Search results for: relation problems.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3054

Search results for: relation problems.

3054 Solving Definition and Relation Problems in English Navigation Terminology

Authors: Ayşe Yurdakul, Eckehard Schnieder

Abstract:

Because of the increasing multidisciplinarity and multilinguality, communication problems in different technical fields grow more and more. Therefore, each technical field has its own specific language, terminology which is characterized by the different definition of terms. In addition to definition problems, there are also relation problems between terms. Among these problems of relation, there are the synonymy, antonymy, hypernymy/hyponymy, ambiguity, risk of confusion and translation problems etc.

Thus, the terminology management system iglos of the Institute for Traffic Safety and Automation Engineering of the Technische Universität Braunschweig has the target to solve these problems by a methodological standardisation of term definitions with the aid of the iglos sign model and iglos relation types. The focus of this paper should be on solving definition and relation problems between terms in English navigation terminology.

Keywords: Iglos, iglos sign model, methodological resolutions, navigation terminology, common language, technical language, positioning, definition problems, relation problems.

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3053 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems

Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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3052 Variable-Relation Criterion for Analysis of the Memristor

Authors: Qingjiang Li, Hui Xu, Haijun Liu, Xiaobo Tian

Abstract:

To judge whether the memristor can be interpreted as the fourth fundamental circuit element, we propose a variable-relation criterion of fundamental circuit elements. According to the criterion, we investigate the nature of three fundamental circuit elements and the memristor. From the perspective of variables relation, the memristor builds a direct relation between the voltage across it and the current through it, instead of a direct relation between the magnetic flux and the charge. Thus, it is better to characterize the memristor and the resistor as two special cases of the same fundamental circuit element, which is the memristive system in Chua-s new framework. Finally, the definition of memristor is refined according to the difference between the magnetic flux and the flux linkage.

Keywords: Memristor, Fundamental, Variable-Relation Criterion, Memristive system

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3051 GPU Implementation for Solving in Compressible Two-Phase Flows

Authors: Sheng-Hsiu Kuo, Pao-Hsiung Chiu, Reui-Kuo Lin, Yan-Ting Lin

Abstract:

A one-step conservative level set method, combined with a global mass correction method, is developed in this study to simulate the incompressible two-phase flows. The present framework do not need to solve the conservative level set scheme at two separated steps, and the global mass can be exactly conserved. The present method is then more efficient than two-step conservative level set scheme. The dispersion-relation-preserving schemes are utilized for the advection terms. The pressure Poisson equation solver is applied to GPU computation using the pCDR library developed by National Center for High-Performance Computing, Taiwan. The SMP parallelization is used to accelerate the rest of calculations. Three benchmark problems were done for the performance evaluation. Good agreements with the referenced solutions are demonstrated for all the investigated problems.

Keywords: Conservative level set method, two-phase flow, dispersion-relation-preserving, graphics processing unit (GPU), multi-threading.

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3050 Causal Relation Identification Using Convolutional Neural Networks and Knowledge Based Features

Authors: Tharini N. de Silva, Xiao Zhibo, Zhao Rui, Mao Kezhi

Abstract:

Causal relation identification is a crucial task in information extraction and knowledge discovery. In this work, we present two approaches to causal relation identification. The first is a classification model trained on a set of knowledge-based features. The second is a deep learning based approach training a model using convolutional neural networks to classify causal relations. We experiment with several different convolutional neural networks (CNN) models based on previous work on relation extraction as well as our own research. Our models are able to identify both explicit and implicit causal relations as well as the direction of the causal relation. The results of our experiments show a higher accuracy than previously achieved for causal relation identification tasks.

Keywords: Causal relation identification, convolutional neural networks, natural Language Processing, Machine Learning.

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3049 Relational Framework and its Applications

Authors: Lidia Obojska

Abstract:

This paper has, as its point of departure, the foundational axiomatic theory of E. De Giorgi (1996, Scuola Normale Superiore di Pisa, Preprints di Matematica 26, 1), based on two primitive notions of quality and relation. With the introduction of a unary relation, we develop a system totally based on the sole primitive notion of relation. Such a modification enables a definition of the concept of dynamic unary relation. In this way we construct a simple language capable to express other well known theories such as Robinson-s arithmetic or a piece of a theory of concatenation. A key role in this system plays an abstract relation designated by “( )", which can be interpreted in different ways, but in this paper we will focus on the case when we can perform computations and obtain results.

