Search results for: distributed type-2 fuzzy algorithm

Authors: Kouzi Katia

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This paper proposes a Direct Torque Control (DTC) algorithm of dual Stator Induction Motor (DSIM) drive using two approach intelligent techniques: Artificial Neural Network (ANN) approach replaces the switching table selector block of conventional DTC and Mamdani Fuzzy Logic controller (FLC) is used for stator resistance estimation. The fuzzy estimation method is based on an online stator resistance correction through the variations of stator current estimation error and its variation. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of suggested algorithm control is to reduce the hardware complexity of conventional selectors, to avoid the drive instability that may occur in certain situation and ensure the tracking of the actual of the stator resistance. The effectiveness of the technique and the improvement of the whole system performance are proved by results.

Keywords: artificial neural network, direct torque control, dual stator induction motor, fuzzy logic estimator, switching table

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Nousheen Hashmi, Shoab Ahmad Khan

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Active collaboration among the green energy sources and the load demand leads to serious issues related to power quality and stability. The growing number of green energy resources and Distributed-Generators need newer strategies to be incorporated for their operations to keep the power energy stability among green energy resources and micro-grid/Utility Grid. This paper presents a novel technique for energy power management in Grid-Connected Photovoltaic with energy storage system under set of constraints including weather conditions, Load Shedding Hours, Peak pricing Hours by using rule-based fuzzy smart grid controller to schedule power coming from multiple Power sources (photovoltaic, grid, battery) under the above set of constraints. The technique fuzzifies all the inputs and establishes fuzzify rule set from fuzzy outputs before defuzzification. Simulations are run for 24 hours period and rule base power scheduler is developed. The proposed fuzzy controller control strategy is able to sense the continuous fluctuations in Photovoltaic power generation, Load Demands, Grid (load Shedding patterns) and Battery State of Charge in order to make correct and quick decisions.The suggested Fuzzy Rule-based scheduler can operate well with vague inputs thus doesn’t not require any exact numerical model and can handle nonlinearity. This technique provides a framework for the extension to handle multiple special cases for optimized working of the system.

Keywords: photovoltaic, power, fuzzy logic, distributed generators, state of charge, load shedding, membership functions

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Authors: Nattachote Rugthaicharoencheep

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This paper presents a feeder reconfiguration problem in distribution systems. The objective is to minimize the system power loss and to improve bus voltage profile. The optimization problem is subjected to system constraints consisting of load-point voltage limits, radial configuration format, no load-point interruption, and feeder capability limits. A method based on genetic algorithm, a search algorithm based on the mechanics of natural selection and natural genetics, is proposed to determine the optimal pattern of configuration. The developed methodology is demonstrated by a 33-bus radial distribution system with distributed generations and feeder capacitors. The study results show that the optimal on/off patterns of the switches can be identified to give the minimum power loss while respecting all the constraints.

Keywords: network reconfiguration, distributed generation capacitor placement, loss reduction, genetic algorithm

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Authors: Xiong Xie, Yuhang Chen

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Vulnerability discovery technology is a significant field of the current. In this paper, a fuzzy framework based on concolic execution has been proposed. Fuzzy test and symbolic execution are widely used in the field of vulnerability discovery technology. But each of them has its own advantages and disadvantages. During the path generation stage, path traversal algorithm based on generation is used to get more accurate path. During the constraint solving stage, dynamic concolic execution is used to avoid the path explosion. If there is external call, the concolic based on function summary is used. Experiments show that the framework can effectively improve the ability of triggering vulnerabilities and code coverage.

Keywords: concolic execution, constraint solving, fuzzy test, vulnerability discovery

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Authors: Erion Luga, Aksel Seitllari, Kemal Pervanqe

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This study investigates the relation between physical and mechanical properties of concrete paving stones using neuro-fuzzy approach. For this purpose 200 samples of concrete paving stones were selected randomly from different sources. The first phase included the determination of physical properties of the samples such as water absorption capacity, porosity and unit weight. After that the indirect tensile strength test and compressive strength test of the samples were performed. İn the second phase, adaptive neuro-fuzzy approach was employed to simulate nonlinear mapping between the above mentioned physical properties and mechanical properties of paving stones. The neuro-fuzzy models uses Sugeno type fuzzy inference system. The models parameters were adapted using hybrid learning algorithm and input space was fuzzyfied by considering grid partitioning. It is concluded based on the observed data and the estimated data through ANFIS models that neuro-fuzzy system exhibits a satisfactory performance.

