Search results for: uncertainty analysis

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

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

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

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Authors: Amer S. Al-Yahmadi, T.C. Hsia

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This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Keywords: Sliding mode control, cooperative manipulators.

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Authors: H. Zabiri, N. Mazuki

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Several valve stiction models have been proposed in the literature to help understand and study the behavior of sticky valves. In this paper, an alternative black-box modeling approach based on Neural Network (NN) is presented. It is shown that with proper network type and optimum model structures, the performance of the developed NN stiction model is comparable to other established method. The resulting NN model is also tested for its robustness against the uncertainty in the stiction parameter values. Predictive mode operation also shows excellent performance of the proposed model for multi-steps ahead prediction.

Keywords: Control valve stiction, neural network, modeling.

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Authors: A. M. Hassanain, Nader M. A. Mohamed, M. Naguib Aly, Alya A. Badawi, M. A. Gaheen

Abstract:

The thermal, epithermal and fast fluxes were calculated for three irradiation channels at Egypt Second Research Reactor (ETRR-2) using CITVAP code. The validity of the calculations was verified by experimental measurements. There are some deviations between measurements and calculations. This is due to approximations in the calculation models used, homogenization of regions, condensation of energy groups and uncertainty in nuclear data used. Neutron flux data for the three irradiation channels are now available. This would enable predicting the irradiation conditions needed for future radioisotope production.

Keywords: ETRR-2, Neutron flux, Radioisotope production, CITVAP

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Authors: Debabrata Das, Pankaj Dutta

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Along with forward supply chain organization needs to consider the impact of reverse logistics due to its economic advantage, social awareness and strict legislations. In this paper, we develop a system dynamics framework for a closed-loop supply chain with fuzzy demand and fuzzy collection rate by incorporating product exchange policy in forward channel and various recovery options in reverse channel. The uncertainty issues associated with acquisition and collection of used product have been quantified using possibility measures. In the simulation study, we analyze order variation at both retailer and distributor level and compare bullwhip effects of different logistics participants over time between the traditional forward supply chain and the closed-loop supply chain. Our results suggest that the integration of reverse logistics can reduce order variation and bullwhip effect of a closed-loop system. Finally, sensitivity analysis is performed to examine the impact of various parameters on recovery process and bullwhip effect.

Keywords: Bullwhip Effect, Fuzzy Possibility Measures, Reverse Supply Chain, System Dynamics.

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Authors: Dorota Kobus-Ostrowska

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Work for everyone, especially for person with disability is a condition in independence; it secures basic needs and develops manual and intellectual capabilities. The work is a source of income, and it builds and strengthens of self-esteem and competence. The purpose of this article is to identify work as an important factor in everyone’s life, despite Polish disabled persons rarely having the chance to undertake a job. In order to achieve this purpose, two methods were used: comparative and qualitative. The theoretical part of this article is based on studies of a wide range of Polish and foreign literature devoted to the issue of the occupational development of people with disabilities. The article was also enriched with the institutional and legal analysis types of support for people with disabilities in Poland. Currently, a Polish person with disability who wants to enter or return to the labor market is under a special protection. Those entities employing workers with disabilities may obtain a subsidy for the salary of a person with disabilities. Unfortunately, people with disability in Poland rarely participate in the workforce. The factors that contribute to this include the difficulty in obtaining work, the uncertainty of keeping it, and the low salary offered. Despite that domestic and foreign literature highlight the important role of disabled people as a workforce, very few people with disability in Poland are economically active.

Keywords: Disabled person, work, employer, rehabilitation.

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Authors: B. Kettana

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Nowadays, financial and economic crises are growing more and reach more countries and sectors. These events have, as a result, a considerable impact on the activities of the firms which think unstable and in danger. But besides this heavy uncertainty which weighs on the different firms, the family firm, object of our research, is not only confronted with these external difficulties but also with an internal challenge and of size: that of transmission. Indeed, the transmission of an organization from one generation to another can succeed as it can fail; leaving considerable damage. Our research registers as part of these problems since we tried to understand relation between the behavior of two main actors of the process of succession, predecessor and successor; and the success of transmission.

Keywords: Family business, transmission, success, predecessor, successor.

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Authors: A. Ehsani, A. Karimizadeh, H. Fallahi, A. Jalali

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In an electric power system, spinning reserve requirements can be determined by using deterministic and/or probabilistic measures. Although deterministic methods are usual in many systems, application of probabilistic methods becomes increasingly important in the new environment of the electric power utility industry. This is because of the increased uncertainty associated with competition. In this paper 1) a new probabilistic method is presented which considers the reliability of transmission system in a simplified manner and 2) deterministic and probabilistic methods are compared. The studied methods are applied to the Roy Billinton Test System (RBTS).