Keywords: language, unary relations, arithmetic, computability

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3048 The Differential Transform Method for Advection-Diffusion Problems

Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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3047 An Improved Variable Tolerance RSM with a Proportion Threshold

Authors: Chen Wu, Youquan Xu, Dandan Li, Ronghua Yang, Lijuan Wang

Abstract:

In rough set models, tolerance relation, similarity relation and limited tolerance relation solve different situation problems for incomplete information systems in which there exists a phenomenon of missing value. If two objects have the same few known attributes and more unknown attributes, they cannot distinguish them well. In order to solve this problem, we presented two improved limited and variable precision rough set models. One is symmetric, the other one is non-symmetric. They all use more stringent condition to separate two small probability equivalent objects into different classes. The two models are needed to engage further study in detail. In the present paper, we newly form object classes with a different respect comparing to the first suggested model. We overcome disadvantages of non-symmetry regarding to the second suggested model. We discuss relationships between or among several models and also make rule generation. The obtained results by applying the second model are more accurate and reasonable.

Keywords: Incomplete information system, rough set, symmetry, variable precision.

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3046 Toward An Agreement on Semantic Web Architecture

Authors: Haytham Al-Feel, M.A.Koutb, Hoda Suoror

Abstract:

There are many problems associated with the World Wide Web: getting lost in the hyperspace; the web content is still accessible only to humans and difficulties of web administration. The solution to these problems is the Semantic Web which is considered to be the extension for the current web presents information in both human readable and machine processable form. The aim of this study is to reach new generic foundation architecture for the Semantic Web because there is no clear architecture for it, there are four versions, but still up to now there is no agreement for one of these versions nor is there a clear picture for the relation between different layers and technologies inside this architecture. This can be done depending on the idea of previous versions as well as Gerber-s evaluation method as a step toward an agreement for one Semantic Web architecture.

Keywords: Semantic Web Architecture, XML, RDF and Ontology.

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3045 Analyzing Methods of the Relation between Concepts based on a Concept Hierarchy

Authors: Ke Lu, Tetsuya Furukawa

Abstract:

Data objects are usually organized hierarchically, and the relations between them are analyzed based on a corresponding concept hierarchy. The relation between data objects, for example how similar they are, are usually analyzed based on the conceptual distance in the hierarchy. If a node is an ancestor of another node, it is enough to analyze how close they are by calculating the distance vertically. However, if there is not such relation between two nodes, the vertical distance cannot express their relation explicitly. This paper tries to fill this gap by improving the analysis method for data objects based on hierarchy. The contributions of this paper include: (1) proposing an improved method to evaluate the vertical distance between concepts; (2) defining the concept horizontal distance and a method to calculate the horizontal distance; and (3) discussing the methods to confine a range by the horizontal distance and the vertical distance, and evaluating the relation between concepts.

Keywords: Concept Hierarchy, Horizontal Distance, Relation Analysis, Vertical Distance

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3044 A Critical Study of Media Profiling on Society-s Social Problems from a British Perspective

Authors: Cj Gletus Matthews Cn Jacobs, Kogilah Narayanasamy

Abstract:

This article explores the sociological perspectives on social problems and the role of the media which has a delicate role to tread in balancing its duty to the public and the victim Whilst social problems have objective conditions, it is the subjective definition of such problems that ensure which social problem comes to the fore and which doesn-t. Further it explores the roles and functions of policymakers when addressing social problems and the impact of the inception of media profiling as well as the advantages and disadvantages of media profiling towards social problems. It focuses on the inception of media profiling due to its length and a follow up article will explore how current media profiling towards social problems have evolved since its inception.

Keywords: Media Profiling, Policy Response, Social Problems

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3043 Some Geodesics in Open Surfaces Classified by Clairaut's Relation

Authors: Wongvisarut Khuangsatung, Pakkinee Chitsakul

Abstract:

In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.

Keywords: Geodesic, Surface of revolution, Clairaut's relation, Clairaut parameterization.

