Search results for: Decision rule
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1736

Search results for: Decision rule

1676 Strategic Decision Making Practice in Croatia – Which Decision Making Style is More Effective?

Authors: Ivana Bulog

Abstract:

Decision making is a vital part of the business world and any other field of human endeavor. Which way a business organization will take, and where that way will lead it, depends on broad range of decisions made by managers in the managerial structure. Strategic decisions are of the greatest importance for organizational success. Although much empirical research has been done trying to describe and explain its nature and effectiveness, knowledge about strategic decision making is still incomplete. This paper explores the nature of strategic decision making in particular setting - in Croatian companies. The main focus of this research is on the style that decision makers on strategic management level are following when making decisions of life importance for their companies. Two main decision making style that explain the way decision maker collects and processes available information and performs all the activities in strategic decision making process were empirical tested: rational and intuitive one. Besides analyzing their existence on strategic management level in Croatian companies, their effectiveness is analyzed as well. Results showed that decision makers at strategic management level are following both styles somewhat equally in order to function effectively, and that intuitive style is more effective when considering decisions outcomes.

Keywords: Decision making style, decision making effectiveness, strategic decisions.

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1675 Analysis of Causality between Defect Causes Using Association Rule Mining

Authors: Sangdeok Lee, Sangwon Han, Changtaek Hyun

Abstract:

Construction defects are major components that result in negative impacts on project performance including schedule delays and cost overruns. Since construction defects generally occur when a few associated causes combine, a thorough understanding of defect causality is required in order to more systematically prevent construction defects. To address this issue, this paper uses association rule mining (ARM) to quantify the causality between defect causes, and social network analysis (SNA) to find indirect causality among them. The suggested approach is validated with 350 defect instances from concrete works in 32 projects in Korea. The results show that the interrelationships revealed by the approach reflect the characteristics of the concrete task and the important causes that should be prevented.

Keywords: Causality, defect causes, social network analysis, association rule mining.

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1674 Discovery of Quantified Hierarchical Production Rules from Large Set of Discovered Rules

Authors: Tamanna Siddiqui, M. Afshar Alam

Abstract:

Automated discovery of Rule is, due to its applicability, one of the most fundamental and important method in KDD. It has been an active research area in the recent past. Hierarchical representation allows us to easily manage the complexity of knowledge, to view the knowledge at different levels of details, and to focus our attention on the interesting aspects only. One of such efficient and easy to understand systems is Hierarchical Production rule (HPRs) system. A HPR, a standard production rule augmented with generality and specificity information, is of the following form: Decision If < condition> Generality Specificity . HPRs systems are capable of handling taxonomical structures inherent in the knowledge about the real world. This paper focuses on the issue of mining Quantified rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses Quantified production rules as initial individuals of GP and discovers hierarchical structure. In proposed approach rules are quantified by using Dempster Shafer theory. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Quantified Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy, using Dempster Shafer theory. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Knowledge discovery in database, quantification, dempster shafer theory, genetic programming, hierarchy, subsumption matrix.

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1673 Adolescents’ Role in Family Buying Decision Making

Authors: Harleen Kaur, Deepika Jindal Singla

Abstract:

Buying decision making is a complicated process, in which consumer’s decision is under the impact of others. The buying decision making is directed in a way that they have to act as customers in the society. Media and family are key socialising agents for adolescents’. Moreover, changes in the socio-cultural environment in India necessitate that adolescents’ influence in family’s buying decision-making should be investigated. In comparison to Western society, Indian is quite different, when compared in terms of family composition and structure, behaviour, values and norms which effect adolescents’ buying decision-making.

Keywords: Adolescents’, buying behaviour, Indian urban families, consumer socialization.

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1672 Pruning Method of Belief Decision Trees

Authors: Salsabil Trabelsi, Zied Elouedi, Khaled Mellouli

Abstract:

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

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

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1671 An Interval-Based Multi-Attribute Decision Making Approach for Electric Utility Resource Planning

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

This paper presents an interval-based multi-attribute decision making (MADM) approach in support of the decision process with imprecise information. The proposed decision methodology is based on the model of linear additive utility function but extends the problem formulation with the measure of composite utility variance. A sample study concerning with the evaluation of electric generation expansion strategies is provided showing how the imprecise data may affect the choice toward the best solution and how a set of alternatives, acceptable to the decision maker (DM), may be identified with certain confidence.