Keywords: Reliability, Spinning Reserve, Risk, Transmission, Unit Commitment.

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Authors: Ali Salehipour

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After presenting the theory of calendar function of Iran-s cross-vaults especially “Niasar" cross-vault in recent years, there has been lots of doubts and uncertainty about this theory by astrologists and archaeologists. According to this theory “Niasar cross-vault and other cross-vaults of Iran has calendar function and are constructed in a way that sunrise and sunset can be seen from one of its openings in the beginning and middle of each season of year". But, mentioning historical documentaries we conclude here that the theory of calendar function of Iran-s cross-vaults does not have any strong basis and individual cross-vaults had only religious function in Iran.

Keywords: cross-vault, fire temple, Calendar function, Sassanid period

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: Optimal control, ensemble Kalman Filter, topography reconstruction, data assimilation, shallow water equations.

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Authors: Leszek Chybowski, Artur Bejger, Katarzyna Gawdzińska

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Subversion analysis is a tool used in the TRIZ (Theory of Inventive Problem Solving) methodology. This article introduces the history and describes the process of subversion analysis, as well as function analysis and analysis of the resources, used at the design stage when generating possible undesirable situations. The article charts the course of subversion analysis when applied to a fuel injection nozzle of a marine engine. The work describes the fuel injector nozzle as a technological system and presents principles of analysis for the causes of a cracked tip of the nozzle body. The system is modelled with functional analysis. A search for potential causes of the damage is undertaken and a cause-and-effect analysis for various hypotheses concerning the damage is drawn up. The importance of particular hypotheses is evaluated and the most likely causes of damage identified.

Keywords: Complex technical system, fuel injector, function analysis, importance analysis, resource analysis, sabotage analysis, subversion analysis, TRIZ.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

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Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Aparna Viswanath

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Electricity spot prices are highly volatile under optimal generation capacity scenarios due to factors such as nonstorability of electricity, peak demand at certain periods, generator outages, fuel uncertainty for renewable energy generators, huge investments and time needed for generation capacity expansion etc. As a result market participants are exposed to price and volume risk, which has led to the development of risk management practices. This paper provides an overview of risk management practices by market participants in electricity markets using financial derivatives.

Keywords: Financial Derivatives, Forward, Futures, Options, Risk Management.

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Authors: D. Kubiliute

Abstract:

The Republic of Lithuania is known as a trusted location for global business institutions and it attracts investors with its competitive environment for financial service providers. Along with the aspiration to offer a strong results-oriented and innovations-driven environment for financial service providers, Lithuanian regulatory authorities consistently implement the European Union's high regulatory standards for financial activities including sustainability-related disclosures. Since the European Union directed its policy towards transition to a climate-neutral, green, competitive and inclusive economy, additional regulatory requirements for financial market participants are adopted: disclosure of sustainable activities, transparency, prevention of greenwashing, and other. The financial sector is one of the key factors influencing the implementation of sustainability objectives in the European Union policies and mitigating the negative effects of climate change – public funds are not enough to make a significant impact on sustainable investments, therefore directing public and private capital to green projects may help to finance the necessary changes. The topic of the study is original and has not yet been widely analyzed in Lithuanian legal discourse. There are used quantitative and qualitative methodologies, logical, systematic and critical analysis principles, hence the aim of this study is to reveal the problematic of the implementation of regulation on sustainability in the Lithuanian financial sector. Additional regulatory requirements could cause serious changes in financial business operations: additional funds, employees and time have to be dedicated in order the companies could implement these regulations. Lack of knowledge and data on how to implement new regulatory requirements towards sustainable reporting causes a lot of uncertainty for financial market participants. And for some companies it might even be an essential point in terms of business continuity. It is considered that the supervisory authorities should find a balance between financial market needs and legal regulation.

Keywords: Financial, market participant, legal, regulation, sustainability.

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Authors: Adam Niewiadomski

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Political transition of agricultural properties in Poland and the former German Democratic Republic (GDR) after 1989 had to include not only Reprivatization but also the issue of returning the properties in kind to their former owners. Restitution in kind applied in GDR to all forms of ownership which were subject to expropriation between 1933 and 1989 except for properties taken over during Soviet occupation in 1945-49. This issue was one of the flashpoints during the process of ownership changes. Privatization, limited as it was, took place in unequal legal environment where only one group of owners was privileged. Executing restitution in kind created a feeling of uncertainty among potential real estate buyers.

