Large Scale Interactive Fuzzy Multiobjective Programming

Download Large Scale Interactive Fuzzy Multiobjective Programming PDF Online Free

Author :
Publisher : Physica
ISBN 13 : 3790818518
Total Pages : 228 pages
Book Rating : 4.7/5 (98 download)

DOWNLOAD NOW!


Book Synopsis Large Scale Interactive Fuzzy Multiobjective Programming by : Masatoshi Sakawa

Download or read book Large Scale Interactive Fuzzy Multiobjective Programming written by Masatoshi Sakawa and published by Physica. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simultaneous considerations of multiobjectiveness, fuzziness and block angular structures involved in the real-world decision making problems lead us to the new field of interactive multiobjective optimization for large scale programming problems under fuzziness. The aim of this book is to introduce the latest advances in the new field of interactive multiobjective optimization for large scale programming problems under fuzziness on the basis of the author's continuing research. Special stress is placed on interactive decision making aspects of fuzzy multiobjective optimization for human-centered systems in most realistic situations when dealing with fuzziness. The book is intended for graduate students, researchers and practitioners in the fields of operations research, industrial engineering, management science and computer science.

Multiobjective and Large-scale Linear Programming

Download Multiobjective and Large-scale Linear Programming PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4.:/5 (199 download)

DOWNLOAD NOW!


Book Synopsis Multiobjective and Large-scale Linear Programming by : Noel Anthony Bryson

Download or read book Multiobjective and Large-scale Linear Programming written by Noel Anthony Bryson and published by . This book was released on 1988 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiobjective Linear Programming

Download Multiobjective Linear Programming PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319210912
Total Pages : 328 pages
Book Rating : 4.3/5 (192 download)

DOWNLOAD NOW!


Book Synopsis Multiobjective Linear Programming by : Dinh The Luc

Download or read book Multiobjective Linear Programming written by Dinh The Luc and published by Springer. This book was released on 2015-07-31 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.

Linear Multiobjective Programming

Download Linear Multiobjective Programming PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642808085
Total Pages : 233 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!


Book Synopsis Linear Multiobjective Programming by : M. Zeleny

Download or read book Linear Multiobjective Programming written by M. Zeleny and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1. The origin of the multiobjective problem and a short historical review The continuing search for a discovery of theories, tools and c- cepts applicable to decision-making processes has increased the complexity of problems eligible for analytical treatment. One of the more pertinent criticisms of current decision-making theory and practice is directed against the traditional approximation of multiple goal behavior of men and organizations by single, technically-convenient criterion. Reins- tementof the role of human judgment in more realistic, multiple goal se,ttings has been one of the ma~or recent developments in the literature. Consider the following simplified problem. There is a large number of people to be transported daily between two industrial areas and their adjacent residential areas. Given some budgetary and technological c- straints we would like to determine optimal transportation modes as well as the number of units of each to be scheduled for service. What is the optimal solution? Are we interested in the cheapest transportation? Do we want the fastest, the safest, the cleanest, the most profitable, the most durable? There are many criteria which are to be considered: travel times, consumer's cost, construction cost, operating cost, expected fatalities and injuries, probability of delays, etc.

Large Scale Linear and Integer Optimization: A Unified Approach

Download Large Scale Linear and Integer Optimization: A Unified Approach PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461549752
Total Pages : 739 pages
Book Rating : 4.4/5 (615 download)

DOWNLOAD NOW!


Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin

Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.

Evolutionary Large-Scale Multi-Objective Optimization and Applications

Download Evolutionary Large-Scale Multi-Objective Optimization and Applications PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1394178417
Total Pages : 358 pages
Book Rating : 4.3/5 (941 download)

DOWNLOAD NOW!


Book Synopsis Evolutionary Large-Scale Multi-Objective Optimization and Applications by : Xingyi Zhang

Download or read book Evolutionary Large-Scale Multi-Objective Optimization and Applications written by Xingyi Zhang and published by John Wiley & Sons. This book was released on 2024-09-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tackle the most challenging problems in science and engineering with these cutting-edge algorithms Multi-objective optimization problems (MOPs) are those in which more than one objective needs to be optimized simultaneously. As a ubiquitous component of research and engineering projects, these problems are notoriously challenging. In recent years, evolutionary algorithms (EAs) have shown significant promise in their ability to solve MOPs, but challenges remain at the level of large-scale multi-objective optimization problems (LSMOPs), where the number of variables increases and the optimized solution is correspondingly harder to reach. Evolutionary Large-Scale Multi-Objective Optimization and Applications constitutes a systematic overview of EAs and their capacity to tackle LSMOPs. It offers an introduction to both the problem class and the algorithms before delving into some of the cutting-edge algorithms which have been specifically adapted to solving LSMOPs. Deeply engaged with specific applications and alert to the latest developments in the field, it’s a must-read for students and researchers facing these famously complex but crucial optimization problems. The book’s readers will also find: Analysis of multi-optimization problems in fields such as machine learning, network science, vehicle routing, and more Discussion of benchmark problems and performance indicators for LSMOPs Presentation of a new taxonomy of algorithms in the field Evolutionary Large-Scale Multi-Objective Optimization and Applications is ideal for advanced students, researchers, and scientists and engineers facing complex optimization problems.