Keywords: paving stones, physical properties, mechanical properties, ANFIS

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Authors: Ferinar Moaidi, Mahdi Moaidi

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Environmental issues and the ever-increasing in demand of electrical energy make it necessary to have distributed generation (DG) resources in the power system. In this research, in order to realize the goals of reducing losses and improving the voltage profile in a microgrid, the allocation and sizing of DGs have been used. The proposed Genetic Algorithm (GA) is described from the array of artificial intelligence methods for solving the problem. The algorithm is implemented on the IEEE 33 buses network. This study is presented in two scenarios, primarily to illustrate the effect of location and determination of DGs has been done to reduce losses and improve the voltage profile. On the other hand, decisions made with the one-level assumptions of load are not universally accepted for all levels of load. Therefore, in this study, load modelling is performed and the results are presented for multi-levels load state.

Keywords: distributed generation, genetic algorithm, microgrid, load modelling, loss reduction, voltage improvement

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Authors: Mary Anne Roa

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Congestion in network occurs due to exceed in aggregate demand as compared to the accessible capacity of the resources. Network congestion will increase as network speed increases and new effective congestion control methods are needed, especially for today’s very high speed networks. To address this undeniably global issue, the study focuses on the development of a fuzzy-based congestion control model concerned with allocating the resources of a computer network such that the system can operate at an adequate performance level when the demand exceeds or is near the capacity of the resources. Fuzzy logic based models have proven capable of accurately representing a wide variety of processes. The model built is based on bandwidth, the aggregate incoming traffic and the waiting time. The theoretical analysis and simulation results show that the proposed algorithm provides not only good utilization but also low packet loss.

Keywords: congestion control, queue management, computer networks, fuzzy logic

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Authors: Parth Patel, Ying Zhu

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Distributed systems have become ubiquitous, and they continue their growth through a range of services. With advances in resource virtualization technology such as Virtual Machines (VM) and software containers, developers no longer require high-end servers to test and develop distributed software. Even in commercial production, virtualization has streamlined the process of rapid deployment and service management. This paper introduces a distributed systems testbed that utilizes virtualization to enable distributed systems development on commodity computers. The testbed can be used to develop new services, implement theoretical distributed systems concepts for understanding, and experiment with virtual network topologies. We show its versatility through two case studies that utilize the testbed for implementing a theoretical algorithm and developing our own methodology to find high-risk edges. The results of using the testbed for these use cases have proven the effectiveness and versatility of this testbed across a range of scenarios.

Keywords: distributed systems, experimental testbed, peer-to-peer networks, virtual container technology

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Authors: Soha A. Bahanshal, Byung G. Kim

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Identification of patients at high risk for hospital readmission is of crucial importance for quality health care and cost reduction. Predicting hospital readmissions among diabetic patients has been of great interest to many researchers and health decision makers. We build a prediction model to predict hospital readmission for diabetic patients within 30 days of discharge. The core of the prediction model is a modified k Nearest Neighbor called Hybrid Fuzzy Weighted k Nearest Neighbor algorithm. The prediction is performed on a patient dataset which consists of more than 70,000 patients with 50 attributes. We applied data preprocessing using different techniques in order to handle data imbalance and to fuzzify the data to suit the prediction algorithm. The model so far achieved classification accuracy of 80% compared to other models that only use k Nearest Neighbor.

Keywords: machine learning, prediction, classification, hybrid fuzzy weighted k-nearest neighbor, diabetic hospital readmission

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Authors: M. M. Othman, Walid El-Khattam, Y. G. Hegazy, A. Y. Abdelaziz

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This paper presents a method for finding the optimal location and capacity of dispatchable DGs connected to the distribution feeders for optimal planning for a specified power loss without violating the system practical constraints. The distributed generation units in the proposed algorithm is modeled as voltage controlled node with the flexibility to be converted to constant power node in case of reactive power limit violation. The proposed algorithm is implemented in MATLAB and tested on the IEEE 37-nodes feeder. The results that are validated by comparing it with results obtained from other competing methods show the effectiveness, accuracy and speed of the proposed method.

Keywords: distributed generators, firefly technique, optimization, power loss

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Authors: Tumadhir Fahim M Alsulami

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The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication.