Keywords: Reprivatization, agricultural properties, German Democratic Republic, Privatization

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Authors: L. Bennaceur Farah, I. R. Farah, R. Bennaceur, Z. Belhadj, M. R. Boussema

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The overall objective of this paper is to retrieve soil surfaces parameters namely, roughness and soil moisture related to the dielectric constant by inverting the radar backscattered signal from natural soil surfaces. Because the classical description of roughness using statistical parameters like the correlation length doesn't lead to satisfactory results to predict radar backscattering, we used a multi-scale roughness description using the wavelet transform and the Mallat algorithm. In this description, the surface is considered as a superposition of a finite number of one-dimensional Gaussian processes each having a spatial scale. A second step in this study consisted in adapting a direct model simulating radar backscattering namely the small perturbation model to this multi-scale surface description. We investigated the impact of this description on radar backscattering through a sensitivity analysis of backscattering coefficient to the multi-scale roughness parameters. To perform the inversion of the small perturbation multi-scale scattering model (MLS SPM) we used a multi-layer neural network architecture trained by backpropagation learning rule. The inversion leads to satisfactory results with a relative uncertainty of 8%.

Keywords: Remote sensing, rough surfaces, inverse problems, SAR, radar scattering, Neural networks and Fractals.

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Authors: Ali Haroonabadi, Mohammad Teshnehlab

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None of the processing models in the software development has explained the software systems performance evaluation and modeling; likewise, there exist uncertainty in the information systems because of the natural essence of requirements, and this may cause other challenges in the processing of software development. By definition an extended version of UML (Fuzzy- UML), the functional requirements of the software defined uncertainly would be supported. In this study, the behavioral description of uncertain information systems by the aid of fuzzy-state diagram is crucial; moreover, the introduction of behavioral diagrams role in F-UML is investigated in software performance modeling process. To get the aim, a fuzzy sub-profile is used.

Keywords: Fuzzy System, Software Development Model, Software Performance Evaluation, UML

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Authors: Dominykas Broga

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Until recently it would have been unusual to consider classifying population movements and refugees as security problem. However, efforts at shaping our world to make ourselves secure have paradoxically led to ever greater insecurity. The feeling of uncertainty, pertinent throughout all discourses of security, has led to the creation of security production into seemingly benign routines of everyday life. Yet, the paper argues, neither of security discourses accounted for, disclosed and challenged the fundamental aporias embedded in Western security narratives. In turn, the paper aims to unpick the conventional security wisdom, which is haunted with strong ontologies, embedded in the politics of Orientalism, and (in)security nexus. The paper concludes that current security affair conceals the integral impossibility of fulfilling its very own promise of assured security. The paper also provides suggestions about alternative security discourse based on mutual dialogue.

Keywords: Identity, (in)security, migration, ontology

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Authors: A. Aydarous, M. El Ghazaly

Abstract:

The purpose of this study was to investigate the response of the newly released Gafchromic HD-V2 film for alpha particle of 5.5 MeV. Gafchromic HD-V2 was exposed to alpha particles of energy 5 MeV from 241Am for different durations. Then the films were scanned with a flatbed scanner. The dose response curve up to 2200 Gy has been achieved. The film’s reproducibility and sensitivity were evaluated. The results obtained show that the net optical density increases almost exponentially with the increase in the exposure time, and it becomes saturated after prolonged exposure times. The red channel shows the highest sensitivity, with a value of 4 x 10-3 Gy-1 at netOD of 0.4. The inter-film reproducibility was measured and the relative uncertainty found was 1.7 %, 2.1 % and 2.3 % for grey, red and green channels, respectively.

Keywords: Alpha dosimetry, 241Am, Gafchromic film.

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Authors: Musbah M. Aqel, P. K. Mahanti, Soumya Banerjee

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This paper describes a simulation model for analyzing artificial emotion injected to design the game characters. Most of the game storyboard is interactive in nature and the virtual characters of the game are equipped with an individual personality and dynamic emotion value which is similar to real life emotion and behavior. The uncertainty in real expression, mood and behavior is also exhibited in game paradigm and this is focused in the present paper through a fuzzy logic based agent and storyboard. Subsequently, a pheromone distribution or labeling is presented mimicking the behavior of social insects.

Keywords: Artificial Emotion, Fuzzy logic, Game character, Pheromone label

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Authors: Bogdan Walek, Vladimir Bradac, Radim Farana

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Distance learning systems offer useful methods of learning and usually contain a final course test or another form of test. The paper proposes a web application for evaluating tests using an expert system in distance learning systems. The proposed web application is appropriate for didactic tests or tests with results for subsequent studying follow-up courses. The web application works with test questions and uses an expert system and LFLC tool for test evaluation. After test evaluation, the results are visualized and shown to the student.