Multiobjective Linear and Integer Programming

Download Multiobjective Linear and Integer Programming PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 331928746X
Total Pages : 216 pages
Book Rating : 4.3/5 (192 download)

DOWNLOAD NOW!


Book Synopsis Multiobjective Linear and Integer Programming by : Carlos Henggeler Antunes

Download or read book Multiobjective Linear and Integer Programming written by Carlos Henggeler Antunes and published by Springer. This book was released on 2016-04-08 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book opens the door to multiobjective optimization for students in fields such as engineering, management, economics and applied mathematics. It offers a comprehensive introduction to multiobjective optimization, with a primary emphasis on multiobjective linear programming and multiobjective integer/mixed integer programming. A didactic book, it is mainly intended for undergraduate and graduate students, but can also be useful for researchers and practitioners. Further, it is accompanied by an interactive software package - developed by the authors for Windows platforms - which can be used for teaching and decision-making support purposes in multiobjective linear programming problems. Thus, besides the textbook’s coverage of the essential concepts, theory and methods, complemented with illustrative examples and exercises, the computational tool enables students to experiment and enhance their technical skills, as well as to capture the essential characteristics of real-world problems.

Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty

Download Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 940092111X
Total Pages : 425 pages
Book Rating : 4.4/5 (9 download)

DOWNLOAD NOW!


Book Synopsis Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty by : Shi-Yu Huang

Download or read book Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty written by Shi-Yu Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

Linear and Multiobjective Programming with Fuzzy Stochastic Extensions

Download Linear and Multiobjective Programming with Fuzzy Stochastic Extensions PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461493994
Total Pages : 347 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!


Book Synopsis Linear and Multiobjective Programming with Fuzzy Stochastic Extensions by : Masatoshi Sakawa

Download or read book Linear and Multiobjective Programming with Fuzzy Stochastic Extensions written by Masatoshi Sakawa and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although several books or monographs on multiobjective optimization under uncertainty have been published, there seems to be no book which starts with an introductory chapter of linear programming and is designed to incorporate both fuzziness and randomness into multiobjective programming in a unified way. In this book, five major topics, linear programming, multiobjective programming, fuzzy programming, stochastic programming, and fuzzy stochastic programming, are presented in a comprehensive manner. Especially, the last four topics together comprise the main characteristics of this book, and special stress is placed on interactive decision making aspects of multiobjective programming for human-centered systems in most realistic situations under fuzziness and/or randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is a concise and condensed description of the theory of linear programming and its algorithms. Chapter 3 discusses fundamental notions and methods of multiobjective linear programming and concludes with interactive multiobjective linear programming. In Chapter 4, starting with clear explanations of fuzzy linear programming and fuzzy multiobjective linear programming, interactive fuzzy multiobjective linear programming is presented. Chapter 5 gives detailed explanations of fundamental notions and methods of stochastic programming including two-stage programming and chance constrained programming. Chapter 6 develops several interactive fuzzy programming approaches to multiobjective stochastic programming problems. Applications to purchase and transportation planning for food retailing are considered in Chapter 7. The book is self-contained because of the three appendices and answers to problems. Appendix A contains a brief summary of the topics from linear algebra. Pertinent results from nonlinear programming are summarized in Appendix B. Appendix C is a clear explanation of the Excel Solver, one of the easiest ways to solve optimization problems, through the use of simple examples of linear and nonlinear programming.

Multi-Objective Combinatorial Optimization Problems and Solution Methods

Download Multi-Objective Combinatorial Optimization Problems and Solution Methods PDF Online Free

Author :
Publisher : Academic Press
ISBN 13 : 0128238003
Total Pages : 316 pages
Book Rating : 4.1/5 (282 download)

DOWNLOAD NOW!


Book Synopsis Multi-Objective Combinatorial Optimization Problems and Solution Methods by : Mehdi Toloo

Download or read book Multi-Objective Combinatorial Optimization Problems and Solution Methods written by Mehdi Toloo and published by Academic Press. This book was released on 2022-02-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms

Large-Scale Modelling and Interactive Decision Analysis

Download Large-Scale Modelling and Interactive Decision Analysis PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 366202473X
Total Pages : 374 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!


