, and allows an easy design and tuning of the fuzzy knowledge base.

Keywords: Autonomous mobile robot, obstacle avoidance, MEMS, hybrid control mode, navigation control.

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Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen

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Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.

Keywords: Natural Language Inference, explanation generation, variational auto-encoder, generative model.

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Authors: Fatemeh Amiri, Caro Lucas, Nasser Yazdani

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As the network based technologies become omnipresent, demands to secure networks/systems against threat increase. One of the effective ways to achieve higher security is through the use of intrusion detection systems (IDS), which are a software tool to detect anomalous in the computer or network. In this paper, an IDS has been developed using an improved machine learning based algorithm, Locally Linear Neuro Fuzzy Model (LLNF) for classification whereas this model is originally used for system identification. A key technical challenge in IDS and LLNF learning is the curse of high dimensionality. Therefore a feature selection phase is proposed which is applicable to any IDS. While investigating the use of three feature selection algorithms, in this model, it is shown that adding feature selection phase reduces computational complexity of our model. Feature selection algorithms require the use of a feature goodness measure. The use of both a linear and a non-linear measure - linear correlation coefficient and mutual information- is investigated respectively

Keywords: anomaly Detection, feature selection, Locally Linear Neuro Fuzzy (LLNF), Mutual Information (MI), liner correlation coefficient.

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Authors: C. Ardil

Abstract:

Aircraft selection decisions can be challenging due to their multidimensional and interdisciplinary nature. They involve multiple stakeholders with conflicting objectives and numerous alternative options with uncertain outcomes. This study focuses on the analysis of aerial firefighting aircraft that can be chosen for the Air Fire Service to extinguish forest fires. To make such a selection, the characteristics of the fire zones must be considered, and the capability to manage the logistics involved in such operations, as well as the purchase and maintenance of the aircraft, must be determined. The selection of firefighting aircraft is particularly complex because they have longer fleet lives and require more demanding operation and maintenance than scheduled passenger air service. This paper aims to use the fuzzy proximity measure method to select the most appropriate aerial firefighting aircraft based on decision criteria using multiple attribute decision making analysis. Following fuzzy decision analysis, the most suitable aerial firefighting aircraft is ranked and determined for the Air Fire Service.

Keywords: Aerial firefighting aircraft selection, multiple criteria decision making, fuzzy sets, standard fuzzy sets, determinate fuzzy sets, indeterminate fuzzy sets, proximity measure method, Minkowski distance family function, Hausdorff distance function, MCDM, PMM, PMM-F

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Authors: Hamid Reza Boveiri

Abstract:

Classification of Persian printed numeral characters has been considered and a proposed system has been introduced. In representation stage, for the first time in Persian optical character recognition, extended moment invariants has been utilized as characters image descriptor. In classification stage, four different classifiers namely minimum mean distance, nearest neighbor rule, multi layer perceptron, and fuzzy min-max neural network has been used, which first and second are traditional nonparametric statistical classifier. Third is a well-known neural network and forth is a kind of fuzzy neural network that is based on utilizing hyperbox fuzzy sets. Set of different experiments has been done and variety of results has been presented. The results showed that extended moment invariants are qualified as features to classify Persian printed numeral characters.

Keywords: Extended moment invariants, optical characterrecognition, Persian numerals classification.

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Authors: Kuo-Lung Wu

Abstract:

The weighting exponent m is called the fuzzifier that can have influence on the clustering performance of fuzzy c-means (FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this paper, we will discuss the robust properties of FCM and show that the parameter m will have influence on the robustness of FCM. According to our analysis, we find that a large m value will make FCM more robust to noise and outliers. However, if m is larger than the theoretical upper bound proposed by Yu et al. [14], the sample mean will become the unique optimizer. Here, we suggest to implement the FCM algorithm with mÎ[1.5,4] under the restriction when m is smaller than the theoretical upper bound.

Keywords: Fuzzy c-means, robust, fuzzifier.