Keywords: Distance learning, test, uncertainty, fuzzy, expert system, student.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

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Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE work parameters have fuzzy character. Hence consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics changes- dynamics of GTE work parameters allows drawing conclusion on necessity of the Fuzzy Statistical Analysis at preliminary identification of the engines' technical condition. Researches of correlation coefficients values- changes shows also on their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (Hard Computing technology is used) on measurements of input and output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stageby- stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha

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Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.

Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.

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Authors: George Yungchih Wang

Abstract:

Real options theory suggests that managerial flexibility embedded within irreversible investments can account for a significant value in project valuation. Although the argument has become the dominant focus of capital investment theory over decades, yet recent survey literature in capital budgeting indicates that corporate practitioners still do not explicitly apply real options in investment decisions. In this paper, we explore how real options decision criteria can be transformed into equivalent capital budgeting criteria under the consideration of uncertainty, assuming that underlying stochastic process follows a geometric Brownian motion (GBM), a mixed diffusion-jump (MX), or a mean-reverting process (MR). These equivalent valuation techniques can be readily decomposed into conventional investment rules and “option impacts", the latter of which describe the impacts on optimal investment rules with the option value considered. Based on numerical analysis and Monte Carlo simulation, three major findings are derived. First, it is shown that real options could be successfully integrated into the mindset of conventional capital budgeting. Second, the inclusion of option impacts tends to delay investment. It is indicated that the delay effect is the most significant under a GBM process and the least significant under a MR process. Third, it is optimal to adopt the new capital budgeting criteria in investment decision-making and adopting a suboptimal investment rule without considering real options could lead to a substantial loss in value.

Keywords: real options, capital budgeting, geometric Brownianmotion, mixed diffusion-jump, mean-reverting process

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Authors: K. M. Alsager, N. O. Alshehri

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In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

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Authors: Nan-Ying Yu, Shao-Hsia Chang

Abstract:

This study explores the clinical features of neurodegenerative disease patients with tremor. We study the motor impairments in patients with Parkinson’s disease (PD) and essential tremor (ET). Since uncertainty exists on whether Parkinson's disease (PD) and essential tremor (ET) patients have similar degree of impairment during motor tasks, this study based on the self-developed computerized handwriting movement analysis to characterize motor functions of these two impairments. The recruited subjects were diagnosed and confirmed one of neurodegenerative diseases. They were undergone general clinical evaluations by physicians in the first year. We recruited 8 participants with PD and 10 with ET. Additional 12 participants without any neuromuscular dysfunction were recruited as control group. This study used fine motor control of penmanship on digital tablet for sensorimotor function tests. The movement speed in PD/ET group is found significant slower than subjects in normal control group. In movement intensity and speed, the result found subject with ET has similar clinical feature with PD subjects. The ET group shows smaller and slower movements than control group but not to the same extent as PD group. The results of this study contribute to the early screening and detection of diseases and the evaluation of disease progression.

Keywords: Parkinson’s disease, essential tremor, motor function, fine motor movement, computerized handwriting evaluation.

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Authors: M. Sedighizadeh, M. Rezaei, V. Najmi

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The Proton Exchange Membrane Fuel Cell (PEMFC) control system has an important effect on operation of cell. Traditional controllers couldn-t lead to acceptable responses because of time- change, long- hysteresis, uncertainty, strong- coupling and nonlinear characteristics of PEMFCs, so an intelligent or adaptive controller is needed. In this paper a neural network predictive controller have been designed to control the voltage of at the presence of fluctuations of temperature. The results of implementation of this designed NN Predictive controller on a dynamic electrochemical model of a small size 5 KW, PEM fuel cell have been simulated by MATLAB/SIMULINK.

Keywords: PEMFC, Neural Network, Predictive Control..

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Authors: Agnes Achs

Abstract:

The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of multivalued knowledgebase will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a function set of the program, which help us to determine the uncertainty levels of the results. At first the concept of fuzzy Datalog will be summarized, then its extensions for intuitionistic- and interval-valued fuzzy logic is given and the concept of bipolar fuzzy Datalog is introduced. Based on these extensions the concept of multivalued knowledge-base will be defined. This knowledge-base can be a possible background of a future agent-model.

Keywords: Fuzzy-, intuitionistic-, bipolar datalog, multivalued knowledge-base

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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