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3042 Coordination for Synchronous Cooperative Systems Based on Fuzzy Causal Relations

Authors: Luis A. Morales Rosales, Saul E. Pomares Hernandez, Gustavo Rodriguez Gomez

Abstract:

Synchronous cooperative systems (SCS) bring together users that are geographically distributed and connected through a network to carry out a task. Examples of SCS include Tele- Immersion and Tele-Conferences. In SCS, the coordination is the core of the system, and it has been defined as the act of managing interdependencies between activities performed to achieve a goal. Some of the main problems that SCS present deal with the management of constraints between simultaneous activities and the execution ordering of these activities. In order to resolve these problems, orderings based on Lamport-s happened-before relation have been used, namely, causal, Δ-causal, and causal-total orderings. They mainly differ in the degree of asynchronous execution allowed. One of the most important orderings is the causal order, which establishes that the events must be seen in the cause-effect order as they occur in the system. In this paper we show that for certain SCS (e.g. videoconferences, tele-immersion) where some degradation of the system is allowed, ensuring the causal order is still rigid, which can render negative affects to the system. In this paper, we illustrate how a more relaxed ordering, which we call Fuzzy Causal Order (FCO), is useful for such kind of systems by allowing a more asynchronous execution than the causal order. The benefit of the FCO is illustrated by applying it to a particular scenario of intermedia synchronization of an audio-conference system.

Keywords: Event ordering, fuzzy causal ordering, happenedbefore relation and cooperative systems.

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3041 Investigate the Relation between the Correctness and the Number of Versions of Fault Tolerant Software System

Authors: Pham Ba Quang, Nguyen Tien Dat, Huynh Quyet Thang

Abstract:

In this paper, we generalize several techniques in developing Fault Tolerant Software. We introduce property “Correctness" in evaluating N-version Systems and compare it to some commonly used properties such as reliability or availability. We also find out the relation between this property and the number of versions of system. Our experiments to verify the correctness and the applicability of the relation are also presented.

Keywords: Correctness, Fault Tolerant Software, N-versionSystems

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3040 A Fast Block-based Evolutional Algorithm for Combinatorial Problems

Authors: Huang, Wei-Hsiu Chang, Pei-Chann, Wang, Lien-Chun

Abstract:

The problems with high complexity had been the challenge in combinatorial problems. Due to the none-determined and polynomial characteristics, these problems usually face to unreasonable searching budget. Hence combinatorial optimizations attracted numerous researchers to develop better algorithms. In recent academic researches, most focus on developing to enhance the conventional evolutional algorithms and facilitate the local heuristics, such as VNS, 2-opt and 3-opt. Despite the performances of the introduction of the local strategies are significant, however, these improvement cannot improve the performance for solving the different problems. Therefore, this research proposes a meta-heuristic evolutional algorithm which can be applied to solve several types of problems. The performance validates BBEA has the ability to solve the problems even without the design of local strategies.

Keywords: Combinatorial problems, Artificial Chromosomes, Blocks Mining, Block Recombination

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3039 Classification and Resolving Urban Problems by Means of Fuzzy Approach

Authors: F. Habib, A. Shokoohi

Abstract:

Urban problems are problems of organized complexity. Thus, many models and scientific methods to resolve urban problems are failed. This study is concerned with proposing of a fuzzy system driven approach for classification and solving urban problems. The proposed study investigated mainly the selection of the inputs and outputs of urban systems for classification of urban problems. In this research, five categories of urban problems, respect to fuzzy system approach had been recognized: control, polytely, optimizing, open and decision making problems. Grounded Theory techniques were then applied to analyze the data and develop new solving method for each category. The findings indicate that the fuzzy system methods are powerful processes and analytic tools for helping planners to resolve urban complex problems. These tools can be successful where as others have failed because both incorporate or address uncertainty and risk; complexity and systems interacting with other systems.

Keywords: Classification, complexity, Fuzzy theory, urban problems.

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3038 Relation between Significance of Attribute Set and Single Attribute

Authors: Xiuqin Ma, Norrozila Binti Sulaiman, Hongwu Qin

Abstract:

In the research field of Rough Set, few papers concern the significance of attribute set. However, there is important relation between the significance of single attribute and that of attribute set, which should not be ignored. In this paper, we draw conclusions by case analysis that (1) the attribute set including single attributes with high significance is certainly significant, while, (2)the attribute set which consists of single attributes with low significance possibly has high significance. We validate the conclusions on discernibility matrix and the results demonstrate the contribution of our conclusions.

Keywords: relation, attribute set, single attribute, rough set, significance

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3037 How the Decrease of Collagen or Mineral Affect the Fracture in the Turkey Long Bones

Authors: P. Vosynek, T. Návrat, M. Peč, J. Pořízka, P. Diviš

Abstract:

Bone properties and response behavior after static or dynamic activation (loading) are still interesting topics in many fields of the science especially in the biomechanical problems such as bone loss of astronauts in space, osteoporosis, bone remodeling after fracture or remodeling after surgery (endoprosthesis and implants) and in osteointegration. This contribution deals with the relation between physiological, demineralized and deproteinized state of the turkey long bone – tibia. Three methods for comparison were used: 1) densitometry, 2) three point bending and 3) frequency analysis. The main goal of this work was to describe the decrease of the protein (collagen) or mineral of the bone with relation to the fracture in three point bending. The comparison is linked to the problem of different bone mechanical behavior in physiological and osteoporotic state.

