Search results for: Fuzzy Vehicle routing problem

Authors: Vivek Kumar Singh, Tripti Singh

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An ad hoc wireless network consists of mobile networks which creates an underlying architecture for communication without the help of traditional fixed-position routers. Ad-hoc On-demand Distance Vector (AODV) is a routing protocol used for Mobile Ad hoc Network (MANET). Nevertheless, the architecture must maintain communication routes although the hosts are mobile and they have limited transmission range. There are different protocols for handling the routing in the mobile environment. Routing protocols used in fixed infrastructure networks cannot be efficiently used for mobile ad-hoc networks, so that MANET requires different protocols. This paper presents the performance analysis of the routing protocols used various parameter-patterns with Two-ray model.

Keywords: AODV, packet transmission rate, pause time, ZRP, QualNet 6.1

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Authors: Salman Naseer, Usman Zafar, Iqra Zafar

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This study explores the implication of Vehicular Adhoc Network (VANET) - in the rural and urban scenarios that is one domain of Mobile Adhoc Network (MANET). VANET provides wireless communication between vehicle to vehicle and also roadside units. The Federal Commission Committee of United States of American has been allocated 75 MHz of the spectrum band in the 5.9 GHz frequency range for dedicated short-range communications (DSRC) that are specifically designed to enhance any road safety applications and entertainment/information applications. There are several vehicular related projects viz; California path, car 2 car communication consortium, the ETSI, and IEEE 1609 working group that have already been conducted to improve the overall road safety or traffic management. After the critical literature review, the selection of routing protocols is determined, and its performance was well thought-out in the urban and rural scenarios. Numerous routing protocols for VANET are applied to carry out current research. Its evaluation was conceded with the help of selected protocols through simulation via performance metric i.e. throughput and packet drop. Excel and Google graph API tools are used for plotting the graphs after the simulation results in order to compare the selected routing protocols which result with each other. In addition, the sum of the output from each scenario was computed to undoubtedly present the divergence in results. The findings of the current study present that DSR gives enhanced performance for low packet drop and high throughput as compared to AODV and DSDV in an urban congested area and in rural environments. On the other hand, in low-density area, VANET AODV gives better results as compared to DSR. The worth of the current study may be judged as the information exchanged between vehicles is useful for comfort, safety, and entertainment. Furthermore, the communication system performance depends on the way routing is done in the network and moreover, the routing of the data based on protocols implement in the network. The above-presented results lead to policy implication and develop our understanding of the broader spectrum of VANET.

Keywords: AODV, DSDV, DSR, Adhoc network

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Authors: Andrey Lebedev, Ilya Dmitrenok, JooYoung Lee, Leonard Johard

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Top-k shortest path routing problem is an extension of finding the shortest path in a given network. Shortest path is one of the most essential measures as it reveals the relations between two nodes in a network. However, in many real world networks, whose diameters are small, top-k shortest path is more interesting as it contains more information about the network topology. Many variations to compute top-k shortest paths have been studied. In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Then, we also propose a top-k distance based graph matching algorithm.

Keywords: graph matching, link prediction, shortest path, similarity

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Lee Myung-Won, Kwak Keun-Chang

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

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

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Authors: Karunambigai Mevani Govindasamy, Sathishkumar Ayyappan

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In this paper, we formulate the algorithm to find out the dominating function parameters of Intuitionistic Fuzzy Graphs(IFG). The methodology we adopted here is converting any physical problem into an IFG, and that has been transformed into Intuitionistic Fuzzy Matrix. Using Linear Program Solver software (LiPS), we found the defined parameters for the given IFG. We obtained these parameters for a path and cycle IFG. This study can be extended to other varieties of IFG. In particular, we obtain the definition of edge dominating function, minimal edge dominating function, fractional edge domination number (γ_if^') and upper fractional edge domination number (Γ_if^') of an intuitionistic fuzzy graph. Also, we formulated an algorithm which is appropriate to work on LiPS to find fractional edge domination number and upper fractional edge domination number of an IFG.

Keywords: fractional edge domination number, intuitionistic fuzzy cycle, intuitionistic fuzzy graph, intuitionistic fuzzy path

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Ramin Karimi

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One of common highly mobile wireless ad hoc networks is Vehicular Ad Hoc Networks. Hence routing in vehicular ad hoc network (VANET) has attracted much attention during the last few years. VANET is characterized by its high mobility of nodes and specific topology patterns. Moreover these networks encounter a significant loss rate and a very short duration of communication. In vehicular ad hoc networks, one of challenging is routing of data due to high speed mobility and changing topology of vehicles. Geographic routing protocols are becoming popular due to advancement and availability of GPS devices. Delay Tolerant Networks (DTNs) are a class of networks that enable communication where connectivity issues like sparse connectivity, intermittent connectivity; high latency, long delay, high error rates, asymmetric data rate, and even no end-to-end connectivity exist. In this paper, we review the existing Geographic Routing Protocols for VANETs and also provide a qualitative comparison of them.