Keywords: Decision Making, Power Generation, ElectricUtilities, Resource Planning.

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1670 Multi-Agent Based Modeling Using Multi-Criteria Decision Analysis and OLAP System for Decision Support Problems

Authors: Omar Boutkhoum, Mohamed Hanine, Tarik Agouti, Abdessadek Tikniouine

Abstract:

This paper discusses the intake of combining multi-criteria decision analysis (MCDA) with OLAP systems, to generate an integrated analysis process dealing with complex multi-criteria decision-making situations. In this context, a multi-agent modeling is presented for decision support systems by combining multi-criteria decision analysis (MCDA) with OLAP systems. The proposed modeling which consists in performing the multi-agent system (MAS) architecture, procedure and protocol of the negotiation model is elaborated as a decision support tool for complex decision-making environments. Our objective is to take advantage from the multi-agent system which distributes resources and computational capabilities across interconnected agents, and provide a problem modeling in terms of autonomous interacting component-agents. Thus, the identification and evaluation of criteria as well as the evaluation and ranking of alternatives in a decision support situation will be performed by organizing tasks and user preferences between different agents in order to reach the right decision. At the end, an illustrative example is conducted to demonstrate the function and effectiveness of our MAS modeling.

Keywords: Multidimensional Analysis, OLAP Analysis, Multi-criteria Decision Analysis, Multi-Agent System, Decision Support System.

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1669 Multiple Criteria Decision Making Analysis for Selecting and Evaluating Fighter Aircraft

Authors: C. Ardil, A. M. Pashaev, R.A. Sadiqov, P. Abdullayev

Abstract:

In this paper, multiple criteria decision making analysis technique, is presented for ranking and selection of a set of determined alternatives - fighter aircraft - which are associated with a set of decision factors. In fighter aircraft design, conflicting decision criteria, disciplines, and technologies are always involved in the design process. Multiple criteria decision making analysis techniques can be helpful to effectively deal with such situations and make wise design decisions. Multiple criteria decision making analysis theory is a systematic mathematical approach for dealing with problems which contain uncertainties in decision making. The feasibility and contributions of applying the multiple criteria decision making analysis technique in fighter aircraft selection analysis is explored. In this study, an integrated framework incorporating multiple criteria decision making analysis technique in fighter aircraft analysis is established using entropy objective weighting method. An improved integrated multiple criteria decision making analysis method is utilized to aggregate the multiple decision criteria into one composite figure of merit, which serves as an objective function in the decision process. Therefore, it is demonstrated that the suitable multiple criteria decision making analysis method with decision solution provides an effective objective function for the decision making analysis. Considering that the inherent uncertainties and the weighting factors have crucial decision impacts on the fighter aircraft evaluation, seven fighter aircraft models for the multiple design criteria in terms of the weighting factors are constructed. The proposed multiple criteria decision making analysis model is based on integrated entropy index procedure, and additive multiple criteria decision making analysis theory. Hence, the applicability of proposed technique for fighter aircraft selection problem is considered. The constructed multiple criteria decision making analysis model can provide efficient decision analysis approach for uncertainty assessment of the decision problem. Consequently, the fighter aircraft alternatives are ranked based their final evaluation scores, and sensitivity analysis is conducted.

Keywords: Fighter Aircraft, Fighter Aircraft Selection, Multiple Criteria Decision Making, Multiple Criteria Decision Making Analysis, MCDMA

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1668 Role of Association Rule Mining in Numerical Data Analysis

Authors: Sudhir Jagtap, Kodge B. G., Shinde G. N., Devshette P. M

Abstract:

Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations. The numerical data analysis became key process in research and development of all the fields [6]. In this paper we have made an attempt to analyze the specified numerical patterns with reference to the association rule mining techniques with minimum confidence and minimum support mining criteria. The extracted rules and analyzed results are graphically demonstrated. Association rules are a simple but very useful form of data mining that describe the probabilistic co-occurrence of certain events within a database [7]. They were originally designed to analyze market-basket data, in which the likelihood of items being purchased together within the same transactions are analyzed.