Keywords: Bone properties, long bone, osteoporosis, response behavior.

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3036 Relation between Organizational Climate and Personnel Performance Assessment in a Tourist Service Company

Authors: Daniel A. Montoya, Marta L. Tostes

Abstract:

This investigation aims at analyzing and determining the relation between two very important variables in the human resource management: The organizational climate and the performance assessment. This study aims at contributing with knowledge in the search of the relation between the mentioned variables because the literature still does not provide solid evidence to this respect and the cases revised are incipient to reach conclusions enabling a typology about this relation.To this regard, a correlational and cross-sectional perspective was adopted in which quantitative and qualitative techniques were chosen with the total of the workers of the tourist service company PTS Peru. In order to measure the organizational climate, the OCQ (Organization Climate Questionnaire) from was used; it has 50 items and measures 9 dimensions of the Organizational Climate. Also, to assess performance, a questionnaire with 21 items and 6 dimensions was designed. As a means of assessment, a focus group was prepared and was applied to a worker in every area of the company. Additionally, interviews to human resources experts were conducted. The results of the investigation show a clear relation between the organizational climate and the personnel performance assessment as well as a relation between the nine dimensions of the organizational climate and the work performance in general and with some of its dimensions.

Keywords: Job performance, human resource management, organization climate, performance assessment.

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3035 Isomorphism on Fuzzy Graphs

Authors: A.Nagoor Gani, J.Malarvizhi

Abstract:

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed.

Keywords: complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

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3034 Financial Problems Met in the Tourism Sector in Turkey: A Survey on the Tourism Businesses

Authors: Raif Parlakkaya, Huseyin Cetin, Halil Akmese, Mesut Murat Adabali

Abstract:

As the economies of other countries in the Mediterranean Basin, the tourism sector in our country has a high denominator in economics. Tourism businesses, which are building blocks of tourism, sector faces with a variety of problems during their activities. These problems faced make business efficiency and competition conditions of the businesses difficult. Most of the problems faced by the tourism businesses and the information of consumers about consumers’ rights were used in this study, which is conducted to determine the problems of tourism businesses in the Central Anatolia Region. It is aimed to contribute the awareness of staff and executives working at tourism sector and to attract attention of businesses active concurrently with tourism sector and legislators.

Keywords: Financial Problems, The problems of Tourism businesses, Tourism Businesses, Tourism Sector in Turkey.

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3033 Comparison Results of Two-point Fuzzy Boundary Value Problems

Authors: Hsuan-Ku Liu

Abstract:

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

Keywords: Fuzzy derivative, lateral type of H-derivative, fuzzy differential equations, fuzzy boundary value problems, boundary value problems.

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3032 Variational Iteration Method for the Solution of Boundary Value Problems

Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.

Abstract:

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.

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3031 Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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3030 Effect of Personalization on Students' Achievement and Gender Factor in Mathematics Education

Authors: Nurettin Simsek, Özlem Cakır

Abstract:

The aim of this study is to point out whether personalization of mathematical word problems could affect student achievement or not. The research was applied on two-grades students at spring semester 2008-2009. Before the treatment, students personal data were taken and given to the computer. During the treatment, paper-based personalized problems and paper-based non personalized problems were prepared by computer as the same problems and then these problems were given to students. At the end of the treatment, students- opinion was taken. As a result of this research, it was found out that there were no significant differences between learners through personalized or non-personalized materials, and also there were no significant differences between gender through personalized and non-personalized problems. However, opinion of students was highly positive through the personalized problems.

Keywords: Personalization, word problem, computer aided personalization.

