##
**Multiple criteria decision making.**
*(English)*
Zbl 0588.90019

McGraw-Hill Series in Quantitative Methods for Management. New York etc.: McGraw-Hill Book Company. XXII, 563 p. DM 132.00 (1982).

This book has already been published in 1982. Since then it reached at least University libraries and is no more totally unknown.

As the author says in the Preface: ”This book is meant to be companionable, i.e., suited to be associated with or to complement any standard textbook on operations research, management science, or decision analysis. Most of these books do not provide an adequate treatment of multiple criteria.... Education in the eighties, preparing OR/MS students for their decision-making roles in the year 2000, should not be exclusively rooted in the problems of the forties!” and ”In this respect the present text can provide a structure for the initial design of such courses. It contains introductions to even the most advanced concepts and topics of MCDM and provides references to the necessary technical or applicational papers and monographs. Annotated bibliographical notes follow each chapter.”

Using Zeleny’s sophisticated ability to express himself in English - what the reviewer envies the author - the book is organized as follows:

Chapter 1 (Multiple objectives of individuals and organizations) provides a variety of real-world examples and introduces a discussion of major differences between single-criterion and multicriterion problems. Its goal is to make the reader aware that the decision world is essentially multidimensional and to reinforce commonly shared experiences and intuitions.

Chapter 2 (MCDM in the management sciences and operations research) provides a short historical framework for MCDM, discusses the concept of optimality, and introduces one of the basic ideas of MCDM: nondominated solutions.

Chapters 3 through 7 present various descriptions of decision making as a dynamic process. Chapter 3 (The decision process and its stages) discusses the process as a whole, introducing its individual stages (predecision, decision, and postdecision) and summarizing it in a flow diagram. This chapter thus provides a basic framework for the book.

Chapter 4 (Invention of alternatives in conflict dissolution) is concerned with the predecision stage: generation of new alternatives, realization of the predecision conflict, and initiation of resolution efforts. A self-contained theory of conflict dissolution, as well as some practical examples of its applicability, are presented in this chapter.

Not until chapter 5 (Theory of the displaced ideal) is the actual decision-making stage of the process scrutinized. Alternatives are evaluated, preferences measured, and a search for the ”best” alternative is triggered. It is then shown how a decision maker’s point of reference, the ideal alternative, is used, and how the theory of the displaced ideal naturally emerges from the traditional utility approach. Some axioms of ”rational behavior” are examined, such as transitivity of preferences and independence of irrelevant alternatives, and shown to be of limited usefulness in descriptions of the decision-making behavior.

Chapter 6 (Displaced ideal: An operational model) translates the previously described process into quantifiable form and provides a more formal structure for further discussion. The basic notions of fuzzy sets is briefly introduced and blended in with no mathematical demands made on the reader. ”Good” decisions are then characterized as those most closely resembling the ideal alternative. Various numerical and practical examples of this approach accompany the presentation.

Traditionally, different weighting schemes have been devised to address the problem of differential levels of importance for objectives. Chapter 7 (Measuring attribute importance) is entirely devoted to discussing such schemes. A new, entropy-based concept of weight is introduced, and its numerical properties are explained. It is even proposed that weights might not be the only or the proper way of capturing attribute importance.

Chapter 8 (Linear multi-objective programming), chapter 9 (Goal programming) and chapter 10 (Compromise programming) present more practical and more technical methodologies for decision search: linear multiobjective programming, goal programming, and compromise programming respectively. All three chapters rely on numerical examples, graphic exposition, and discussions of their underlying assumptions. No mathematical theorems and few algorithms are used; they are readily available in the extensive bibliography. Introducing such rigorous material too early could prevent the reader’s reaching a full understanding of these techniques. Instead, these chapters concentrate on the differences between constraints, goals, and objectives, showing how the three techniques are interrelated and how they extend traditional linear programming.

Chapter 10, dealing primarily with compromise programming, is complemented by important practical topics on group decision making and game theory. Problems of compromise and consensus are revisited but now in terms of collective rather than individual choice and ordinal rather than cardinal ranking of preferences. There is also a section on de novo programming, concerned with designing an optimal system rather than optimizing a given system.

Chapter 11 (Multi-dimensional measure of risk) goes a step beyond the traditional and generally unsatisfactory single-dimensional measures of risk, such as variance, and transforms the stochastic dominance criterion into its more practical, partial-information-based form, the prospect ranking vector. This chapter demonstrates how MCDM can be applied to the key concepts of other functional areas of business research to bring about new insights as well as theoretical and practical advances.

