Dymowa Soft Computing in Economics and Finance

1. Auflage 2011
ISBN: 978-3-642-17719-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 6, 295 Seiten

Reihe: Intelligent Systems Reference Library

Currently the methods of Soft Computing are successfully used for risk analysis in: budgeting, e-commerce development, portfolio selection, Black-Scholes option pricing models, corporate acquisition systems, evaluating investments in advanced manufacturing technology, interactive fuzzy interval reasoning for smart web shopping, fuzzy scheduling and logistic.
An essential feature of economic and financial problems it that there are always at least two criteria to be taken into account: profit maximization and risk minimization. Therefore, the economic and financial problems are multiple criteria ones. In this book, a new systematization of the problems of multiple criteria decision making is proposed which allows the author to reveal unsolved problems. The solutions of them are presented as well and implemented to deal with some important real-world problems such as investment project’s evaluation, tool steel material selection problem, stock screening and fuzzy logistic.
It is well known that the best results in real -world applications can be obtained using the synthesis of modern methods of soft computing. Therefore, the developed by the author  new approach to building effective stock trading systems, based on the synthesis of fuzzy logic and the Dempster-Shafer theory, seems to be a considerable contribution to the application of soft computing method in economics and finance.
An important problem of capital budgeting is the fuzzy evaluation of the Internal Rate of Return.   In this book,  this problem is solved using a new method which makes it possible to solve linear and nonlinear interval and fuzzy equations and systems of them. The developed new method allows the author to obtain an effective solution of the Leontjev’s input-output problem in the interval setting.

Autoren/Hrsg.

Dymowa, Ludmila

Inhaltsverzeichnis

1;Title Page;1
2;Foreword;6
3;Contents;8
4;Introduction;12
4.1;References;16
5;Applications of Modern Mathematics in Economics and Finance;17
5.1;Fuzzy Set Theory and Applied Interval Analysis;17
5.2;Economic and Financial Applications of Rough Sets Theory;23
5.3;Artificial Neural Network-Based Applications in Economics and Finance;24
5.4;Applications of Multiple Criteria Decision Making in Economics and Finance;32
5.5;Summary and Discussion;39
5.6;References;40
6;The Methods for Uncertainty Modeling;50
6.1;Fuzzy Set Theory;50
6.1.1;Basic Definitions;50
6.1.2;Operations on Fuzzy Sets;53
6.1.3;Operations on Fuzzy Numbers;57
6.1.4;Generalizations of Fuzzy Set Theory;61
6.2;Interval Arithmetic;70
6.3;Dempster-Shafer Theory of Evidence;75
6.3.1;Basic Definitions;75
6.3.2;Combination of Evidence in the Dempster-Shafer Theory;79
6.3.3;The Methods for Interval and Fuzzy Numbers Comparison Based on the Probabilistic Approach and Dempster-Shafer Theory;82
6.3.4;Intuitionistic Fuzzy Sets in the Framework of Dempster-Shafer Theory;101
6.4;Summary and Discussion;106
6.5;References;107
7;MCDM with Applications in Economics and Finance;115
7.1;MCDM in the Fuzzy Setting;115
7.2;Tool Steel Material Selection Problem;120
7.2.1;Subsethood Measure for Linguistic Representation of Fuzzy Numbers;124
7.2.2;Common Representation of Different Types of Local Criteria;128
7.2.3;Probabilistic Method for Fuzzy Numbers Comparison;132
7.2.4;Aggregation of Local Criteria and Aggregating Modes;135
7.3;Multiple Criteria Investment Project Evaluation in the Fuzzy Setting;145
7.3.1;Local Criteria Building;145
7.3.2;Ranking the Local Criteria;148
7.3.3;Numerical Evaluation of the Comparing Investment Projects;151
7.3.4;Hierarchical Structure of Local Criteria;153
7.4;Fuzzy MCDM and Optimization in the Stock Screening;154
7.4.1;Multiple Criteria Performance of Firms;157
7.4.2;General Criterion of Firm's ``Health'' Based on Financial Rations;158
7.4.3;Two-Criteria Performance of Firm Based on Stocks Prices History;160
7.4.4;The Comparison of Stocks Ranking Methods;162
7.4.5;Stock Ranking with the Use of Multiple Criteria Optimization;166
7.5;Multiple Criteria Fuzzy Evaluation and Optimization in Budgeting;171
7.5.1;The Problem Formulation;171
7.5.2;Fuzzy NPV and Risk Evaluation;174
7.5.3;The Set of Crisp IRR Estimations Based on Fuzzy Cash Flows;179
7.5.4;A Method for Numerical Solution of the Project Optimization Problem;183
7.6;Summary and Discussion;186
7.7;References;187
8;Interval and Fuzzy Arithmetic in Logistic;195
8.1;Fuzzy Linear Programming Approach to the Distribution Planning Problem;196
8.1.1;The Methods for the Solution of Fuzzy Linear Programming Problem;196
8.1.2;The Direct Fuzzy Extension of the Simplex Method;198
8.1.3;Numerical Studies;201
8.2;Multiple Criteria Fuzzy Distribution Planning Problem;204
8.2.1;The Problem Formulation;205
8.2.2;The Solution of Multiple Criteria Fuzzy Distribution Problem Using the Aggregation of Aggregation Modes;207
8.3;Summary and Discussion;210
8.4;References;211
9;The Synthesis of Fuzzy Logic and DST in Stock Trading Decision Support Systems;215
9.1;Stock Trading Systems Based on Conventional Fuzzy Logic;216
9.1.1;Modern Approaches to Building Stock Trading Systems;216
9.1.2;Technical Analysis Indicators and Their Fuzzy Representation;218
9.1.3;Stock Trading System Based on the Mamdani's Approach;221
9.1.4;Expert System Based on Logic-Motivated Fuzzy Logic Operators;222
9.1.5;Comparing the Trading Systems Based on Mamdani's Approach and Logic-Motivated Fuzzy Logic Operators;226
9.2;The Stock Trading System Based on Fuzzy Logic and Evidential Reasoning;229
9.2.1;Experts Systems Based on Rule-Base Evidential Reasoning;229
9.2.2;A Modern Approach to the Rule-Base Evidential Reasoning;232
9.2.3;Stock Trading Expert System;237
9.3;Summary and Discussion;245
9.4;References;246
10;Application of Interval and Fuzzy Analysis in Economic Modeling;249
10.1;Basics of ``Interval Zero Extension'' Method;249
10.1.1;The Problem Formulation;250
10.1.2;Solution Linear Fuzzy Equations;263
10.2;Solving Interval Linear Systems and the Interval Leontiev's Input-Output Problem;266
10.2.1;Solving Systems of Interval Linear Equations;266
10.2.2;Application to the Interval Leontief'S Input-Output Model of Economics;272
10.3;Solving Nonlinear Interval and Fuzzy Equations;275
10.4;Fuzzy Internal Rate of Return in Budgeting;283
10.4.1;The Problem Formulation;284
10.4.2;Fuzzy Internal Rate of Return for Crisp Interval Cash Flows. Basics.;286
10.4.3;Numerical Solution of the Nonlinear Fuzzy Problem of Internal Rate of Return Calculation;288
10.4.4;Possible Applications;293
10.5;Summary and Discussion;295
10.6;References;296
11;Index;300