Search results for: default definite decision rule
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1823

Search results for: default definite decision rule

1793 Learning Algorithms for Fuzzy Inference Systems Composed of Double- and Single-Input Rule Modules

Authors: Hirofumi Miyajima, Kazuya Kishida, Noritaka Shigei, Hiromi Miyajima

Abstract:

Most of self-tuning fuzzy systems, which are automatically constructed from learning data, are based on the steepest descent method (SDM). However, this approach often requires a large convergence time and gets stuck into a shallow local minimum. One of its solutions is to use fuzzy rule modules with a small number of inputs such as DIRMs (Double-Input Rule Modules) and SIRMs (Single-Input Rule Modules). In this paper, we consider a (generalized) DIRMs model composed of double and single-input rule modules. Further, in order to reduce the redundant modules for the (generalized) DIRMs model, pruning and generative learning algorithms for the model are suggested. In order to show the effectiveness of them, numerical simulations for function approximation, Box-Jenkins and obstacle avoidance problems are performed.

Keywords: Box-Jenkins’s problem, Double-input rule module, Fuzzy inference model, Obstacle avoidance, Single-input rule module.

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1792 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories

Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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1791 Aircraft Supplier Selection using Multiple Criteria Group Decision Making Process with Proximity Measure Method for Determinate Fuzzy Set Ranking Analysis

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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1790 Analyzing the Relation of Community Group for Research Paper Bookmarking by Using Association Rule

Authors: P. Jomsri

Abstract:

Currently searching through internet is very popular especially in a field of academic. A huge of educational information such as research papers are overload for user. So community-base web sites have been developed to help user search information more easily from process of customizing a web site to need each specifies user or set of user. In this paper propose to use association rule analyze the community group on research paper bookmarking. A set of design goals for community group frameworks is developed and discussed. Additionally Researcher analyzes the initial relation by using association rule discovery between the antecedent and the consequent of a rule in the groups of user for generate the idea to improve ranking search result and development recommender system.

Keywords: association rule, information retrieval, research paper bookmarking.

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1789 Computer-aided Lenke Classification of Scoliotic Spines

Authors: Neila Mezghani, Philippe Phan, Hubert Labelle, Carl Eric Aubin, Jacques de Guise

Abstract:

The identification and classification of the spine deformity play an important role when considering surgical planning for adolescent patients with idiopathic scoliosis. The subject of this article is the Lenke classification of scoliotic spines using Cobb angle measurements. The purpose is two-fold: (1) design a rulebased diagram to assist clinicians in the classification process and (2) investigate a computer classifier which improves the classification time and accuracy. The rule-based diagram efficiency was evaluated in a series of scoliotic classifications by 10 clinicians. The computer classifier was tested on a radiographic measurement database of 603 patients. Classification accuracy was 93% using the rule-based diagram and 99% for the computer classifier. Both the computer classifier and the rule based diagram can efficiently assist clinicians in their Lenke classification of spine scoliosis.

Keywords: Scoliosis, Lenke model, decision-rules, computer aided classifier.

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1788 Linguistic, Pragmatic and Evolutionary Factors in Wason Selection Task

Authors: Olimpia Matarazzo, Fabrizio Ferrara

Abstract:

In two studies we tested the hypothesis that the appropriate linguistic formulation of a deontic rule – i.e. the formulation which clarifies the monadic nature of deontic operators - should produce more correct responses than the conditional formulation in Wason selection task. We tested this assumption by presenting a prescription rule and a prohibition rule in conditional vs. proper deontic formulation. We contrasted this hypothesis with two other hypotheses derived from social contract theory and relevance theory. According to the first theory, a deontic rule expressed in terms of cost-benefit should elicit a cheater detection module, sensible to mental states attributions and thus able to discriminate intentional rule violations from accidental rule violations. We tested this prevision by distinguishing the two types of violations. According to relevance theory, performance in selection task should improve by increasing cognitive effect and decreasing cognitive effort. We tested this prevision by focusing experimental instructions on the rule vs. the action covered by the rule. In study 1, in which 480 undergraduates participated, we tested these predictions through a 2 x 2 x 2 x 2 (type of the rule x rule formulation x type of violation x experimental instructions) between-subjects design. In study 2 – carried out by means of a 2 x 2 (rule formulation x type of violation) between-subjects design - we retested the hypothesis of rule formulation vs. the cheaterdetection hypothesis through a new version of selection task in which intentional vs. accidental rule violations were better discriminated. 240 undergraduates participated in this study. Results corroborate our hypothesis and challenge the contrasting assumptions. However, they show that the conditional formulation of deontic rules produces a lower performance than what is reported in literature.