Chapter 12 (Multiattribute utility measurement) and chapter 13 (Regression analysis of human judgement) are devoted to multiattribute utility theory and social judgment theory. These are more traditional methodologies, prescriptive in nature, which attempt to assess or to capture the decision maker’s utility or preference function. These topics are presented in some details and in a more critical mode because they provide an excellent comparative base for MCDM. Without the precision and formalism of such rationalistic theories there would certainly have been less progress in developing descriptive insights.

Chapter 14 (Decision making is a very human business) emphasizes again that decision making cannot be reduced to an application of a simple logico-mathematical formula. Decision making is a very human business, even in the business environment itself. The problems of implementation, decision politics information, and confidence, as well as the role of intuition, are discussed. This chapter concludes with some reflections on the emerging area of decision support systems and the future of MCDM.

Each chapter is preceded by a summary noting its relationship to other chapters. At the conclusion of each chapter, a short bibliographical note lists the most important references related to that chapter, and there is also an extensive bibliography at the end of the book. At the end of each chapter problems are also given.

The author really tries to avoid formalisms as far as possible and expresses, describes and discusses the problems from various views: economic, social, human behaviour. Inavoidable mathematics is introduced and used, of course, throughout the text.

The reviewer should emphasis that this book treats MCDM comprehensively and in an unusual form. Comparing this book with e.g. the recently published book ”Theory of multiobjective optimization” by Y. Sawaragi, H. Nakayama and T. Tanino (1985; Zbl 0566.90053) (see also the corresponding review in ZOR, to appear 1986) this book is much better suitable for students and researchers in economics and social sciences, whereas the book by Sawaragi et al. is more suitable for students of OR/MS and special fields of applied mathematics.

The author stresses in many places that the determination of the set of all nondominated solutions has little sense for the practice. Nevertheless, he describes in detail his own method and neglects interactive methods which are really interesting for the practice. Instead he overemphasizes - in the reviewer’s opinion - a compromise programming based on his idea of the displaced ideal. Nevertheless, this book turned out well and it can be recommended to anybody (students, researchers, practitioners) who is dealing with MCDM.

As the author says in the Preface: ”This book is meant to be companionable, i.e., suited to be associated with or to complement any standard textbook on operations research, management science, or decision analysis. Most of these books do not provide an adequate treatment of multiple criteria.... Education in the eighties, preparing OR/MS students for their decision-making roles in the year 2000, should not be exclusively rooted in the problems of the forties!” and ”In this respect the present text can provide a structure for the initial design of such courses. It contains introductions to even the most advanced concepts and topics of MCDM and provides references to the necessary technical or applicational papers and monographs. Annotated bibliographical notes follow each chapter.”

Using Zeleny’s sophisticated ability to express himself in English - what the reviewer envies the author - the book is organized as follows:

Chapter 1 (Multiple objectives of individuals and organizations) provides a variety of real-world examples and introduces a discussion of major differences between single-criterion and multicriterion problems. Its goal is to make the reader aware that the decision world is essentially multidimensional and to reinforce commonly shared experiences and intuitions.

Chapter 2 (MCDM in the management sciences and operations research) provides a short historical framework for MCDM, discusses the concept of optimality, and introduces one of the basic ideas of MCDM: nondominated solutions.

Chapters 3 through 7 present various descriptions of decision making as a dynamic process. Chapter 3 (The decision process and its stages) discusses the process as a whole, introducing its individual stages (predecision, decision, and postdecision) and summarizing it in a flow diagram. This chapter thus provides a basic framework for the book.

Chapter 4 (Invention of alternatives in conflict dissolution) is concerned with the predecision stage: generation of new alternatives, realization of the predecision conflict, and initiation of resolution efforts. A self-contained theory of conflict dissolution, as well as some practical examples of its applicability, are presented in this chapter.

Not until chapter 5 (Theory of the displaced ideal) is the actual decision-making stage of the process scrutinized. Alternatives are evaluated, preferences measured, and a search for the ”best” alternative is triggered. It is then shown how a decision maker’s point of reference, the ideal alternative, is used, and how the theory of the displaced ideal naturally emerges from the traditional utility approach. Some axioms of ”rational behavior” are examined, such as transitivity of preferences and independence of irrelevant alternatives, and shown to be of limited usefulness in descriptions of the decision-making behavior.