Keywords: BCK, BCI, algebras, derivation

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Authors: Khadidja Belbachir, Hafida Belbachir

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subsequently the expansion of the physical supports storage and the needs ceaseless to accumulate several data, the sequential algorithms of associations’ rules research proved to be ineffective. Thus the introduction of the new parallel versions is imperative. We propose in this paper, a parallel version of a sequential algorithm “Partition”. This last is fundamentally different from the other sequential algorithms, because it scans the data base only twice to generate the significant association rules. By consequence, the parallel approach does not require much communication between the sites. The proposed approach was implemented for an experimental study. The obtained results, shows a great reduction in execution time compared to the sequential version and Count Distributed algorithm.

Keywords: association rules, distributed data mining, partition, parallel algorithms

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Authors: P. Bharathiraja

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Computer Aided decision making system is used to enhance diagnosis and prognosis of diseases and also to assist clinicians and junior doctors in clinical decision making. Medical Data used for decision making should be definite and consistent. Data Mining and soft computing techniques are used for cleaning the data and for incorporating human reasoning in decision making systems. Fuzzy rule based inference technique can be used for classification in order to incorporate human reasoning in the decision making process. In this work, missing values are imputed using the mean or mode of the attribute. The data are normalized using min-ma normalization to improve the design and efficiency of the fuzzy inference system. The fuzzy inference system is used to handle the uncertainties that exist in the medical data. Equal-width-partitioning is used to partition the attribute values into appropriate fuzzy intervals. Fuzzy rules are generated using Class Based Associative rule mining algorithm. The system is trained and tested using heart disease data set from the University of California at Irvine (UCI) Machine Learning Repository. The data was split using a hold out approach into training and testing data. From the experimental results it can be inferred that classification using fuzzy inference system performs better than trivial IF-THEN rule based classification approaches. Furthermore it is observed that the use of fuzzy logic and fuzzy inference mechanism handles uncertainty and also resembles human decision making. The system can be used in the absence of a clinical expert to assist junior doctors and clinicians in clinical decision making.

Keywords: decision making, data mining, normalization, fuzzy rule, classification

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Palash Dutta

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More frequently uncertainties are encountered in medical diagnosis and therefore it is the most important and interesting area of applications of fuzzy set theory. In this present study, an attempt has been made to extend Sanchez’s approach for medical diagnosis via interval valued picture fuzzy sets and exhibit the technique with suitable case studies. In this article, it is observed that a refusal can be expressed in the databases concerning the examined objects. The technique is performing diagnosis on the basis of distance measures and as a result, this approach makes it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

Keywords: medical diagnosis, uncertainty, fuzzy set, picture fuzzy set, interval valued picture fuzzy set

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Authors: Weizhi Zhong, Xiaoyi Lu, Lei Xu

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In order to solve the problem of inaccurate synchronization for distributed multiple-input multiple-output (MIMO) system in multipath environment, a golay pair aided timing synchronization method is proposed in this paper. A new synchronous training sequence based on golay pair is designed. By utilizing the aperiodic auto-correlation complementary property of the new training sequence, the fine timing point is obtained at the receiver. Simulation results show that, compared with the tradition timing synchronization approaches, the proposed algorithm can provide high accuracy in synchronization, especially under multipath condition.

Keywords: distributed MIMO system, golay pair, multipath, synchronization

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Authors: Farahnaz Karami

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Routing is an important, challenging task in mobile ad hoc networks due to node mobility, lack of central control, unstable links, and limited resources. An ant colony has been found to be an attractive technique for routing in Mobile Ad Hoc Networks (MANETs). However, existing swarm intelligence based routing protocols find an optimal path by considering only one or two route selection metrics without considering correlations among such parameters making them unsuitable lonely for routing real time applications. Fuzzy logic combines multiple route selection parameters containing uncertain information or imprecise data in nature, but does not have multipath routing property naturally in order to provide load balancing. The objective of this paper is to design a routing algorithm using fuzzy logic and ant colony that can solve some of routing problems in mobile ad hoc networks, such as nodes energy consumption optimization to increase network lifetime, link failures rate reduction to increase packet delivery reliability and providing load balancing to optimize available bandwidth. In proposed algorithm, the path information will be given to fuzzy inference system by ants. Based on the available path information and considering the parameters required for quality of service (QoS), the fuzzy cost of each path is calculated and the optimal paths will be selected. NS2.35 simulation tools are used for simulation and the results are compared and evaluated with the newest QoS based algorithms in MANETs according to packet delivery ratio, end-to-end delay and routing overhead ratio criterions. The simulation results show significant improvement in the performance of these networks in terms of decreasing end-to-end delay, and routing overhead ratio, and also increasing packet delivery ratio.

