Search results for: uncertainty proximity analysis

Authors: Zhen Wu, David Lupien St-Pierre, Georges Abdul-Nour

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In decision making under strict uncertainty, decision makers have to choose a decision without any information about the states of nature. The classic criteria of Laplace, Wald, Savage, Hurwicz and Starr are introduced and compared in a case study of sewer network planning. Furthermore, results from different criteria are discussed and analyzed. Moreover, this paper discusses the idea that decision making under strict uncertainty (DMUSU) can be viewed as a two-player game and thus be solved by a solution concept in game theory: Nash equilibrium.

Keywords: Decision criteria, decision making, sewer network planning, strict uncertainty.

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Authors: Markus Reichhartinger, Martin Horn

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In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: Yung-Ting Chang, Chung-You Tsai, Yu-Chuan Li

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Nosocomial (i.e., hospital-acquired) infections (NI) is a major cause of morbidity and mortality in hospitals. NI rate is higher in intensive care units (ICU) than in the general ward due to patients with severe symptoms, poor immunity, and accepted many invasive therapies. Contact behaviors between health caregivers and patients is one of the infect factors. It is difficult to obtain complete contact records by traditional method of retrospective analysis of medical records. This paper establishes a contact history inferential model (CHIM) intended to extend the use of Proximity Sensing of rapid frequency identification (RFID) technology to transferring all proximity events between health caregivers and patients into clinical events (close-in events, contact events and invasive events).The results of the study indicated that the CHIM can infer proximity care activities into close-in events and contact events. The infection control team could redesign and build optimal workflow in the ICU according to the patient-specific contact history which provided by our automatic tracing system.

Keywords: Active Radio Frequency Identification, Intensive Care Unit, Nosocomial Infections

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Authors: M. Safaei, M. Seifert, K. D. Thoben

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Supply network management adopts a systematic and integrative approach to managing the operations and relationships of various parties in a supply network. The objective of the manufactures in their supply network is to reduce inventory costs and increase customer satisfaction levels. One way of doing that is to synchronize delivery performance. A supply network can be described by nodes representing the companies and the links (relationships) between these nodes. Uncertainty in delivery time depends on type of network relationship between suppliers. The problem is to understand how the individual uncertainties influence the total uncertainty of the network and identify those parts of the network, which has the highest potential for improving the total delivery time uncertainty.

Keywords: Delivery time uncertainty, Distribution function, Statistical method, Supply Network.

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes

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This article deals with the conceptual modeling under uncertainty. First, the division of information systems with their definition will be described, focusing on those where the construction of a conceptual model is suitable for the design of future information system database. Furthermore, the disadvantages of the traditional approach in creating a conceptual model and database design will be analyzed. A comprehensive methodology for the creation of a conceptual model based on analysis of client requirements and the selection of a suitable domain model is proposed here. This article presents the expert system used for the construction of a conceptual model and is a suitable tool for database designers to create a conceptual model.

Keywords: Conceptual model, conceptual modeling, database, methodology, uncertainty, information system, entity, attribute, relationship, conceptual domain model, fuzzy.

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Authors: Ma Shidong, He Yuncheng, Wang Zhong, Yang Guoqing

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In this paper, enhanced ground proximity warning simulation and validation system is designed and implemented. First, based on square grid and sub-grid structure, the global digital terrain database is designed and constructed. Terrain data searching is implemented through querying the latitude and longitude bands and separated zones of global terrain database with the current aircraft position. A combination of dynamic scheduling and hierarchical scheduling is adopted to schedule the terrain data, and the terrain data can be read and delete dynamically in the memory. Secondly, according to the scope, distance, approach speed information etc. to the dangerous terrain in front, and using security profiles calculating method, collision threat detection is executed in real-time, and provides caution and warning alarm. According to this scheme, the implementation of the enhanced ground proximity warning simulation system is realized. Simulations are carried out to verify a good real-time in terrain display and alarm trigger, and the results show simulation system is realized correctly, reasonably and stable.

Keywords: enhanced ground proximity warning system, digital terrain, look-ahead terrain alarm, terrain display, simulation and validation

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Authors: Hamed Afrasiab, Saeed Khodaygan

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Prediction of machining process capability in the design stage plays a key role to reach the precision design and manufacturing of mechanical products. Inaccuracies in machining process lead to errors in position and orientation of machined features on the part, and strongly affect the process capability in the final quality of the product. In this paper, an efficient systematic approach is given to investigate the machining errors to predict the manufacturing errors of the parts and capability prediction of corresponding machining processes. A mathematical formulation of fixture locators modeling is presented to establish the relationship between the part errors and the related sources. Based on this method, the final machining errors of the part can be accurately estimated by relating them to the combined dimensional and geometric tolerances of the workpiece – fixture system. This method is developed for uncertainty analysis based on the Worst Case and statistical approaches. The application of the presented method is illustrated through presenting an example and the computational results are compared with the Monte Carlo simulation results.