Keywords: vehicular ad hoc networks, mobility, geographic routing, delay tolerant networks

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Authors: Zeynep Sener, Mehtap Dursun

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Supplier evaluation and selection is one of the most important components of an effective supply chain management system. Due to the expanding competition in healthcare, selecting the right medical device suppliers offers great potential for increasing quality while decreasing costs. This paper proposes a fuzzy decision making approach for medical supplier selection. A real-world medical device supplier selection problem is presented to illustrate the application of the proposed decision methodology.

Keywords: fuzzy decision making, fuzzy multiple objective programming, medical supply chain, supplier selection

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Authors: Tomáš Vyčítal

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In a simulation model of a railway system it is important, besides other crucial algorithms, to have correct behaviour of train overtaking in stochastic conditions. This problem is being addressed in many simulation tools focused on railway traffic, however these are not very human-realistic. The goal of this paper is to create a more human-realistic overtaking decision support system for the use in railway traffic simulations. A fuzzy system has been chosen for this task as fuzzy systems are well-suited for human-like decision making. The fuzzy system designed takes into account timetables, train positions, delays and buffer times as inputs and provides an instruction to overtake or not overtake.

Keywords: decision-making support, fuzzy systems, simulation, railway, transport

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Authors: Ali Shareef, Aliha Shareef, Yifeng Zhu

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Energy minimization is of great importance in wireless sensor networks in extending the battery lifetime. One of the key activities of nodes in a WSN is communication and the routing of their data to a centralized base-station or sink. Routing using the shortest path to the sink is not the best solution since it will cause nodes along this path to fail prematurely. We propose a cross-layer energy efficient routing protocol Optrix that utilizes a convex formulation to maximize the lifetime of the network as a whole. We further propose, Optrix-BW, a novel convex formulation with bandwidth constraint that allows the channel conditions to be accounted for in routing. By considering this key channel parameter we demonstrate that Optrix-BW is capable of congestion control. Optrix is implemented in TinyOS, and we demonstrate that a relatively large topology of 40 nodes can converge to within 91% of the optimal routing solution. We describe the pitfalls and issues related with utilizing a continuous form technique such as convex optimization with discrete packet based communication systems as found in WSNs. We propose a routing controller mechanism that allows for this transformation. We compare Optrix against the Collection Tree Protocol (CTP) and we found that Optrix performs better in terms of convergence to an optimal routing solution, for load balancing and network lifetime maximization than CTP.

Keywords: wireless sensor network, Energy Efficient Routing

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Authors: Amin Jamili

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Nowadays, the majority of international trade in goods is carried by sea, and especially by ships deployed in the industrial and tramp segments. This paper addresses routing the tramp ships and determining the schedules including the arrival times to the ports, berthing times at the ports, and the departure times in an operational planning level. In the operational planning level, the weather can be almost exactly forecasted, however in some routes some uncertainties may remain. In this paper, the voyaging times between some of the ports are considered to be uncertain. To that end, a two-stage stochastic mathematical model is proposed. Moreover, a case study is tested with the presented model. The computational results show that this mathematical model is promising and can represent acceptable solutions.

Keywords: routing, scheduling, tram ships, two stage stochastic model, uncertainty

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Authors: Mikheil Kalmakhelidze

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Record linkage (RL) problem has become more and more important in recent years due to the growing interest towards big data analysis. The problem can be formulated in a very simple way: Given two entries a and b of a database, decide whether they represent the same object or not. There are two classical deterministic and probabilistic ways of solving the RL problem. Using simple Bayes classifier in many cases produces useful results but sometimes they show to be poor. In recent years several successful approaches have been made towards solving specific RL problems by neural network algorithms including single layer perception, multilayer back propagation network etc. In our work, we model the RL problem for specific dataset of student applications in fuzzy description logic (FDL) where linkage of specific pair (a,b) depends on the truth value of corresponding formula A(a,b) in a canonical FDL model. As a main result, we build neural network for deciding truth value of FDL formulas in a canonical model and thus link RL problem to machine learning. We apply the approach to dataset with 10000 entries and also compare to classical RL solving approaches. The results show to be more accurate than standard probabilistic approach.

