Lodwick W.A., Kacprzyk J. (eds.) Fuzzy Optimization. Recent Advances and Applications

Springer, 2010. — 552 p.Optimization is an extremely important area in science and technology which provides powerful and useful tools and techniques for the formulation and solution of a multitude of problems in which we wish, or need, to find a best possible option or solution. It has been an important area of research for more than half a century, and particularly since the advent of digital computers. Over those years great progress has been attained in the area with the development of powerful theoretical and algorithmic results. A multitude of academic and commercial software packages have been developed which have made it possible to solve virtually all kinds of optimization problems. Applications of optimization tools and techniques span practically the entire spectrum of science and technology.
Real applications of optimization often contain information and data that is imperfect. Thus, attempts have been made since the early days to develop optimization models for handling such cases. As the first, natural approaches in this respect one can mention value intervals and probability distributions as representations of uncertain data. They have led to the development of various interval and stochastic optimization models.
Fuzzy sets theory has provided conceptually powerful and constructive tools and techniques to handle another aspect of imperfect information related to vagueness and imprecision. This has resulted in the emergence – more or less in the mid-1970s––of a new field, called fuzzy optimization (and its related fuzzy mathematical programming), in which many powerful theoretical and algorithmic results have been proposed too. Many books and edited volumes, and a multitude of articles have been published. Moreover, numerous applications have been reported too.
Due to the importance and a constant growth of interest, both among theoreticians and practitioners, we have decided to prepare this edited volume on fuzzy optimization. A substantial number of the most active researchers and practitioners in the field have responded positively to our application, and therefore we have been able to present to the readers a comprehensive account of many new and relevant developments in fuzzy optimization, in its theoretical direction and also in real world applications.Part I: Introductory Sections
Fuzziness, Rationality, Optimality and Equilibrium in Decision and Economic Theories
Introduction to Fuzzy and Possibilistic Optimization
Part II: Basic Issues
Aggregation Operators for Evaluating Alternatives
Optimization and Aggregation Functions
Chebyshev Approximation of Inconsistent Fuzzy Relational Equations with Max-T Composition
Part III: Various Types of Fuzzy Optimization and Fuzzy
Mathematical Programming Models A Survey of Fuzzy Convex Programming Models
Approaches to Linear Programming Problems with Interactive Fuzzy Numbers
Possibilistic Optimization Tasks with Mutually T-Related Parameters: Solution Methods and Comparative Analysis
A Parametrized Model for Optimization with Mixed Fuzzy and Possibilistic Uncertainty
On Solving Optimization Problems with Ordered Average Criteria and Constraints
Fuzzy Dynamic Programming Problem for Extremal Fuzzy Dynamic System
Vaguely Motivated Cooperation
Part IV: Fuzzy Network and Combinatorial Optimization
Computing Min-Max Regret Solutions in Possibilistic Combinatorial Optimization Problems
Stochastic Bottleneck Spanning Tree Problem on a Fuzzy Network
The Use of Fuzzy Numbers in Practical Project Planning and Control
Part V: Applications
Ant Feature Selection Using Fuzzy Decision Functions
Application of Fuzzy Theory to the Investment Decision Process
Decision Making Techniques in Political Management
Mathematical Approaches for Fuzzy Portfolio Selection Problems with Normal Mixture Distributions
Fuzzy Random Redundancy Allocation Problems
Reliable Biological Circuit Design Including Uncertain Kinetic Parameters
Fuzzy Optimal Algorithms for Multiple Target Convergence
Fuzzy Linear Programming in Practice: An Application to the Spanish Football League