Book Synopsis Large-Scale Modelling and Interactive Decision Analysis by : Günter Fandel

Download or read book Large-Scale Modelling and Interactive Decision Analysis written by Günter Fandel and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings report the scientific results of an International Workshop on Large-Scale Modelling and Interactive Decision Analysis organized Jointly by the System and Decision Sciences Program of the International Institute for Applied Systems Analysis (IIASA, located in Laxenburg, Austria), and the Institute for Informatics of the Academy of Sciences of the GDR (located in Berlin, GDR). The Workshop was held at a historically well-known place - the Wartburg Castl- near Eisenach (GDR). (Here Martin Luther translated the Bible into German.) More than fifty scientists representing thirteen countries participated. This Workshop is one of a series of meetings organizE!d by or In collaboration with IIASA about which two of the Lecture Notes In Economics and Mathematical Systems have already reported (Voi. 229 and Vol. 246). This time the aim of the meeting was to discuss methodological and practical problems associated with the modelling of large-scale systems and new approaches In interactive decision analysis based on advanced information processing systems.

Multi-Objective Programming and Goal Programming

Download Multi-Objective Programming and Goal Programming PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642875610
Total Pages : 365 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!


Book Synopsis Multi-Objective Programming and Goal Programming by : Mehrdad Tamiz

Download or read book Multi-Objective Programming and Goal Programming written by Mehrdad Tamiz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most real-life problems involve making decisions to optimally achieve a number of criteria while satisfying some hard or soft constraints. In this book several methods for solving such problems are presented by the leading experts in the area. The book also contains a number of very interesting application papers which demonstrate theoretical modelling, analysing and solution of real-life problems.

Multiple Criteria and Multiple Constraint Levels Linear Programming

Download Multiple Criteria and Multiple Constraint Levels Linear Programming PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9789810237387
Total Pages : 562 pages
Book Rating : 4.2/5 (373 download)

DOWNLOAD NOW!


Book Synopsis Multiple Criteria and Multiple Constraint Levels Linear Programming by : Shi Yong

Download or read book Multiple Criteria and Multiple Constraint Levels Linear Programming written by Shi Yong and published by World Scientific. This book was released on 2001 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces multiple criteria and multiple constraint levels linear programming (MC2LP), which is an extension of linear programming (LP) and multiple criteria linear programming (MCLP). In the last decade, the author and a group of researchers from the USA, China, Korea, Germany, and Hungary have been working on the theory and applications of MC2LP problems. This volume integrates their main research results ranging from theoretical bases to broad areas of real world applications. The theoretical bases include the formulation of MC2LP; integer MC2LP and MC2 transportation model; fuzzy MC2LP and fuzzy duality of MC2LP; optimal system designs and contingency plans; MC2 decision support system; and MC2 computer software development. The application areas are accounting, management information systems, production planning, and telecommunications management.The book serves as a seminar text for both undergraduates and graduates who have a linear algebra or equivalent background. For practitioners, it will help in handling LP type problems in multiple decision making environment.

Fuzzy Sets and Interactive Multiobjective Optimization

Download Fuzzy Sets and Interactive Multiobjective Optimization PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1489916334
Total Pages : 319 pages
Book Rating : 4.4/5 (899 download)

DOWNLOAD NOW!


Book Synopsis Fuzzy Sets and Interactive Multiobjective Optimization by : Masatoshi Sakawa

Download or read book Fuzzy Sets and Interactive Multiobjective Optimization written by Masatoshi Sakawa and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main characteristics of the real-world decision-making problems facing humans today are multidimensional and have multiple objectives including eco nomic, environmental, social, and technical ones. Hence, it seems natural that the consideration of many objectives in the actual decision-making process re quires multiobjective approaches rather than single-objective. One ofthe major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. Although multiobjective optimization problems differ from single objective optimization problems only in the plurality of objective functions, it is significant to realize that multiple objectives are often noncom mensurable and conflict with each other in multiobjective optimization problems. With this ob servation, in multiobjective optimization, the notion of Pareto optimality or effi ciency has been introduced instead of the optimality concept for single-objective optimization. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected from among the set of Pareto optimal or efficient solutions. Therefore, the question is, how does one find the preferred point as a compromise or satisficing solution with rational pro cedure? This is the starting point of multiobjective optimization. To be more specific, the aim is to determine how one derives a compromise or satisficing so lution of a decision maker (DM), which well represents the subjective judgments, from a Pareto optimal or an efficient solution set.