Keywords: description logic, fuzzy logic, neural networks, record linkage

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Authors: M. Devamanalan, K. Pothiraj, M. Sudhan

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In competitive market like India, there is a high demand on the equal contribution on performance and its durability aspect of any system. In General vehicle has multiple sub-systems such as powertrain, BIW, Brakes, Actuations, Suspension and Seats etc., To withstand the market challenges, the contribution of each sub-system is very vital. The malfunction of any one sub system will directly have an impact on the performance of the major system which lead to dis-satisfaction to the end user. The Powertrain system consists of several sub-systems in which clutch is one of the prime sub-systems in MT vehicles which assist for smoother gear shifts with proper clutch dis-engagement and engagement. In general, most of the vehicles will have a mechanical or semi or full hydraulic clutch release system, whereas in small Commercial Vehicles (SCV) the majorly used clutch release system is mechanical cable release system due to its lesser cost and functional requirements. The major bottle neck in the cable type clutch release system is increase in pedal effort due to hysteresis increase and Gear shifting hard due to efficiency loss / cable slackness over the mileage accumulation of the vehicle. This study is to mainly focus on how the efficiency and hysteresis change over the mileage of the vehicle occurs because of the design architecture of outer and inner cable. The study involves several cable design validation results from vehicle level and rig level through the defined cable routing and test procedures. Results are compared to evaluate the suitable cable design architecture based on better efficiency and lower hysteresis parameters at initial and end of the validation.

Keywords: clutch, clutch cable, efficiency, architecture, cable routing

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Authors: Brahim Ferdi, Samira Dib

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The unified power quality conditioner (UPQC), a combination of shunt and series active power filter, is one of the best solutions towards the mitigation of voltage and current harmonics problems in distribution power system. PI controller is very common in the control of UPQC. However, one disadvantage of this conventional controller is the difficulty in tuning its gains (Kp and Ki). To overcome this problem, an adaptive fuzzy logic PI controller is proposed. The controller is composed of fuzzy controller and PI controller. According to the error and error rate of the control system and fuzzy control rules, the fuzzy controller can online adjust the two gains of the PI controller to get better performance of UPQC. Simulations using MATLAB/SIMULINK are carried out to verify the performance of the proposed controller. The results show that the proposed controller has fast dynamic response and high accuracy of tracking the current and voltage references.

Keywords: adaptive fuzzy PI controller, current harmonics, PI controller, voltage harmonics, UPQC

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Authors: Manoj Kumar

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Routing protocols have a central role in any mobile ad hoc network (MANET). There are many routing protocols that exhibit different performance levels in different scenarios. In this paper, we compare AODV, DSDV, DSR, and ZRP routing protocol in mobile ad hoc networks to determine the best operational conditions for each protocol. We analyze these routing protocols by extensive simulations in OPNET simulator and show how to pause time and the number of nodes affect their performance. In this study, performance is measured in terms of control traffic received, control traffic sent, data traffic received, sent data traffic, throughput, retransmission attempts.

Keywords: AODV, DSDV, DSR, ZRP

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Authors: Si-Gwan Kim

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Small-size and low-power sensors with sensing, signal processing and wireless communication capabilities is suitable for the wireless sensor networks. Due to the limited resources and battery constraints, complex routing algorithms used for the ad-hoc networks cannot be employed in sensor networks. In this paper, we propose node-disjoint multi-path hexagon-based routing algorithms in wireless sensor networks. We suggest the details of the algorithm and compare it with other works. Simulation results show that the proposed scheme achieves better performance in terms of efficiency and message delivery ratio.

Keywords: clustering, multi-path, routing protocol, sensor network

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Authors: U. Chattaraj, K. Dhusiya, M. Raviteja

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Perception reaction time of drivers is an outcome of human thought process, which is vague and approximate in nature and also varies from driver to driver. So, in this study a fuzzy logic based model for prediction of the same has been presented, which seems suitable. The control factors, like, age, experience, intensity of driving of the driver, speed of the vehicle and distance of stimulus have been considered as premise variables in the model, in which the perception reaction time is the consequence variable. Results show that the model is able to explain the impacts of the control factors on perception reaction time properly.