Keywords: Numerical data analysis, Data Mining, Association Rule Mining

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1667 Three Computational Mathematics Techniques: Comparative Determination of Area under Curve

Authors: Khalid Pervaiz Akhter, Mahmood Ahmad, Ghulam Murtaza, Ishrat Shafi, Zafar Javed

Abstract:

The objective of this manuscript is to find area under the plasma concentration- time curve (AUC) for multiple doses of salbutamol sulphate sustained release tablets (Ventolin® oral tablets SR 8 mg, GSK, Pakistan) in the group of 18 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin® tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. AUC, an important pharmacokinetic parameter, was measured using integrated equation of multiple oral dose regimens. The approximated AUC was also calculated by using computational mathematics techniques such as repeated rectangular, repeated trapezium and repeated Simpson's rule and compared with exact value of AUC calculated by using integrated equation of multiple oral dose regimens to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin® oral tablets were 150.5819473, 157.8131756, 164.4178231 and 162.78 ng.h/ml while the closest values approximated AUC values were 149.245962, 157.336171, 164.2585768 and 162.289224 ng.h/ml, respectively as found by repeated rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the repeated rectangular rule gives slightly better approximated values of AUC as compared to repeated trapezium and repeated Simpson's rules.

Keywords: Salbutamol sulphate, Area under curve (AUC), repeated rectangular rule, repeated trapezium rule, repeated Simpson's rule.

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1666 Fuzzy Multi-Criteria Decision-Making Based on Ignatian Discernment Process

Authors: Pathinathan Theresanathan, Ajay Minj

Abstract:

Ignatian Discernment Process (IDP) is an intense decision-making tool to decide on life-issues. Decisions are influenced by various factors outside of the decision maker and inclination within. This paper develops IDP in the context of Fuzzy Multi-criteria Decision Making (FMCDM) process. Extended VIKOR method is a decision-making method which encompasses even conflict situations and accommodates weightage to various issues. Various aspects of IDP, namely three ways of decision making and tactics of inner desires, are observed, analyzed and articulated within the frame work of fuzzy rules. The decision-making situations are broadly categorized into two types. The issues outside of the decision maker influence the person. The inner feeling also plays vital role in coming to a conclusion. IDP integrates both the categories using Extended VIKOR method. Case studies are carried out and analyzed with FMCDM process. Finally, IDP is verified with an illustrative case study and results are interpreted. A confused person who could not come to a conclusion is able to take decision on a concrete way of life through IDP. The proposed IDP model recommends an integrated and committed approach to value-based decision making.

Keywords: Analytical hierarchy process, fuzzy multi-criteria decision making, Ignatian discernment process, Ignatian discernment, multi-criteria decision making, VIKOR.

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1665 Fuzzy Decision Making via Multiple Attribute

Authors: Behnaz Zohouri, Mahdi Zowghiand, Mohsen haghighi

Abstract:

In this paper, a method for decision making in fuzzy environment is presented.A new subjective and objective integrated approach is introduced that used to assign weight attributes in fuzzy multiple attribute decision making (FMADM) problems and alternatives and fmally ranked by proposed method.

Keywords: Multiple Attribute Decision Making, Triangular fuzzy numbers, ranking index, Fuzzy Entropy.

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1664 Decision-Making Criteria of PPP Projects: Stakeholder Theoretic Perspective

Authors: Xueqin Shan, Wenhua Hou, Xiaosu Ye, Chuanming Wu

Abstract:

Any decision-making is based on certain theory. Taking the public rental housing in Chongqing municipality as an example, this essay states that the stakeholder theory can provide innovative criteria and evaluation methods for Public Private Partnership (PPP) projects. It gives an analysis of how to choose decision-making criteria for different stakeholders in the PPP model and what measures to take to meet the criteria to form “symbiotic" decision-making mode through contracts and to boost the application of PPP model in large-scale public programs in China.

Keywords: PPP, Stakeholder Theory, Stakeholders, Decision- making Criteria

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1663 Roof Material Detection Based on Object-Based Approach Using WorldView-2 Satellite Imagery

Authors: Ebrahim Taherzadeh, Helmi Z. M. Shafri, Kaveh Shahi

Abstract:

One of the most important tasks in urban remote sensing is the detection of impervious surfaces (IS), such as roofs and roads. However, detection of IS in heterogeneous areas still remains one of the most challenging tasks. In this study, detection of concrete roof using an object-based approach was proposed. A new rule-based classification was developed to detect concrete roof tile. This proposed rule-based classification was applied to WorldView-2 image and results showed that the proposed rule has good potential to predict concrete roof material from WorldView-2 images, with 85% accuracy.

Keywords: Urban remote sensing, impervious surface, Object- Based, Roof Material, Concrete tile, WorldView-2.