Chapter 6 (Displaced ideal: An operational model) translates the previously described process into quantifiable form and provides a more formal structure for further discussion. The basic notions of fuzzy sets is briefly introduced and blended in with no mathematical demands made on the reader. ”Good” decisions are then characterized as those most closely resembling the ideal alternative. Various numerical and practical examples of this approach accompany the presentation.

Traditionally, different weighting schemes have been devised to address the problem of differential levels of importance for objectives. Chapter 7 (Measuring attribute importance) is entirely devoted to discussing such schemes. A new, entropy-based concept of weight is introduced, and its numerical properties are explained. It is even proposed that weights might not be the only or the proper way of capturing attribute importance.

Chapter 8 (Linear multi-objective programming), chapter 9 (Goal programming) and chapter 10 (Compromise programming) present more practical and more technical methodologies for decision search: linear multiobjective programming, goal programming, and compromise programming respectively. All three chapters rely on numerical examples, graphic exposition, and discussions of their underlying assumptions. No mathematical theorems and few algorithms are used; they are readily available in the extensive bibliography. Introducing such rigorous material too early could prevent the reader’s reaching a full understanding of these techniques. Instead, these chapters concentrate on the differences between constraints, goals, and objectives, showing how the three techniques are interrelated and how they extend traditional linear programming.

Chapter 10, dealing primarily with compromise programming, is complemented by important practical topics on group decision making and game theory. Problems of compromise and consensus are revisited but now in terms of collective rather than individual choice and ordinal rather than cardinal ranking of preferences. There is also a section on de novo programming, concerned with designing an optimal system rather than optimizing a given system.

Chapter 11 (Multi-dimensional measure of risk) goes a step beyond the traditional and generally unsatisfactory single-dimensional measures of risk, such as variance, and transforms the stochastic dominance criterion into its more practical, partial-information-based form, the prospect ranking vector. This chapter demonstrates how MCDM can be applied to the key concepts of other functional areas of business research to bring about new insights as well as theoretical and practical advances.

Chapter 12 (Multiattribute utility measurement) and chapter 13 (Regression analysis of human judgement) are devoted to multiattribute utility theory and social judgment theory. These are more traditional methodologies, prescriptive in nature, which attempt to assess or to capture the decision maker’s utility or preference function. These topics are presented in some details and in a more critical mode because they provide an excellent comparative base for MCDM. Without the precision and formalism of such rationalistic theories there would certainly have been less progress in developing descriptive insights.

Chapter 14 (Decision making is a very human business) emphasizes again that decision making cannot be reduced to an application of a simple logico-mathematical formula. Decision making is a very human business, even in the business environment itself. The problems of implementation, decision politics information, and confidence, as well as the role of intuition, are discussed. This chapter concludes with some reflections on the emerging area of decision support systems and the future of MCDM.

Each chapter is preceded by a summary noting its relationship to other chapters. At the conclusion of each chapter, a short bibliographical note lists the most important references related to that chapter, and there is also an extensive bibliography at the end of the book. At the end of each chapter problems are also given.

The author really tries to avoid formalisms as far as possible and expresses, describes and discusses the problems from various views: economic, social, human behaviour. Inavoidable mathematics is introduced and used, of course, throughout the text.

The reviewer should emphasis that this book treats MCDM comprehensively and in an unusual form. Comparing this book with e.g. the recently published book ”Theory of multiobjective optimization” by Y. Sawaragi, H. Nakayama and T. Tanino (1985; Zbl 0566.90053) (see also the corresponding review in ZOR, to appear 1986) this book is much better suitable for students and researchers in economics and social sciences, whereas the book by Sawaragi et al. is more suitable for students of OR/MS and special fields of applied mathematics.

The author stresses in many places that the determination of the set of all nondominated solutions has little sense for the practice. Nevertheless, he describes in detail his own method and neglects interactive methods which are really interesting for the practice. Instead he overemphasizes - in the reviewer’s opinion - a compromise programming based on his idea of the displaced ideal. Nevertheless, this book turned out well and it can be recommended to anybody (students, researchers, practitioners) who is dealing with MCDM.

Reviewer: T.Gal

### MSC:

90B50 | Management decision making, including multiple objectives |

90C31 | Sensitivity, stability, parametric optimization |

90-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming |

90C05 | Linear programming |

03E72 | Theory of fuzzy sets, etc. |

91B06 | Decision theory |

91B16 | Utility theory |