Keywords: Deontic reasoning; Evolutionary, linguistic, logical, pragmatic factors; Wason selection task

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1787 An MCDM Approach to Selection Scheduling Rule in Robotic Flexibe Assembly Cells

Authors: Khalid Abd, Kazem Abhary, Romeo Marian

Abstract:

Multiple criteria decision making (MCDM) is an approach to ranking the solutions and finding the best one when two or more solutions are provided. In this study, MCDM approach is proposed to select the most suitable scheduling rule of robotic flexible assembly cells (RFACs). Two MCDM approaches, Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are proposed for solving the scheduling rule selection problem. The AHP method is employed to determine the weights of the evaluation criteria, while the TOPSIS method is employed to obtain final ranking order of scheduling rules. Four criteria are used to evaluate the scheduling rules. Also, four scheduling policies of RFAC are examined to choose the most appropriate one for this purpose. A numerical example illustrates applications of the suggested methodology. The results show that the methodology is practical and works in RFAC settings.

Keywords: AHP, TOPSIS, Scheduling rules selection

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1786 Integrated Reasoning Approach for Car Faulty Diagnosis

Authors: Diana M.L. Wong

Abstract:

This paper presents an integrated case based and rule based reasoning method for car faulty diagnosis. The reasoning method is done through extracting the past cases from the Proton Service Center while comparing with the preset rules to deduce a diagnosis/solution to a car service case. New cases will be stored to the knowledge base. The test cases examples illustrate the effectiveness of the proposed integrated reasoning. It has proven accuracy of similar reasoning if carried out by a service advisor from the service center.

Keywords: component; case based reasoning (CBR), rule basedreasoning (RBR), decision support systems, diagnosis tool.

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1785 Parallel and Distributed Mining of Association Rule on Knowledge Grid

Authors: U. Sakthi, R. Hemalatha, R. S. Bhuvaneswaran

Abstract:

In Virtual organization, Knowledge Discovery (KD) service contains distributed data resources and computing grid nodes. Computational grid is integrated with data grid to form Knowledge Grid, which implements Apriori algorithm for mining association rule on grid network. This paper describes development of parallel and distributed version of Apriori algorithm on Globus Toolkit using Message Passing Interface extended with Grid Services (MPICHG2). The creation of Knowledge Grid on top of data and computational grid is to support decision making in real time applications. In this paper, the case study describes design and implementation of local and global mining of frequent item sets. The experiments were conducted on different configurations of grid network and computation time was recorded for each operation. We analyzed our result with various grid configurations and it shows speedup of computation time is almost superlinear.

Keywords: Association rule, Grid computing, Knowledge grid, Mobility prediction.

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1784 On the Positive Definite Solutions of Nonlinear Matrix Equation

Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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1783 Learning User Keystroke Patterns for Authentication

Authors: Ying Zhao

Abstract:

Keystroke authentication is a new access control system to identify legitimate users via their typing behavior. In this paper, machine learning techniques are adapted for keystroke authentication. Seven learning methods are used to build models to differentiate user keystroke patterns. The selected classification methods are Decision Tree, Naive Bayesian, Instance Based Learning, Decision Table, One Rule, Random Tree and K-star. Among these methods, three of them are studied in more details. The results show that machine learning is a feasible alternative for keystroke authentication. Compared to the conventional Nearest Neighbour method in the recent research, learning methods especially Decision Tree can be more accurate. In addition, the experiment results reveal that 3-Grams is more accurate than 2-Grams and 4-Grams for feature extraction. Also, combination of attributes tend to result higher accuracy.

Keywords: Keystroke Authentication, Pattern recognition, MachineLearning, Instance-based Learning, Bayesian, Decision Tree.

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1782 Optimal Allocation Between Subprime Structured Mortgage Products and Treasuries

Authors: MP. Mulaudzi, MA. Petersen, J. Mukuddem-Petersen , IM. Schoeman, B. de Waal, JM. Manale

Abstract:

This conference paper discusses a risk allocation problem for subprime investing banks involving investment in subprime structured mortgage products (SMPs) and Treasuries. In order to solve this problem, we develop a L'evy process-based model of jump diffusion-type for investment choice in subprime SMPs and Treasuries. This model incorporates subprime SMP losses for which credit default insurance in the form of credit default swaps (CDSs) can be purchased. In essence, we solve a mean swap-at-risk (SaR) optimization problem for investment which determines optimal allocation between SMPs and Treasuries subject to credit risk protection via CDSs. In this regard, SaR is indicative of how much protection investors must purchase from swap protection sellers in order to cover possible losses from SMP default. Here, SaR is defined in terms of value-at-risk (VaR). Finally, we provide an analysis of the aforementioned optimization problem and its connections with the subprime mortgage crisis (SMC).