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1662 Evolutionary Decision Trees and Software Metrics for Module Defects Identification

Authors: Monica Chiş

Abstract:

Software metric is a measure of some property of a piece of software or its specification. The aim of this paper is to present an application of evolutionary decision trees in software engineering in order to classify the software modules that have or have not one or more reported defects. For this some metrics are used for detecting the class of modules with defects or without defects.

Keywords: Evolutionary decision trees, decision trees, softwaremetrics.

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1661 Discovery of Fuzzy Censored Production Rules from Large Set of Discovered Fuzzy if then Rules

Authors: Tamanna Siddiqui, M. Afshar Alam

Abstract:

Censored Production Rule is an extension of standard production rule, which is concerned with problems of reasoning with incomplete information, subject to resource constraints and problem of reasoning efficiently with exceptions. A CPR has a form: IF A (Condition) THEN B (Action) UNLESS C (Censor), Where C is the exception condition. Fuzzy CPR are obtained by augmenting ordinary fuzzy production rule “If X is A then Y is B with an exception condition and are written in the form “If X is A then Y is B Unless Z is C. Such rules are employed in situation in which the fuzzy conditional statement “If X is A then Y is B" holds frequently and the exception condition “Z is C" holds rarely. Thus “If X is A then Y is B" part of the fuzzy CPR express important information while the unless part acts only as a switch that changes the polarity of “Y is B" to “Y is not B" when the assertion “Z is C" holds. The proposed approach is an attempt to discover fuzzy censored production rules from set of discovered fuzzy if then rules in the form: A(X) ÔçÆ B(Y) || C(Z).

Keywords: Uncertainty Quantification, Fuzzy if then rules, Fuzzy Censored Production Rules, Learning algorithm.

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1660 Evaluation Factors of Clinical Decision Support System in u_Healthcare Service

Authors: Sun K. Yoo, Ki-Chang Nam, Hyun-Young Shin, Ho-Seong Moon, Hee Cheol Kang

Abstract:

Automated intelligent, clinical decision support systems generally promote to help or to assist physicians and patients regarding to prevention of diseases or treatment of illnesses using computer represented knowledge and information. In this paper, assessment factors affecting the proper design of clinical decision support system were investigated. The required procedure steps for gathering the data from clinical trial and extracting the information from large volume of healthcare repositories were listed, which are necessary for validation and verification of evidence-based implementation of clinical decision support system. The goal of this paper is to extract useful evaluation factors affecting the quality of the clinical decision support system in the design, development, and implementation of a computer-based decision support system.

Keywords: Evaluation, Clinical Decision Support System.

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1659 Analysis of Blind Decision Feedback Equalizer Convergence: Interest of a Soft Decision

Authors: S. Cherif, S. Marcos, M. Jaidane

Abstract:

In this paper the behavior of the decision feedback equalizers (DFEs) adapted by the decision-directed or the constant modulus blind algorithms is presented. An analysis of the error surface of the corresponding criterion cost functions is first developed. With the intention of avoiding the ill-convergence of the algorithm, the paper proposes to modify the shape of the cost function error surface by using a soft decision instead of the hard one. This was shown to reduce the influence of false decisions and to smooth the undesirable minima. Modified algorithms using the soft decision during a pseudo-training phase with an automatic switch to the properly tracking phase are then derived. Computer simulations show that these modified algorithms present better ability to avoid local minima than conventional ones.

Keywords: Blind DFEs, decision-directed algorithm, constant modulus algorithm, cost function analysis, convergence analysis, soft decision.

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1658 Constructing of Classifier for Face Recognition on the Basis of the Conjugation Indexes

Authors: Vladimir A. Fursov, Nikita E. Kozin

Abstract:

In this work the opportunity of construction of the qualifiers for face-recognition systems based on conjugation criteria is investigated. The linkage between the bipartite conjugation, the conjugation with a subspace and the conjugation with the null-space is shown. The unified solving rule is investigated. It makes the decision on the rating of face to a class considering the linkage between conjugation values. The described recognition method can be successfully applied to the distributed systems of video control and video observation.

Keywords: Conjugation, Eigenfaces, Recognition.