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3029 Evaluation of the Effect of Nursing Services Provided in a Correctional Institution on the Physical Health Levels and Health Behaviors of Female Inmates

Authors: Şenay Pehli̇van, Gülümser Kublay

Abstract:

Female inmates placed in a Correctional Institution (CI) have more physical health problems than other women and their male counterparts. Thus, they require more health care services in the CI and nursing services in particular. CI nurses also have the opportunity to teach behaviors which will protect and improve their health to these women who are difficult to reach in the community. The aim of this study was to evaluate effect of nursing services provided in a CI on the physical health levels and health behaviors of female inmates. The study has a quasi-experimental design. The study was done in Female Closed CI in Ankara, Turkey. The study was conducted on 30 female inmates. Before the implementation of nursing interventions in the initial phase of the study, female inmates were evaluated in terms of physical health problems and health behavior using forms, a physical examination, medical history, health files (file containing medical information related to prisons) and the Omaha System (OS). Findings obtained from evaluations were grouped and symptoms-findings were expressed with OS diagnosis codes. Knowledge, behavior and status scores of prisoners in relation to health problems were determined. After the implementation of the nursing interventions, female inmates were evaluated in terms of physical health problems and health behavior using OS. The research data were collected using the Female Evaluation Form developed by the researcher and the OS. It was found that knowledge, behavior and status scores of prisoners significantly increased after the implementation of nursing interventions (p < 0.05).

Keywords: Correctional institution, correctional nursing, prison nursing, female inmates, physical health problems, health behaviors.

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3028 The Interaction between Human and Environment on the Perspective of Environmental Ethics

Authors: Mella Ismelina Farma Rahayu

Abstract:

Environmental problems could not be separated from unethical human perspectives and behaviors toward the environment. There is a fundamental error in the philosophy of people’s perspective about human and nature and their relationship with the environment, which in turn will create an inappropriate behavior in relation to the environment. The aim of this study is to investigate and to understand the ethics of the environment in the context of humans interacting with the environment by using the hermeneutic approach. The related theories and concepts collected from literature review are used as data, which were analyzed by using interpretation, critical evaluation, internal coherence, comparisons, and heuristic techniques. As a result of this study, there will be a picture related to the interaction of human and environment in the perspective of environmental ethics, as well as the problems of the value of ecological justice in the interaction of humans and environment. We suggest that the interaction between humans and environment need to be based on environmental ethics, in a spirit of mutual respect between humans and the natural world.

Keywords: The environment, environmental ethics, the interaction, value.

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3027 Extraction of Temporal Relation by the Creation of Historical Natural Disaster Archive

Authors: Suguru Yoshioka, Seiichi Tani, Seinosuke Toda

Abstract:

In historical science and social science, the influence of natural disaster upon society is a matter of great interest. In recent years, some archives are made through many hands for natural disasters, however it is inefficiency and waste. So, we suppose a computer system to create a historical natural disaster archive. As the target of this analysis, we consider newspaper articles. The news articles are considered to be typical examples that prescribe the temporal relations of affairs for natural disaster. In order to do this analysis, we identify the occurrences in newspaper articles by some index entries, considering the affairs which are specific to natural disasters, and show the temporal relation between natural disasters. We designed and implemented the automatic system of “extraction of the occurrences of natural disaster" and “temporal relation table for natural disaster."

Keywords: Database, digital library, corpus, historical natural disaster, temporal relation

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3026 Applications of Rough Set Decompositions in Information Retrieval

Authors: Chen Wu, Xiaohua Hu

Abstract:

This paper proposes rough set models with three different level knowledge granules in incomplete information system under tolerance relation by similarity between objects according to their attribute values. Through introducing dominance relation on the discourse to decompose similarity classes into three subclasses: little better subclass, little worse subclass and vague subclass, it dismantles lower and upper approximations into three components. By using these components, retrieving information to find naturally hierarchical expansions to queries and constructing answers to elaborative queries can be effective. It illustrates the approach in applying rough set models in the design of information retrieval system to access different granular expanded documents. The proposed method enhances rough set model application in the flexibility of expansions and elaborative queries in information retrieval.

Keywords: Incomplete information system, Rough set model, tolerance relation, dominance relation, approximation, decomposition, elaborative query.

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3025 Joint Optimization of Pricing and Advertisement for Seasonal Branded Products

Authors: Mohammad Modarres, Shirin Aslani

Abstract:

The goal of this paper is to develop a model to integrate “pricing" and “advertisement" for short life cycle products, such as branded fashion clothing products. To achieve this goal, we apply the concept of “Dynamic Pricing". There are two classes of advertisements, for the brand (regardless of product) and for a particular product. Advertising the brand affects the demand and price of all the products. Thus, the model considers all these products in relation with each other. We develop two different methods to integrate both types of advertisement and pricing. The first model is developed within the framework of dynamic programming. However, due to the complexity of the model, this method cannot be applicable for large size problems. Therefore, we develop another method, called hieratical approach, which is capable of handling the real world problems. Finally, we show the accuracy of this method, both theoretically and also by simulation.

Keywords: Advertising, Dynamic programming, Dynamic pricing, Promotion.

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