Keywords: Investors; Jump Diffusion Process, Structured Mortgage Products, Treasuries, Credit Risk, Credit Default Swaps, Tranching Risk, Counterparty Risk, Value-at-Risk, Swaps-at-Risk, Subprime Mortgage Crisis.

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1781 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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1780 Predication Model for Leukemia Diseases Based on Data Mining Classification Algorithms with Best Accuracy

Authors: Fahd Sabry Esmail, M. Badr Senousy, Mohamed Ragaie

Abstract:

In recent years, there has been an explosion in the rate of using technology that help discovering the diseases. For example, DNA microarrays allow us for the first time to obtain a "global" view of the cell. It has great potential to provide accurate medical diagnosis, to help in finding the right treatment and cure for many diseases. Various classification algorithms can be applied on such micro-array datasets to devise methods that can predict the occurrence of Leukemia disease. In this study, we compared the classification accuracy and response time among eleven decision tree methods and six rule classifier methods using five performance criteria. The experiment results show that the performance of Random Tree is producing better result. Also it takes lowest time to build model in tree classifier. The classification rules algorithms such as nearest- neighbor-like algorithm (NNge) is the best algorithm due to the high accuracy and it takes lowest time to build model in classification.

Keywords: Data mining, classification techniques, decision tree, classification rule, leukemia diseases, microarray data.

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1779 Decision Rule Induction in a Learning Content Management System

Authors: Nittaya Kerdprasop, Narin Muenrat, Kittisak Kerdprasop

Abstract:

A learning content management system (LCMS) is an environment to support web-based learning content development. Primary function of the system is to manage the learning process as well as to generate content customized to meet a unique requirement of each learner. Among the available supporting tools offered by several vendors, we propose to enhance the LCMS functionality to individualize the presented content with the induction ability. Our induction technique is based on rough set theory. The induced rules are intended to be the supportive knowledge for guiding the content flow planning. They can also be used as decision rules to help content developers on managing content delivered to individual learner.

Keywords: Decision rules, Knowledge induction, Learning content management system, Rough set.

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1778 Implementing an Intuitive Reasoner with a Large Weather Database

Authors: Yung-Chien Sun, O. Grant Clark

Abstract:

In this paper, the implementation of a rule-based intuitive reasoner is presented. The implementation included two parts: the rule induction module and the intuitive reasoner. A large weather database was acquired as the data source. Twelve weather variables from those data were chosen as the “target variables" whose values were predicted by the intuitive reasoner. A “complex" situation was simulated by making only subsets of the data available to the rule induction module. As a result, the rules induced were based on incomplete information with variable levels of certainty. The certainty level was modeled by a metric called "Strength of Belief", which was assigned to each rule or datum as ancillary information about the confidence in its accuracy. Two techniques were employed to induce rules from the data subsets: decision tree and multi-polynomial regression, respectively for the discrete and the continuous type of target variables. The intuitive reasoner was tested for its ability to use the induced rules to predict the classes of the discrete target variables and the values of the continuous target variables. The intuitive reasoner implemented two types of reasoning: fast and broad where, by analogy to human thought, the former corresponds to fast decision making and the latter to deeper contemplation. . For reference, a weather data analysis approach which had been applied on similar tasks was adopted to analyze the complete database and create predictive models for the same 12 target variables. The values predicted by the intuitive reasoner and the reference approach were compared with actual data. The intuitive reasoner reached near-100% accuracy for two continuous target variables. For the discrete target variables, the intuitive reasoner predicted at least 70% as accurately as the reference reasoner. Since the intuitive reasoner operated on rules derived from only about 10% of the total data, it demonstrated the potential advantages in dealing with sparse data sets as compared with conventional methods.

Keywords: Artificial intelligence, intuition, knowledge acquisition, limited certainty.

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1777 Analysis of Student Motivation Behavior on e-Learning Based on Association Rule Mining

Authors: Kunyanuth Kularbphettong, Phanu Waraporn, Cholticha Tongsiri

Abstract:

This research aims to create a model for analysis of student motivation behavior on e-Learning based on association rule mining techniques in case of the Information Technology for Communication and Learning Course at Suan Sunandha Rajabhat University. The model was created under association rules, one of the data mining techniques with minimum confidence. The results showed that the student motivation behavior model by using association rule technique can indicate the important variables that influence the student motivation behavior on e-Learning.