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1657 Rule Insertion Technique for Dynamic Cell Structure Neural Network

Authors: Osama Elsarrar, Marjorie Darrah, Richard Devin

Abstract:

This paper discusses the idea of capturing an expert’s knowledge in the form of human understandable rules and then inserting these rules into a dynamic cell structure (DCS) neural network. The DCS is a form of self-organizing map that can be used for many purposes, including classification and prediction. This particular neural network is considered to be a topology preserving network that starts with no pre-structure, but assumes a structure once trained. The DCS has been used in mission and safety-critical applications, including adaptive flight control and health-monitoring in aerial vehicles. The approach is to insert expert knowledge into the DCS before training. Rules are translated into a pre-structure and then training data are presented. This idea has been demonstrated using the well-known Iris data set and it has been shown that inserting the pre-structure results in better accuracy with the same training.

Keywords: Neural network, rule extraction, rule insertion, self-organizing map.

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1656 Using Data Mining Technique for Scholarship Disbursement

Authors: J. K. Alhassan, S. A. Lawal

Abstract:

This work is on decision tree-based classification for the disbursement of scholarship. Tree-based data mining classification technique is used in other to determine the generic rule to be used to disburse the scholarship. The system based on the defined rules from the tree is able to determine the class (status) to which an applicant shall belong whether Granted or Not Granted. The applicants that fall to the class of granted denote a successful acquirement of scholarship while those in not granted class are unsuccessful in the scheme. An algorithm that can be used to classify the applicants based on the rules from tree-based classification was also developed. The tree-based classification is adopted because of its efficiency, effectiveness, and easy to comprehend features. The system was tested with the data of National Information Technology Development Agency (NITDA) Abuja, a Parastatal of Federal Ministry of Communication Technology that is mandated to develop and regulate information technology in Nigeria. The system was found working according to the specification. It is therefore recommended for all scholarship disbursement organizations.

Keywords: Decision tree, classification, data mining, scholarship.

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1655 Research on Platform of Testing Reference Point Effect under Managerial Decision-making Simulation Environment

Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

Abstract:

Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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1654 Negotiation Support for Value-based Decision in Construction

Authors: Christiono Utomo, Arazi Idrus, Isnanto, Annisa Nugraheni, Farida Rahmawati

Abstract:

A Negotiation Support is required on a value-based decision to enable each stakeholder to evaluate and rank the solution alternatives before engaging into negotiation with the other stakeholders. This study demonstrates a process of negotiation support model for selection of a building system from value-based design perspective. The perspective is based on comparison of function and cost of a building system. Multi criteria decision techniques were applied to determine the relative value of the alternative solutions for performing the function. A satisfying option game theory are applied to the criteria of value-based decision which are LCC (life cycle cost) and function based FAST. The results demonstrate a negotiation process to select priorities of a building system. The support model can be extended to an automated negotiation by combining value based decision method, group decision and negotiation support.

Keywords: NSS, Value-based, Decision, Construction.

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1653 Improved C-Fuzzy Decision Tree for Intrusion Detection

Authors: Krishnamoorthi Makkithaya, N. V. Subba Reddy, U. Dinesh Acharya

Abstract:

As the number of networked computers grows, intrusion detection is an essential component in keeping networks secure. Various approaches for intrusion detection are currently being in use with each one has its own merits and demerits. This paper presents our work to test and improve the performance of a new class of decision tree c-fuzzy decision tree to detect intrusion. The work also includes identifying best candidate feature sub set to build the efficient c-fuzzy decision tree based Intrusion Detection System (IDS). We investigated the usefulness of c-fuzzy decision tree for developing IDS with a data partition based on horizontal fragmentation. Empirical results indicate the usefulness of our approach in developing the efficient IDS.

Keywords: Data mining, Decision tree, Feature selection, Fuzzyc- means clustering, Intrusion detection.

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1652 Bayesian Decision Approach to Protection on the Flood Event in Upper Ayeyarwady River, Myanmar

Authors: Min Min Swe Zin

Abstract:

This paper introduces the foundations of Bayesian probability theory and Bayesian decision method. The main goal of Bayesian decision theory is to minimize the expected loss of a decision or minimize the expected risk. The purposes of this study are to review the decision process on the issue of flood occurrences and to suggest possible process for decision improvement. This study examines the problem structure of flood occurrences and theoretically explicates the decision-analytic approach based on Bayesian decision theory and application to flood occurrences in Environmental Engineering. In this study, we will discuss about the flood occurrences upon an annual maximum water level in cm, 43-year record available from 1965 to 2007 at the gauging station of Sagaing on the Ayeyarwady River with the drainage area - 120193 sq km by using Bayesian decision method. As a result, we will discuss the loss and risk of vast areas of agricultural land whether which will be inundated or not in the coming year based on the two standard maximum water levels during 43 years. And also we forecast about that lands will be safe from flood water during the next 10 years.