Keywords: mobile ad hoc networks, routing, quality of service, ant colony, fuzzy logic

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: Bing Li

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The primitive code-level design patterns (PDP) are the rudimentary programming elements to develop any distributed systems in the generic distributed programming environment, GreatFree. The PDP works with the primitive distributed application programming interfaces (PDA), the distributed modeling, and the distributed concurrency for scaling-up. They not only hide developers from underlying technical details but also support sufficient adaptability to a variety of distributed computing environments. Programming with them, the simplest distributed system, the lightweight messaging two-node client/server (TNCS) system, is constructed rapidly with straightforward and repeatable behaviors, copy-paste-replace (CPR). As any distributed systems are made up of the simplest ones, those PDAs, as well as the PDP, are generic for distributed programming.

Keywords: primitive APIs, primitive code-level design patterns, generic distributed programming, distributed systems, highly patterned development environment, messaging

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Authors: G. S. Thakur

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This paper presents a Fuzzy Soft Recruitment Model (FSRM) for faculty selection of MHRD technical institutions. The selection criteria are based on 4-tier flexible structure in the institutions. The Advisory Committee on Faculty Recruitment (ACoFAR) suggested nine criteria for faculty in the proposed FSRM. The model Fuzzy Soft is proposed with consultation of ACoFAR based on selection criteria. The Fuzzy Soft distance similarity measures are applied for finding best faculty from the applicant pool.

Keywords: fuzzy soft set, fuzzy sets, fuzzy soft distance, fuzzy soft similarity measures, ACoFAR

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Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn

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The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Purnima Pandit

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Malaria remains one of the world’s most deadly infectious disease and arguably, the greatest menace to modern society in terms of morbidity and mortality. To choose the right treatment and to ensure a quality of life suitable for a specific patient condition, early and accurate diagnosis of malaria is essential. It reduces transmission of disease and prevents deaths. Our work focuses on designing an efficient, accurate fuzzy inference system for malaria diagnosis.

Keywords: fuzzy inference system, fuzzy logic, malaria disease, triangular fuzzy number

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Authors: Vahid Anari, Mina Bakhshi

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Visual search and identification of immunohistochemically stained tissue of meningioma was performed manually in pathologic laboratories to detect and diagnose the cancers type of meningioma. This task is very tedious and time-consuming. Moreover, because of cell's complex nature, it still remains a challenging task to segment cells from its background and analyze them automatically. In this paper, we develop and test a computerized scheme that can automatically identify cells in microscopic images of meningioma and classify them into positive (proliferative) and negative (normal) cells. Dataset including 150 images are used to test the scheme. The scheme uses Fuzzy C-means algorithm as a color clustering method based on perceptually uniform hue, saturation, value (HSV) color space. Since the cells are distinguishable by the human eye, the accuracy and stability of the algorithm are quantitatively compared through application to a wide variety of real images.

Keywords: positive cell, color segmentation, HSV color space, immunohistochemistry, meningioma, thresholding, fuzzy c-means

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

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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: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: C. Iraklis, G. Evmiridis, A. Iraklis

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Renewable energy sources and distributed power generation units already have an important role in electrical power generation. A mixture of different technologies penetrating the electrical grid, adds complexity in the management of distribution networks. High penetration of distributed power generation units creates node over-voltages, huge power losses, unreliable power management, reverse power flow and congestion. This paper presents an optimization algorithm capable of reducing congestion and power losses, both described as a function of weighted sum. Two factors that describe congestion are being proposed. An upgraded selective particle swarm optimization algorithm (SPSO) is used as a solution tool focusing on the technique of network reconfiguration. The upgraded SPSO algorithm is achieved with the addition of a heuristic algorithm specializing in reduction of power losses, with several scenarios being tested. Results show significant improvement in minimization of losses and congestion while achieving very small calculation times.

Keywords: congestion, distribution networks, loss reduction, particle swarm optimization, smart grid

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Authors: B. Güney, Ç. Teke

Abstract:

In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Li Ni, Pen ManMan, Li KenLi

Abstract:

Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: chemical reaction optimization, expection maimization, initia, objective function clustering

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