Keywords: Motivation behavior, e-learning, moodle log, association rule mining.

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1776 A Straightforward Approach for Determining the Weights of Decision Makers Based on Angle Cosine and Projection Method

Authors: Qiang Yang, Ping-An Du

Abstract:

Group decision making with multiple attribute has attracted intensive concern in the decision analysis area. This paper assumes that the contributions of all the decision makers (DMs) are not equal to the decision process based on different knowledge and experience in group setting. The aim of this paper is to develop a novel approach to determine weights of DMs in the group decision making problems. In this paper, the weights of DMs are determined in the group decision environment via angle cosine and projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, we define the weight of each decision maker (DM) by aggregating the angle cosine and projection between individual decision and ideal decision with associated direction indicator μ. By using the weights of DMs, all individual decisions are aggregated into a collective decision. Further, the preference order of alternatives is ranked in accordance with the overall row value of collective decision. Finally, an example in a chemical company is provided to illustrate the developed approach.

Keywords: Angel cosine, ideal decision, projection method, weights of decision makers.

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1775 Decision Support Framework in Managerial Learning Environment for Organization

Authors: M. Mazhar Manzoor, Nasar.A, A. Sattar

Abstract:

In the open space of decision support system the mental impression of a manager-s decision has been the subject of large importance than the ordinary famous one, when helped by decision support system. Much of this study is an attempt to realize the relation of decision support system usage and decision outcomes that governs the system. For example, several researchers have proposed so many different models to analyze the linkage between decision support system processes and results of decision making. This study draws the important relation of manager-s mental approach with the use of decision support system. The findings of this paper are theoretical attempts to provide Decision Support System (DSS) in a way to exhibit and promote the learning in semi structured area. The proposed model shows the points of one-s learning improvements and maintains a theoretical approach in order to explore the DSS contribution in enhancing the decision forming and governing the system.

Keywords: Decision Support System , Learning Organization,

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1774 Fuzzy Processing of Uncertain Data

Authors: Petr Morávek, Miloš Šeda

Abstract:

In practice, we often come across situations where it is necessary to make decisions based on incomplete or uncertain data. In control systems it may be due to the unknown exact mathematical model, or its excessive complexity (e.g. nonlinearity) when it is necessary to simplify it, respectively, to solve it using a rule base. In the case of databases, searching data we compare a similarity measure with of the requirements of the selection with stored data, where both the select query and the data itself may contain vague terms, for example in the form of linguistic qualifiers. In this paper, we focus on the processing of uncertain data in databases and demonstrate it on the example multi-criteria decision making in the selection of variants, specified by higher number of technical parameters.

Keywords: fuzzy logic, linguistic variable, multicriteria decision

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1773 Analysis of DNA Microarray Data using Association Rules: A Selective Study

Authors: M. Anandhavalli Gauthaman

Abstract:

DNA microarrays allow the measurement of expression levels for a large number of genes, perhaps all genes of an organism, within a number of different experimental samples. It is very much important to extract biologically meaningful information from this huge amount of expression data to know the current state of the cell because most cellular processes are regulated by changes in gene expression. Association rule mining techniques are helpful to find association relationship between genes. Numerous association rule mining algorithms have been developed to analyze and associate this huge amount of gene expression data. This paper focuses on some of the popular association rule mining algorithms developed to analyze gene expression data.

Keywords: DNA microarray, gene expression, association rule mining.

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1772 Influence of Adaptation Gain and Reference Model Parameters on System Performance for Model Reference Adaptive Control

Authors: Jan Erik Stellet

Abstract:

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.

Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.

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1771 An Improved Limited Tolerance Rough Set Model

Authors: Chen Wu, Komal Narejo, Dandan Li

Abstract:

Some extended rough set models in incomplete information system cannot distinguish the two objects that have few known attributes and more unknown attributes; some cannot make a flexible and accurate discrimination. In order to solve this problem, this paper suggests an improved limited tolerance rough set model using two thresholds to control what two objects have a relationship between them in limited tolerance relation and to classify objects. Our practical study case shows the model can get fine and reasonable decision results.

Keywords: Decision rule, incomplete information system, limited tolerance relation, rough set model.

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1770 On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations

Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

Abstract:

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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1769 Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule

Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

Abstract:

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: Chaos theory, GMM estimator, Lyapunov Exponent, Monetary System, Taylor Rule.