Multiobjective Decision Making

Download Multiobjective Decision Making PDF Online Free

Author :
Publisher : Courier Dover Publications
ISBN 13 : 0486462897
Total Pages : 430 pages
Book Rating : 4.4/5 (864 download)

DOWNLOAD NOW!


Book Synopsis Multiobjective Decision Making by : Vira Chankong

Download or read book Multiobjective Decision Making written by Vira Chankong and published by Courier Dover Publications. This book was released on 2008-02-04 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first-rate text explores the theory and methodology of systems engineering in evaluating alternative courses of action and associated decision-making policies. It treats criteria as multidimensional, rather than scalar, in the development of normative theories. These contribute to a behavioral theory of decision making and provide guidance for exercising judgment. An introductory discussion of the systemic approach to judgment and decision is followed by explorations of psychological value measurements, utility, classical decision analysis, and vector optimization theory. The second section chiefly deals with methods of assessing and evaluating alternatives, including both noninteractive and interactive methods. A taxonomy and a comparative evaluation of methods conclude the text.

Apors: Development In Diversity And Hearmony - Proceedings Of The Third Conference

Download Apors: Development In Diversity And Hearmony - Proceedings Of The Third Conference PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814549606
Total Pages : 640 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!


Book Synopsis Apors: Development In Diversity And Hearmony - Proceedings Of The Third Conference by : Kaoru Tone

Download or read book Apors: Development In Diversity And Hearmony - Proceedings Of The Third Conference written by Kaoru Tone and published by World Scientific. This book was released on 1995-02-28 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of selected papers presented at the Third Conference of the Asian-Pacific Operational Research Societies. The selected papers cover broad areas of operations research, ranging from traditional to new directions in theory, algorithm and applications. Typical topics are linear and nonlinear programming, interior point method, combinatorial programming, scheduling, queueing theory, simulation, forecasting, inventory, telecommunication, finance, organizational intelligence, analytic hierarchy process, data envelopment analysis, fuzzy programming and others.

Aiding Decisions with Multiple Criteria

Download Aiding Decisions with Multiple Criteria PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461508436
Total Pages : 551 pages
Book Rating : 4.4/5 (615 download)

DOWNLOAD NOW!


Book Synopsis Aiding Decisions with Multiple Criteria by : Denis Bouyssou

Download or read book Aiding Decisions with Multiple Criteria written by Denis Bouyssou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aiding Decisions With Multiple Criteria: Essays in Honor of Bernard Roy is organized around two broad themes: Graph Theory with path-breaking contributions on the theory of flows in networks and project scheduling, Multiple Criteria Decision Aiding with the invention of the family of ELECTRE methods and methodological contribution to decision-aiding which lead to the creation of Multi-Criteria Decision Analysis (MCDA). Professor Bernard Roy has had considerable influence on the development of these two broad areas. £/LIST£ Part one contains papers by Jacques Lesourne, and Dominique de Werra & Pierre Hansen related to the early career of Bernard Roy when he developed many new techniques and concepts in Graph Theory in order to cope with complex real-world problems. Part two of the book is devoted to Philosophy and Epistemology of Decision-Aiding with contributions from Valerie Belton & Jacques Pictet and Jean-Luis Genard & Marc Pirlot. Part three includes contributions based on Theory and Methodology of Multi-Criteria Decision-Aiding based on a general framework for conjoint measurement that allows intrasitive preferences. Denis Bouyssou & Marc Pirlot; Alexis Tsoukiàs, Patrice Perny & Philippe Vincke; Luis Dias & João Clímaco; Daniel Vanderpooten; Michael Doumpos & Constantin Zopounidis; and Marc Roubens offer a considerable range of examinations of this aspect of MCDA. Part four is devoted to Perference Modeling with contributions from Peter Fishburn; Salvatore Greco, Benedetto Matarazzo & Roman Slowinski; Salem Benferhat, Didier Dubois & Henri Prade; Oscar Franzese & Mark McCord; Bertrand Munier; and Raymond Bisdorff. Part five groups Applications of Multi-Criteria Decision-Aiding, and Carlos Henggeler Antunes, Carla Oliveira & João Clímaco; Carlos Bana e Costa, Manuel da Costa-Lobo, Isabel Ramos & Jean-Claude Vansnick; Yannis Siskos & Evangelos Grigoroudis; Jean-Pierre Brans, Pierre Kunsch & Bertrand Mareschal offer a wide variety of application problems. Finally, Part six includes contributions on Multi-Objective Mathematical Programming from Jacques Teghem, Walter Habenicht and Pekka Korhonen.