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Authors: C. Ardil

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Neutrosophic logic decision analysis is proposed as a method of stealth fighter aircraft selection for Turkish Air Force. The opinion of experts is employed to rank the alternatives across a set of criteria. The analyst uses neutrosophic logic numbers to describe the experts' preferences. This approach can handle the situation in the case of unavailability of precise data, which is most commonly the case in stealth fighter aircraft selection. Neutrosophic logic numbers can consider the imprecision of the factors affecting decision making such as stealth analysis, survivability analysis, and performance analysis. Neutrosophic logic ranking is achieved using weighted arithmetic operator and weighted geometric operator and the alternatives are ranked from best to worst. An example is also presented to illustrate the applicability and effectiveness of the proposed method. 

Keywords: Neutrosophic set theory, stealth fighter aircraft selection, multiple criteria decision-making, neutrosophic logic decision making, Turkish Air Force, MCDM

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Authors: Yang Li, Xiaorong Guan, Cheng Xu

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In order to design a suitable control scheme for human extremity exoskeleton, the interaction force control scheme with traditional PI controller was presented, and the simulation study of the electromechanical system of the human extremity exoskeleton was carried out by using a MATLAB/Simulink module. By analyzing the simulation calculation results, it was shown that the traditional PI controller is not very suitable for every movement speed of human body. So, at last the fuzzy self-adaptive PI controller was presented to solve this problem. Eventually, the superiority and feasibility of the fuzzy self-adaptive PI controller was proved by the simulation results and experimental results.

Keywords: Human extremity exoskeleton, interaction force control scheme, simulation study, fuzzy self-adaptive pi controller, man-machine coordinated walking, bear payload.

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Authors: Ali Asadian, Behzad Moshiri, Ali Khaki Sedigh, Caro Lucas

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Most integrated inertial navigation systems (INS) and global positioning systems (GPS) have been implemented using the Kalman filtering technique with its drawbacks related to the need for predefined INS error model and observability of at least four satellites. Most recently, a method using a hybrid-adaptive network based fuzzy inference system (ANFIS) has been proposed which is trained during the availability of GPS signal to map the error between the GPS and the INS. Then it will be used to predict the error of the INS position components during GPS signal blockage. This paper introduces a genetic optimization algorithm that is used to update the ANFIS parameters with respect to the INS/GPS error function used as the objective function to be minimized. The results demonstrate the advantages of the genetically optimized ANFIS for INS/GPS integration in comparison with conventional ANFIS specially in the cases of satellites- outages. Coping with this problem plays an important role in assessment of the fusion approach in land navigation.

Keywords: Adaptive Network based Fuzzy Inference System (ANFIS), Genetic optimization, Global Positioning System (GPS), Inertial Navigation System (INS).

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Authors: Maithem Al-Saadi, Min An

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During airport planning and design stages, the major issues of capacity and safety in construction and operation of an airport need to be taken into consideration. The airside of an airport is a major and critical infrastructure that usually consists of runway(s), taxiway system, and apron(s) etc., which have to be designed according to the international standards and recommendations, and local limitations to accommodate the forecasted demands. However, in many cases, airport airsides are suffering from unexpected risks that occurred during airport operations. Therefore, safety risk assessment should be applied in the planning and design of airsides to cope with the probability of risks and their consequences, and to make decisions to reduce the risks to as low as reasonably practicable (ALARP) based on safety risk assessment. This paper presents a combination approach of Failure Modes, Effect, and Criticality Analysis (FMECA), Fuzzy Reasoning Approach (FRA), and Fuzzy Analytic Hierarchy Process (FAHP) to develop a risk analysis model for safety risk assessment. An illustrated example is used to the demonstrate risk assessment process on how the design of an airside in an airport can be analysed by using the proposed safety design risk assessment model.

Keywords: Airport airside planning and design, design for safety, fuzzy reasoning approach, fuzzy AHP, risk assessment.

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Authors: André Trudel, Haiyi Zhang

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Over the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks.

Keywords: Constraint logic programming, CSP, logic, temporalreasoning.