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1768 The Ethio-Eritrea Claims Commission on Use of Force: Issue of Self-Defense or Violation of Sovereignty

Authors: Isaias Teklia Berhe

Abstract:

A decision that deals with international disputes, be it arbitral or judicial, has to properly reflect objectivity and coherence with existing rules of international law. This paper shows the decision of the Ethio-Eritrea Claims Commission on the jus ad bellum case is bereft of objectivity and coherence, which contributed a disservice to international law on many aspects. The Commission’s decision that holds Eritrea in contravention to Art 2(4) of the UN Charter based on Ethiopia’s contention is flawed. It fails to consider: the illegitimacy of an actual authority established over contested territory through hostile acts, the proper determination of effectivites under international law, the sanctity of colonially determined boundaries, Ethiopia’s prior firm political recognition and undergirds to respect colonial boundary, and Ethio-Eritrea Border Commission’s decision. The paper will also argue that the Commission confused Eritrea’s right of self-defense with the rule against the non-use of force to settle territorial disputes; wherefore its decision sanitizes or sterilizes unlawful change of territory resulted through unlawful use of force to the effect of advantaging aggressions. The paper likewise argues that the decision is so sacrilegious that it disregards the ossified legal finality of colonial boundaries. Moreover, its approach toward armed attack does not reflect the peculiarity of the jus ad bellum case rather it brings about definitional uncertainties and sustains the perception that the law on self-defense is unsettled.

Keywords: Armed attack, self-defense, territorial integrity, use of force.

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1767 Rule-Based Expert System for Headache Diagnosis and Medication Recommendation

Authors: Noura Al-Ajmi, Mohammed A. Almulla

Abstract:

With the increased utilization of technology devices around the world, healthcare and medical diagnosis are critical issues that people worry about these days. Doctors are doing their best to avoid any medical errors while diagnosing diseases and prescribing the wrong medication. Subsequently, artificial intelligence applications that can be installed on mobile devices such as rule-based expert systems facilitate the task of assisting doctors in several ways. Due to their many advantages, the usage of expert systems has increased recently in health sciences. This work presents a backward rule-based expert system that can be used for a headache diagnosis and medication recommendation system. The structure of the system consists of three main modules, namely the input unit, the processing unit, and the output unit.

Keywords: Headache diagnosis system, treatment recommender system, rule-based expert system.

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1766 Induction of Expressive Rules using the Binary Coding Method

Authors: Seyed R Mousavi

Abstract:

In most rule-induction algorithms, the only operator used against nominal attributes is the equality operator =. In this paper, we first propose the use of the inequality operator, , in addition to the equality operator, to increase the expressiveness of induced rules. Then, we present a new method, Binary Coding, which can be used along with an arbitrary rule-induction algorithm to make use of the inequality operator without any need to change the algorithm. Experimental results suggest that the Binary Coding method is promising enough for further investigation, especially in cases where the minimum number of rules is desirable.

Keywords: Data mining, Inequality operator, Number of rules, Rule-induction.

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1765 The Role of the Injured Party's Fault in the Apportionment of Damages in Tort Law: A Comparative-Historical Study between Common Law and Islamic Law

Authors: Alireza Tavakolinia

Abstract:

In order to understand the role of the injured party's fault in dividing liability, we studied its historical background. In common law, the traditional contributory negligence rule was a complete defense. Then the legislature and judicial procedure modified that rule to one of apportionment. In Islamic law, too, the Action rule was at first used when the injured party was the sole cause, but jurists expanded the scope of this rule, so this rule was used in cases where both the injured party's fault and that of the other party are involved. There are some popular approaches for apportionment of damages. Some common law countries like Britain had chosen ‘the causal potency approach’ and ‘fixed apportionment’. Islamic countries like Iran have chosen both ‘the relative blameworthiness’ and ‘equal apportionment’ approaches. The article concludes that both common law and Islamic law believe in the division of responsibility between a wrongdoer claimant and the defendant. In contrast, in the apportionment of responsibility, Islamic law mostly believes in equal apportionment that is way easier and saves time and money, but common law legal systems have chosen the causal potency approach which is more complicated than the rival approach but is fairer.

Keywords: Contributory negligence, common law, Islamic Law, Tort Law.

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1764 A New Proof on the Growth Factor in Gaussian Elimination for Generalized Higham Matrices

Authors: Qian-Ping Guo, Hou-Biao Li

Abstract:

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords: CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.

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