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The book is dedicated to multi-objective methods in decision making. The first part which is devoted to theoretical aspects, covers a broad range of multi-objective methods such as multiple linear programming, vector optimisation, fuzzy goal programming, data envelopment analysis, game theory, and dynamic programming. The reader who is interested in practical applications, will find in the remaining parts a variety of approaches applied in numerous fields including production planning, logistics, marketing, and finance.
This book proposes a set of models to describe fuzzy multi-objective decision making (MODM), fuzzy multi-criteria decision making (MCDM), fuzzy group decision making (GDM) and fuzzy multi-objective group decision-making problems, respectively. It also gives a set of related methods (including algorithms) to solve these problems. One distinguishing feature of this book is that it provides two decision support systems software for readers to apply these proposed methods. A set of real-world applications and some new directions in this area are then described to further instruct readers how to use these methods and software in their practice.
Decision making is the process of selecting a possible course of action from all the available alternatives. In almost all such problems the multiplicity of criteria for judging the alternatives is pervasive. That is, for many such problems, the decision maker (OM) wants to attain more than one objective or goal in selecting the course of action while satisfying the constraints dictated by environment, processes, and resources. Another characteristic of these problems is that the objectives are apparently non commensurable. Mathematically, these problems can be represented as: (1. 1 ) subject to: gi(~) ~ 0, ,', . . . ,. ! where ~ is an n dimensional decision variable vector. The problem consists of n decision variables, m constraints and k objectives. Any or all of the functions may be nonlinear. In literature this problem is often referred to as a vector maximum problem (VMP). Traditionally there are two approaches for solving the VMP. One of them is to optimize one of the objectives while appending the other objectives to a constraint set so that the optimal solution would satisfy these objectives at least up to a predetermined level. The problem is given as: Max f. ~) 1 (1. 2) subject to: where at is any acceptable predetermined level for objective t. The other approach is to optimize a super-objective function created by multiplying each 2 objective function with a suitable weight and then by adding them together.
Multi-objective programming (MOP) can simultaneously optimize multi-objectives in mathematical programming models, but the optimization of multi-objectives triggers the issue of Pareto solutions and complicates the derived answers. To address these problems, researchers often incorporate the concepts of fuzzy sets and evolutionary algorithms into M
Under intense scrutiny for the last few decades, Multiple Objective Decision Making (MODM) has been useful for dealing with the multiple-criteria decisions and planning problems associated with many important applications in fields including management science, engineering design, and transportation. Rough set theory has also proved to be an effective mathematical tool to counter the vague description of objects in fields such as artificial intelligence, expert systems, civil engineering, medical data analysis, data mining, pattern recognition, and decision theory. Rough Multiple Objective Decision Making is perhaps the first book to combine state-of-the-art application of rough set theory, rough approximation techniques, and MODM. It illustrates traditional techniques—and some that employ simulation-based intelligent algorithms—to solve a wide range of realistic problems. Application of rough theory can remedy two types of uncertainty (randomness and fuzziness) which present significant drawbacks to existing decision-making methods, so the authors illustrate the use of rough sets to approximate the feasible set, and they explore use of rough intervals to demonstrate relative coefficients and parameters involved in bi-level MODM. The book reviews relevant literature and introduces models for both random and fuzzy rough MODM, applying proposed models and algorithms to problem solutions. Given the broad range of uses for decision making, the authors offer background and guidance for rough approximation to real-world problems, with case studies that focus on engineering applications, including construction site layout planning, water resource allocation, and resource-constrained project scheduling. The text presents a general framework of rough MODM, including basic theory, models, and algorithms, as well as a proposed methodological system and discussion of future research.
This volume constitutes the proceedings of the Fifth International Conference on Multi-Objective Programming and Goal Programming: Theory & Appli cations (MOPGP'02) held in Nara, Japan on June 4-7, 2002. Eighty-two people from 16 countries attended the conference and 78 papers (including 9 plenary talks) were presented. MOPGP is an international conference within which researchers and prac titioners can meet and learn from each other about the recent development in multi-objective programming and goal programming. The participants are from different disciplines such as Optimization, Operations Research, Math ematical Programming and Multi-Criteria Decision Aid, whose common in terest is in multi-objective analysis. The first MOPGP Conference was held at Portsmouth, United Kingdom, in 1994. The subsequent conferenes were held at Torremolinos, Spain in 1996, at Quebec City, Canada in 1998, and at Katowice, Poland in 2000. The fifth conference was held at Nara, which was the capital of Japan for more than seventy years in the eighth century. During this Nara period the basis of Japanese society, or culture established itself. Nara is a beautiful place and has a number of historic monuments in the World Heritage List. The members of the International Committee of MOPGP'02 were Dylan Jones, Pekka Korhonen, Carlos Romero, Ralph Steuer and Mehrdad Tamiz.
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.
Presents more than a dozen different methods for solving multiple criteria decision problems. Each method is briefly described and illustrated and provides at least one application from the literature. This briefing will provide you with some ideas of how the methods work and illustrate the usability of these methods in real decision problems. The first four chapters show you how the multiple criteria methods differ by the type of problem they are designed to solve, the timing of decision maker information, the type of information required from the decision maker, and the availability of supporting software. The last chapter provides further discussions and comparisons that guide you in making the appropriate choice and in the use of various multiple criteria methods.