Keywords: Process capability, machining error, dimensional and geometrical tolerances, uncertainty analysis.

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Authors: Ruibiao J. Guo, Brad Cain, Pierre Meunier

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The Integrated Performance Modelling Environment (IPME) is a powerful simulation engine for task simulation and performance analysis. However, it has no high level cognition such as memory and reasoning for complex simulation. This article introduces a knowledge representation and reasoning scheme that can accommodate uncertainty in simulations of military personnel with IPME. This approach demonstrates how advanced reasoning models that support similarity-based associative process, rule-based abstract process, multiple reasoning methods and real-time interaction can be integrated with conventional task network modelling to provide greater functionality and flexibility when modelling operator performance.

Keywords: Computer-Generated Forces, Human Behaviour Representation, IPME, Modelling and Simulation, Uncertainty Reasoning

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Authors: M. Arja, G. Sauce, B. Souyri

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Overall cost is a significant consideration in any decision-making process. Although many studies were carried out on overall cost in construction, little has treated the uncertainties of real life cycle development. On the basis of several case studies, a feedback process was performed on the historical data of studied buildings. This process enabled to identify some factors causing uncertainty during the operational period. As a result, the research proposes a new method for assessing the overall cost during a part of the building-s life cycle taking account of the building actual value, its end-of-life value and the influence of the identified life cycle uncertainty factors. The findings are a step towards a higher level of reliability in overall cost evaluation taking account of some usually unexpected uncertainty factors.

Keywords: Asset management, building life cycle uncertainty, building value, overall cost.

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Authors: S. Dorbani, M. Badaoui, D. Benouar

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The aim of this paper is to investigate the effect of the building fundamental period of reinforced concrete buildings of (6, 9, and 12-storey), with different floor plans: Symmetric, mono-symmetric, and unsymmetric. These structures are erected at different epicentral distances. Using the Boumerdes, Algeria (2003) earthquake data, we focused primarily on the establishment of the deterministic formulation linking the base shear force to two parameters: The first one is the fundamental period that represents the numerical fingerprint of the structure, and the second one is the epicentral distance used to represent the impact of the earthquake on this force. In a second step, with a view to highlight the effect of uncertainty in these parameters on the analyzed response, these parameters are modeled as random variables with a log-normal distribution. The variability of the coefficients of variation of the chosen uncertain parameters, on the statistics on the seismic base shear force, showed that the effect of uncertainty on fundamental period on this force statistics is low compared to the epicentral distance uncertainty influence.

Keywords: Base shear force, fundamental period, epicentral distance, uncertainty, lognormal variable, statistics.

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Authors: M. Tadi, M. Hadi Mohammad Zadeh, Ozge Ogut

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Although how cities’ forms are structured is studied, more efforts are needed on systemic comprehensions and evaluations of the urban morphology through quantitative metrics that are able to describe the performance of a city in relation to its formal properties. More research is required in this direction in order to better describe the urban form characteristics and their impact on the environmental performance of cities and to increase their sustainability stewardship. With the aim of developing a better understanding of the built environment’s systemic structure, the intention of this paper is to present a holistic methodology for studying the behavior of the built environment and investigate the methods for measuring the effect of urban structure to the environmental performance. This goal will be pursued through an inquiry into the morphological components of the urban systems and the complex relationships between them. Particularly, this paper focuses on proximity, referring to the proximity of different land-uses, is a concept with which Integrated Modification Methodology (IMM) explains how land-use allocation might affect the choice of mobility in neighborhoods, and especially, encourage or discourage non-motived mobility. This paper uses proximity to demonstrate that the structure attributes can quantifiably relate to the performing behavior in the city. The target is to devise a mathematical pattern from the structural elements and correlate it directly with urban performance indicators concerned with environmental sustainability. The paper presents some results of this rigorous investigation of urban proximity and its correlation with performance indicators in four different areas in the city of Milan, each of them characterized by different morphological features.

Keywords: Built environment, ecology, sustainable indicators, sustainability, urban morphology.

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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: Xiaohua Liu, Juan F. Beltran, Nishant Mohanchandra, Godfried T. Toussaint

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Support vector machines (SVMs) are considered to be the best machine learning algorithms for minimizing the predictive probability of misclassification. However, their drawback is that for large data sets the computation of the optimal decision boundary is a time consuming function of the size of the training set. Hence several methods have been proposed to speed up the SVM algorithm. Here three methods used to speed up the computation of the SVM classifiers are compared experimentally using a musical genre classification problem. The simplest method pre-selects a random sample of the data before the application of the SVM algorithm. Two additional methods use proximity graphs to pre-select data that are near the decision boundary. One uses k-Nearest Neighbor graphs and the other Relative Neighborhood Graphs to accomplish the task.

