New Book; Possibilistic Data Analysis for Operations Research

=?ISO-2022-JP?B?GyRCJTQlWiUkJTglZSVzGyhK?= (guo@ie.osakafu-u.ac.jp)
Thu, 25 Mar 1999 20:35:15 +0100 (MET)

Book announcement:

Possibilistic Data Analysis for Operations Research

Prof. Hideo Tanaka and Dr. Peijun Guo

Studies in Fuzziness and Soft Computing, Vol. 29,
Physica-Verlag, 1999, 194pp, Hardcover, DM 98.
http://www.springer.de/economics

This monograph systematically introduces new theories and techniques of
possibility theory for data analysis in operations research. As a
counterpart of multivariate analysis based on probability theory,
possibility data analysis plays an indispensable role in finance, economic,
society fields and upper levels of decision-making system of industrial
engineering. This book focuses on how to use possibility theory to analyze
and model fuzzy or incomplete information inherently existing in real
decision problems. The theoretical work in this book is original and
practical, and problem-solving techniques are simple ones that are linear
programming and quadratic programming. Readers not only can learn
systematical, newest theories in possibility data analysis but also can
learn the detailed methodologies to deal with the practical problems.

The book can be used for anyone concerned with the methodologies and
techniques on dealing with the uncertainty in real world problems,
especially the people related with industrial engineering, informatics,
finance engineering and economics and all people related with
decision-making support system. The balance between the theoretical work and
applications makes the book suitable for both researchers and engineers, as
well as graduate students.

Contents:
Foreword by D. Dubois and H. Prade
Chapter 1. Introduction : Possibility Theory in Operations Research
1.1. Possibility Distribution : A Knowledge Representation
1.2. The Role of Possibility Theory in Regression Analysis
1.3. The Role of Possibility Theory in Portfolio Selection Problems
1.4. The Role of Possibility Theory in Discriminant Analysis
1.5. The Roles of Possibility Theory in Other Topics
1.6. Chapter Description

Chapter 2. Possibility Models
2.1. Possibility Distributions
2.2. Operations on Possibility Distributions
2.2.1. Interval Arithmetic
2.2.2. Fuzzy Number Arithmetic
2.2.3. Fuzzy Vector Arithmetic
2.3. Possibility and Necessity Measures
2.4. Probability Measures of Fuzzy Events
2.5. Possibilistic Linear Systems
2.6. Brief Bibliographical Remarks

Chapter 3. Theory of Possibilistic Systems Based on Exponential Possibility
Distributions
3.1. Combination Rule of Exponential Possibility Distributions
3.2. Marginal and Conditional Possibility Distributions
3.3. Continuous Fuzzy Relation Systems
3.4 Brief Bibliographical Remarks

Chapter 4. Identification of Possibility Distributions
4.1. Principle of Maximum Likelihood
4.2. Identification of Upper and Lower Possibility Distributions
4.3. Numerical Examples
4.4. Brief Bibliographical Remarks

Chapter 5. Possibilistic Regression Analysis
5.1. Statistical Regression analysis
5.2. Interval Regression
5.3. Fuzzy Regression
5.4. Exponential Possibilistic Regression
5.5. Interval Nonlinear Regression
5.6. Brief Bibliographical Remarks

Chapter 6. Possibilistic Portfolio Selection Problems
6.1. Portfolio Selection Models Based on Probability Theory
6.1.1. Markowitz's Portfolio Selection Model
6.1.2. Models Based on Probability Measures
6.1.3 Model Based on Mean-Absolute Deviation
6.2. Portfolio Selection Models Based on Possibility Theory
6.2.1. Portfolio Selection Model Based on Aspiration Levels of
Decision-Makers
6.2.2. Portfolio Selection Models Based on Possibility and Necessity
Measures
6.3. Portfolio Selection Models Based on Fuzzy Probabilities
6.3.1. Definition of Fuzzy Probabilities
6.3.2. Fuzzy Probability Portfolio Selection Model
6.4. Portfolio Selection Models Based on Exponential Possibility
Distributions
6.4.1. Identification of Possibility Distributions from Given Security
Data
6.4.2. Portfolio Selection Model Based on Upper and Lower Possibility
Distributions
6.4.3. Model Based on Necessity Measure
6.5. Numerical Examples
6.5.1. Portfolio Selection Based on Fuzzy Probabilities
6.5.2. Portfolio Selection Based on Upper and Lower Possibility
Distributions
6.6. Brief Bibliographical Remarks

Chapter 7. Discriminant Analysis Based on Possibility Distributions
7.1. discriminant Analysis by Bayes' Formula
7.2. Linear Discriminant Functions
7.3. Possibilistic discriminant Rules
7.4. Feature Vector for Classification by Possibility Measures
7.5. Possibilistic Classification for the Group of Data
7.6. Numerical Example
7.7. Brief Bibliographical Remarks

Chapter 8. Rough Set Analysis
8.1. Basic Notions of Rough Sets
8.2. Reduction of Information Systems by Elementary Sets
8.3. Reduction of Information Systems by Accuracy Measures
8.4. Reduction for Divisions of Attributes
8.5. Fuzzy Inference Models
8.6. Fuzzy Expert System for Medical Diagnosis
8.7. Similarities between Rough Sets and Possibility Models
8.8. Brief Bibliographical Remarks

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