Keywords: Bayesian decision method, conditional binomial distribution, minimax rules, prior beta distribution.

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1651 Distributed Data-Mining by Probability-Based Patterns

Authors: M. Kargar, F. Gharbalchi

Abstract:

In this paper a new method is suggested for distributed data-mining by the probability patterns. These patterns use decision trees and decision graphs. The patterns are cared to be valid, novel, useful, and understandable. Considering a set of functions, the system reaches to a good pattern or better objectives. By using the suggested method we will be able to extract the useful information from massive and multi-relational data bases.

Keywords: Data-mining, Decision tree, Decision graph, Pattern, Relationship.

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1650 Distributed GIS Based Decision Support System for Efficiency Evaluation of Education System: A Case Study of Primary School Education System of Bundelkhand Zone, Uttar Pradesh, India

Authors: Garima Srivastava, R. K. Srivastava, R. C. Vaishya

Abstract:

Decision Support System (DSS), a query-based system meant to help decision makers to use a variety of information for decision making, plays a very vital role in sustainable growth of any country. For this very purpose it is essential to analyze the educational system because education is the only way through which people can be made aware as to how to sustain our planet. The purpose of this paper is to prepare a decision support system for efficiency evaluation of education system with the help of Distributed Geographical Information System.

Keywords: Distributed GIS, Web GIS, Spatial Decision Support System, Bundelkhand Zone, Efficiency, Primary School Education.

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1649 The Fallacy around Inserting Brackets to Evaluate Expressions Involving Multiplication and Division

Authors: Manduth Ramchander

Abstract:

Evaluating expressions involving multiplication and division can give rise to the fallacy that brackets can be arbitrarily inserted into expressions involving multiplication and division. The aim of this article was to draw upon mathematical theory to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division and in particular in expressions where division precedes multiplication. In doing so, it demonstrates that the notion that two different answers are possible, when evaluating expressions involving multiplication and division, is indeed a false one. Searches conducted in a number of scholarly databases unearthed the rules to be applied when removing brackets from expressions, which revealed that consideration needs to be given to sign changes when brackets are removed. The rule pertaining to expressions involving multiplication and division was then extended upon, in its reverse format, to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division. The application of the rule demonstrates that an expression involving multiplication and division can have only one correct answer. It is recommended that both the rule and its reverse be included in the curriculum, preferably at the juncture when manipulation with brackets is introduced.

Keywords: Brackets, multiplication, division, operations, order.

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1648 Neutrosophic Multiple Criteria Decision Making Analysis Method for Selecting Stealth Fighter Aircraft

Authors: C. Ardil

Abstract:

In this paper, a neutrosophic multiple criteria decision analysis method is proposed to select stealth fighter aircraft. Neutrosophic multiple criteria decision analysis methods are used to analyze the neutrosophic environment and give results under uncertainty and incompleteness. Neutrosophic numbers are used to evaluate alternatives over a set of evaluation criteria in decision making problems. Finally, the proposed model is applied to a practical decision problem for selecting stealth fighter aircraft.

Keywords: neutrosophic sets, multiple criteria decision making analysis, stealth fighter aircraft, aircraft selection, MCDMA, SVNNs

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1647 Multilevel Fuzzy Decision Support Model for China-s Urban Rail Transit Planning Schemes

Authors: Jin-Bao Zhao, Wei Deng

Abstract:

This paper aims at developing a multilevel fuzzy decision support model for urban rail transit planning schemes in China under the background that China is presently experiencing an unprecedented construction of urban rail transit. In this study, an appropriate model using multilevel fuzzy comprehensive evaluation method is developed. In the decision process, the followings are considered as the influential objectives: traveler attraction, environment protection, project feasibility and operation. In addition, consistent matrix analysis method is used to determine the weights between objectives and the weights between the objectives- sub-indictors, which reduces the work caused by repeated establishment of the decision matrix on the basis of ensuring the consistency of decision matrix. The application results show that multilevel fuzzy decision model can perfectly deal with the multivariable and multilevel decision process, which is particularly useful in the resolution of multilevel decision-making problem of urban rail transit planning schemes.

Keywords: Urban rail transit, planning schemes, multilevel fuzzy decision support model, consistent matrix analysis

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