Keywords: driver, fuzzy logic, perception reaction time, premise variable

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Authors: Mohammad Ali Farrokhpour

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In the current decade and sustainable transportation systems, scooter sharing has attracted widespread attention as an environmentally-friendly means of public transportation which can help develop public transportation. The combination of scooters and subway in the area of sustainable transportation systems can provide a great many opportunities for developing access to public transportation. Of the challenges which have arisen and initiated discussions of interest about the implementation of a scooter-subway system to replace personal vehicles is the issue of routing in the aforementioned system. This has been chosen as the main subject of the present paper. Thus, the present paper provides an account for routing in this system. Because the issue of routing includes multiple factors such as time, costs, traffic, green spaces, etc., the above-mentioned problem is considered to be a multi-objective NP-hard optimization problem. For this purpose, the hybrid optimization approach of PSO-GA has been put forward in the present paper for the provided answers to be of higher accuracy and validity than those of normal optimization methods. The results obtained from modeling and problem solving for the case study in the MATLAB software are indicative of the efficiency and desirability of the model and the proposed approach for solving the model

Keywords: route planning, scooter sharing, public transportation, sharing system

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Authors: M. H. Fazel Zarandi, N. Moshahedi

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The hub location problem appears in a variety of applications such as medical centers, firefighting facilities, cargo delivery systems and telecommunication network design. The location of service centers has a strong influence on the congestion at each of them, and, consequently, on the quality of service. This paper presents a fuzzy maximal hub covering location problem (FMCHLP) in which travel costs between any pair of nodes is considered as a fuzzy variable. In order to consider the quality of service, we model each hub as a queue. Arrival rate follows Poisson distribution and service rate follows Erlang distribution. In this paper, at first, a nonlinear mathematical programming model is presented. Then, we convert it to the linear one. We solved the linear model using GAMS software up to 25 nodes and for large sizes due to the complexity of hub covering location problems, and simulated annealing algorithm is developed to solve and test the model. Also, we used possibilistic c-means clustering method in order to find an initial solution.

Keywords: fuzzy modeling, location, possibilistic clustering, queuing

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Authors: Habib Gorine, Rabia Saleh

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Mobile Ad-Hoc Networks are the special type of wireless networks which share common security requirements with other networks such as confidentiality, integrity, authentication, and availability, which need to be addressed in order to secure data transfer through the network. Their routing protocols are vulnerable to various malicious attacks which could have a devastating consequence on data security. In this paper, three types of attacks such as selfish, gray hole, and black hole attacks have been applied to the two most important routing protocols in MANET named dynamic source routing and ad-hoc on demand distance vector in order to analyse and compare the impact of these attacks on the Network performance in terms of throughput, average delay, packet loss, and consumption of energy using NS2 simulator.

Keywords: MANET, wireless networks, routing protocols, malicious attacks, wireless networks simulation

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

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Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: group decision making, intuitionistic fuzzy set, intuitionistic fuzzy entropy measure, vendor selection, VIKOR

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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: Babek Erdebilli

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The aim of this study is to develop and describe a new methodology for the Multi-Criteria Decision-Making (MCDM) problem using IFE (Elimination Et Choix Traduisant La Realite (ELECTRE) model. The proposed models enable Decision-Makers (DMs) on the assessment and use Intuitionistic Fuzzy Numbers (IFN). A numerical example is provided to demonstrate and clarify the proposed analysis procedure. Also, an empirical experiment is conducted to validation the effectiveness.

Keywords: multi-criteria decision-making, IFE, DM’s, fuzzy electre model

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Authors: Syed Talib Abbas Raza, Tahseen Ahmed Jilani, Saleem Abdullah

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This paper presents interval-valued intuitionistic fuzzy soft sets based TOPSIS method for group decision making. The interval-valued intuitionistic fuzzy soft set is a mutation of an interval-valued intuitionistic fuzzy set and soft set. In group decision making problems IVIFSS makes the process much more algebraically elegant. We have used weighted arithmetic averaging operator for aggregating the information and define a new Hybrid Score Function as metric tool for comparison between interval-valued intuitionistic fuzzy values. In an illustrative example we have applied the developed method to a criminological problem. We have developed a group decision making model for integrating the imprecise and hesitant evaluations of multiple law enforcement agencies working on target killing cases in the country.