Keywords: Machine learning, data mining, support vector machines, proximity graphs, relative-neighborhood graphs, k-nearestneighbor graphs, random sampling, training data condensation.

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Authors: C. Ardil

Abstract:

Using the aid of Hausdorff distance function and Minkowski distance function, this study proposes a novel method for selecting combat aircraft for Air Force. In order to do this, the proximity measure method was developed with determinate fuzzy degrees based on the relationship between attributes and combat aircraft alternatives. The combat aircraft selection attributes were identified as payloadability, maneuverability, speedability, stealthability, and survivability. Determinate fuzzy data from the combat aircraft attributes was then aggregated using the determinate fuzzy weighted arithmetic average operator. For the selection of combat aircraft, correlation analysis of the ranking order patterns of options was also examined. A numerical example from military aviation is used to demonstrate the applicability and effectiveness of the proposed method.

Keywords: Combat aircraft selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Hausdorff distance function, Minkowski distance function, PMM, MCDM

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Authors: E. A. Tkachenko, E. M. Rogova, V. V. Klimov

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One of the basic issues of development management is connected with performance measurement as a prerequisite for identifying the achievement of development objectives. The aim of our research is to develop an improved model of assessing a company’s development results. The model should take into account the cyclical nature of development and the high degree of uncertainty in dealing with numerous management tasks. Our hypotheses may be formulated as follows: Hypothesis 1. The cycle of a company’s development may be studied from the standpoint of a project cycle. To do that, methods and tools of project analysis are to be used. Hypothesis 2. The problem of the uncertainty when justifying managerial decisions within the framework of a company’s development cycle can be solved through the use of the mathematical apparatus of fuzzy logic. The reasoned justification of the validity of the hypotheses made is given in the suggested article. The fuzzy logic toolkit applies to the case of technology shift within an enterprise. It is proven that some restrictions in performance measurement that are incurred to conventional methods could be eliminated by implementation of the fuzzy logic apparatus in performance measurement models.

Keywords: Fuzzy logic, fuzzy sets, performance measurement, project analysis.

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Authors: C. Ardil

Abstract:

The decision to select an unmanned combat aircraft is complicated since several options and conflicting criteria must be considered at simultaneously. When making multiple criteria decision, it is important to consider the selected evaluation criteria, including priceability, payloadability, stealthability, speedability , and survivability. The fundamental goal of the study is to select the best unmanned combat aircraft by taking these evaluation criteria into account. The optimal aircraft was chosen using the fuzzy proximity measure method, which enables decision-makers to designate preferences as standard fuzzy set numbers during the multiple criteria decision-making process. To assess the applicability of the proposed approach, a numerical example is provided. Finally, by comparing determined unmanned combat aircraft, the proposed method produced a successful application, and the best aircraft was selected.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), multiple criteria group decision making (MCGDM), proximity measure method (PMM)

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Authors: Yi Xu, Zexiang Li

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In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.

Keywords: eigenvalue-optimal optimization, freeform surface inspection, sampling size and location, sampled points.

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Authors: Pulak Swain, A. K. Ojha

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Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: Manisha Rathi, Thierry Chaussalet

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Hospital staff and managers are under pressure and concerned for effective use and management of scarce resources. The hospital admissions require many decisions that have complex and uncertain consequences for hospital resource utilization and patient flow. It is challenging to predict risk of admissions and length of stay of a patient due to their vague nature. There is no method to capture the vague definition of admission of a patient. Also, current methods and tools used to predict patients at risk of admission fail to deal with uncertainty in unplanned admission, LOS, patients- characteristics. The main objective of this paper is to deal with uncertainty in health system variables, and handles uncertain relationship among variables. An introduction of machine learning techniques along with statistical methods like Regression methods can be a proposed solution approach to handle uncertainty in health system variables. A model that adapts fuzzy methods to handle uncertain data and uncertain relationships can be an efficient solution to capture the vague definition of admission of a patient.

Keywords: Admission, Fuzzy, Regression, Uncertainty

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Authors: C. Ardil

Abstract:

Aircraft supplier selection process, which is considered as a fundamental supply chain problem, is a multi-criteria group decision problem that has a significant impact on the performance of the entire supply chain. In practical situations are frequently incomplete and uncertain information, making it difficult for decision-makers to communicate their opinions on candidates with precise and definite values. To solve the aircraft supplier selection problem in an environment of incomplete and uncertain information, proximity measure method is proposed. It uses determinate fuzzy numbers. The weights of each decision maker are equally predetermined and the entropic criteria weights are calculated using each decision maker's decision matrix. Additionally, determinate fuzzy numbers, it is proposed to use the weighted normalized Minkowski distance function and Hausdorff distance function to determine the ranking order patterns of alternatives. A numerical example for aircraft supplier selection is provided to further demonstrate the applicability, effectiveness, validity and rationality of the proposed method.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Minkowski distance function, Hausdorff distance function, PMM, MCDM