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Authors: Fotis N. Koumboulis, Maria P. Tzamtzi

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A supervisory scheme is proposed that implements Stepwise Safe Switching Logic. The functionality of the supervisory scheme is organized in the following eight functional units: Step- Wise Safe Switching unit, Common controllers design unit, Experimentation unit, Simulation unit, Identification unit, Trajectory cruise unit, Operating points unit and Expert system unit. The supervisory scheme orchestrates both the off-line preparative actions, as well as the on-line actions that implement the Stepwise Safe Switching Logic. The proposed scheme is a generic tool, that may be easily applied for a variety of industrial control processes and may be implemented as an automation software system, with the use of a high level programming environment, like Matlab.

Keywords: Supervisory systems, safe switching, nonlinear systems.

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Authors: Rafat Alshorman, Walter Hussak

Abstract:

Existing work in temporal logic on representing the execution of infinitely many transactions, uses linear-time temporal logic (LTL) and only models two-step transactions. In this paper, we use the comparatively efficient branching-time computational tree logic CTL and extend the transaction model to a class of multistep transactions, by introducing distinguished propositional variables to represent the read and write steps of n multi-step transactions accessing m data items infinitely many times. We prove that the well known correspondence between acyclicity of conflict graphs and serializability for finite schedules, extends to infinite schedules. Furthermore, in the case of transactions accessing the same set of data items in (possibly) different orders, serializability corresponds to the absence of cycles of length two. This result is used to give an efficient encoding of the serializability condition into CTL.

Keywords: computational tree logic, serializability, multi-step transactions.

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Authors: Shikha Maheshwari, Amit Srivastava

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In medical investigations, uncertainty is a major challenging problem in making decision for doctors/experts to identify the diseases with a common set of symptoms and also has been extensively increasing in medical diagnosis problems. The theory of cross entropy for intuitionistic fuzzy sets (IFS) is an effective approach in coping uncertainty in decision making for medical diagnosis problem. The main focus of this paper is to propose a new intuitionistic fuzzy cross entropy measure (IFCEM), which aid in reducing the uncertainty and doctors/experts will take their decision easily in context of patient’s disease. It is shown that the proposed measure has some elegant properties, which demonstrates its potency. Further, it is also exemplified in detail the efficiency and utility of the proposed measure by using a real life case study of diagnosis the disease in medical science.

Keywords: Intuitionistic fuzzy cross entropy (IFCEM), intuitionistic fuzzy set (IFS), medical diagnosis, uncertainty.

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Authors: Sanjay K.Srivastava, Bhanu Gupta

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In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: Fuzzy differential equations, Impulsive differential equations, Strict stability, Lyapunov function, Razumikhin technique.

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Authors: Liang Zhao, Jili Zhang, Kai Li

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A microcontroller-based fan coil unit (FCU) fuzzy controller is designed and implemented in this paper. The controller employs the concept of duty ratio on the electric valve control, which could make full use of the cooling and dehumidifying capacity of the FCU when the valve is off. The traditional control method and its limitations are analyzed. The hardware and software design processes are introduced in detail. The experimental results show that the proposed method is more energy efficient compared to the traditional controlling strategy. Furthermore, a more comfortable room condition could be achieved by the proposed method. The proposed low-cost FCU fuzzy controller deserves to be widely used in engineering applications.

Keywords: Fan coil unit, duty ratio, fuzzy controller, experiment.

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Zhu Jiaming, Yu Mengna

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In this article, models based on quantitative analysis, physical geometry and regression analysis are established, by using analytic hierarchy process analysis, fuzzy cluster analysis, fuzzy photographic and data fitting. The reasons of various leaf shapes among different species and the differences between the leaf shapes on same tree have been solved by using software, such as Eviews, VB and Matlab. We also successfully estimate the leaf mass of a tree and the correlation with the tree profile.

Keywords: Leaf shape; Mass; Fuzzy cluster; Regression analysis; Eviews; Matlab

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