Keywords: group decision making, interval-valued intuitionistic fuzzy soft set, TOPSIS, score function, criminology

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Authors: Zabeehullah, Fahim Arif, Yawar Abbas

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Software Defined Network (SDN) is a next genera-tion networking model which simplifies the traditional network complexities and improve the utilization of constrained resources. Currently, most of the SDN based Internet of Things(IoT) environments use traditional network routing strategies which work on the basis of max or min metric value. However, IoT network heterogeneity, dynamic traffic flow and complexity demands intelligent and self-adaptive routing algorithms because traditional routing algorithms lack the self-adaptions, intelligence and efficient utilization of resources. To some extent, SDN, due its flexibility, and centralized control has managed the IoT complexity and heterogeneity but still Software Defined IoT (SDIoT) lacks intelligence. To address this challenge, we proposed a model called Deep Routing Strategy (DRS) which uses Deep Learning algorithm to perform routing in SDIoT intelligently and efficiently. Our model uses real-time traffic for training and learning. Results demonstrate that proposed model has achieved high accuracy and low packet loss rate during path selection. Proposed model has also outperformed benchmark routing algorithm (OSPF). Moreover, proposed model provided encouraging results during high dynamic traffic flow.

Keywords: SDN, IoT, DL, ML, DRS

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Authors: Noman Shabbir, Roheel Nawaz, Muhammad N. Iqbal, Junaid Zafar

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This paper focuses on the performance evaluation of routing protocols in WLAN based Wireless Sensor Networks (WSNs). A comparative analysis of routing protocols such as Ad-hoc On-demand Distance Vector Routing System (AODV), Dynamic Source Routing (DSR) and Optimized Link State Routing (OLSR) is been made against different network parameters like network load, end to end delay and throughput in small, medium and large-scale sensor network scenarios to identify the best performing protocol. Simulation results indicate that OLSR gives minimum network load in all three scenarios while AODV gives the best throughput in small scale network but in medium and large scale networks, DSR is better. In terms of delay, OLSR is more efficient in small and medium scale network while AODV is slightly better in large networks.

Keywords: WLAN, WSN, AODV, DSR, OLSR

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Authors: Behnam Tavakkol

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Uncertain data mining algorithms use different ways to consider uncertainty in data such as by representing a data object as a sample of points or a probability distribution. Fuzzy methods have long been used for clustering traditional (certain) data objects. They are used to produce non-crisp cluster labels. For uncertain data, however, besides some uncertain fuzzy k-medoids algorithms, not many other fuzzy clustering methods have been developed. In this work, we develop a fuzzy kernel k-medoids algorithm for clustering uncertain data objects. The developed fuzzy kernel k-medoids algorithm is superior to existing fuzzy k-medoids algorithms in clustering data sets with non-linearly separable clusters.

Keywords: clustering algorithm, fuzzy methods, kernel k-medoids, uncertain data

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Authors: J. Van Engeland, C. Lavigne, S. De Jaeger

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In the light of the transition towards a more circular economy, recovery of products, parts or materials will gain in importance. Additionally, the EU proximity principle related to waste management and emissions generated by transporting large amounts of end-of-life products, shift attention to local recovery networks. The Flemish inter-communal cooperation for municipal solid waste management Meetjesland (IVM) is currently investigating the set-up of such a network. More specifically, the network encompasses the recycling of polyvinyl chloride (PVC), which is collected in separate containers. When these containers are full, a truck should transport them to the processor which can recycle the PVC into new products. This paper proposes a model to optimize the container collection. The containers are located at different Civic Amenity sites (CA sites) in a certain region. Since people can drop off their waste at these CA sites, the containers will gradually fill up during a planning horizon. If a certain container is full, it has to be collected and replaced by an empty container. The collected waste is then transported to a single processor. To perform this collection and transportation of containers, the responsible firm has a set of vehicles stationed at a single depot and different personnel crews. A vehicle can load exactly one container. If a trailer is attached to the vehicle, it can load an additional container. Each day of the planning horizon, the different crews and vehicles leave the depot to collect containers at the different sites. After loading one or two containers, the crew has to drive to the processor for unloading the waste and to pick up empty containers. Afterwards, the crew can again visit sites or it can return to the depot to end its collection work for that day. All along the collection process, the crew has to respect the opening hours of the sites. In order to allow for some flexibility, a crew is allowed to wait a certain amount of time at the gate of a site until it opens. The problem described can be modelled as a variant to the PVRP-TW (Periodic Vehicle Routing Problem with Time Windows). However, a vehicle can at maximum load two containers, hence only two subsequent site visits are possible. For that reason, we will refer to the model as a model for building tactical waste collection schemes. The goal is to a find a schedule describing which crew should visit which CA site on which day to minimize the number of trucks and the routing costs. The model was coded in IBM CPLEX Optimization studio and applied to a number of test instances. Good results were obtained, and specific suggestions concerning route and truck costs could be made. For a large range of input parameters, collection schemes using two trucks are obtained.

Keywords: container collection, crew scheduling, mixed integer linear programming, waste management

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