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Authors: Salsabil Trabelsi, Zied Elouedi, Khaled Mellouli

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The belief decision tree (BDT) approach is a decision tree in an uncertain environment where the uncertainty is represented through the Transferable Belief Model (TBM), one interpretation of the belief function theory. The uncertainty can appear either in the actual class of training objects or attribute values of objects to classify. In this paper, we develop a post-pruning method of belief decision trees in order to reduce size and improve classification accuracy on unseen cases. The pruning of decision tree has a considerable intention in the areas of machine learning.

Keywords: machine learning, uncertainty, belief function theory, belief decision tree, pruning.

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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: Josip Vasilj, Petar Sarajcev, Damir Jakus

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One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

Keywords: Wind power, Uncertainty, Stochastic process, Monte Carlo simulation.

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

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

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

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Authors: Nasr Al-Hinai, Tarek Y. ElMekkawy

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The performance of schedules released to a shop floor may greatly be affected by unexpected disruptions. Thus, this paper considers the flexible job shop scheduling problem when processing times of some operations are represented by a uniform distribution with given lower and upper bounds. The objective is to find a predictive schedule that can deal with this uncertainty. The paper compares two genetic approaches to obtain predictive schedule. To determine the performance of the predictive schedules obtained by both approaches, an experimental study is conducted on a number of benchmark problems.

Keywords: Genetic algorithm, met-heuristic, robust scheduling, uncertainty of processing times

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Authors: Nabilah Filzah Mohd Radzuan, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

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Uncertain data is believed to be an important issue in building up a prediction model. The main objective in the time series uncertainty analysis is to formulate uncertain data in order to gain knowledge and fit low dimensional model prior to a prediction task. This paper discusses the performance of a number of techniques in dealing with uncertain data specifically those which solve uncertain data condition by minimizing the loss of compression properties.

Keywords: Compression properties, uncertainty, uncertain time series, mining technique, weather prediction.

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Authors: Okay Gunes

Abstract:

Unsatisfactory experiences due to an information shortage regarding the future pay-offs of actual choices, yield satisficing decision-making. This research will examine, for the first time in the literature, the motivation behind suboptimal decisions due to uncertainty by subjecting Adam Smith’s and Jeremy Bentham’s assumptions about the nature of the actions that lead to satisficing behavior, in order to clarify the theoretical background of a “consumption-based satisfactory time” concept. The contribution of this paper with respect to the existing literature is threefold: firstly, it is showed in this paper that Adam Smith’s uncertainty is related to the problem of the constancy of ideas and not related directly to beliefs. Secondly, possessions, as in Jeremy Bentham’s oeuvre, are assumed to be just as pleasing, as protecting and improving the actual or expected quality of life, so long as they reduce any displeasure due to the undesired outcomes of uncertainty. Finally, each consumption decision incurs its own satisfactory time period, owed to not feeling hungry, being healthy, not having transportation…etc. This reveals that the level of satisfaction is indeed a behavioral phenomenon where its value would depend on the simultaneous satisfaction derived from all activities.

Keywords: Decision-making, idea and belief, satisficing, uncertainty.

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Authors: Achim Washington, Reece Clothier, Jose Silva

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System Safety Regulations (SSR) are a central component to the airworthiness certification of Unmanned Aircraft Systems (UAS). There is significant debate on the setting of appropriate SSR for UAS. Putting this debate aside, the challenge lies in how to apply the system safety process to UAS, which lacks the data and operational heritage of conventionally piloted aircraft. The limited knowledge and lack of operational data result in uncertainty in the system safety assessment of UAS. This uncertainty can lead to incorrect compliance findings and the potential certification and operation of UAS that do not meet minimum safety performance requirements. The existing system safety assessment and compliance processes, as used for conventional piloted aviation, do not adequately account for the uncertainty, limiting the suitability of its application to UAS. This paper discusses the challenges of undertaking system safety assessments for UAS and presents current and envisaged research towards addressing these challenges. It aims to highlight the main advantages associated with adopting a risk based framework to the System Safety Performance Requirement (SSPR) compliance process that is capable of taking the uncertainty associated with each of the outputs of the system safety assessment process into consideration. Based on this study, it is made clear that developing a framework tailored to UAS, would allow for a more rational, transparent and systematic approach to decision making. This would reduce the need for conservative assumptions and take the risk posed by each UAS into consideration while determining its state of compliance to the SSR.

Keywords: Part 1309 regulations, unmanned aircraft systems, system safety, uncertainty.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

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Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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