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**Multiobjective decision making. Theory and methodology.**
*(English)*
Zbl 0622.90002

North-Holland Series in System Science and Engineering, 8. New York- Amsterdam: North-Holland Publishing Co. XVII, 406 p. (1983).

This book provides a good survey of various multiobjective decision theories. The key distinctive feature of this book is that it covers both mathematical programming and utility theory approaches. The book also devotes a chapter to the surrogate worth tradeoff method developed by the authors.

The book is divided into two parts. The first part covers the theory and the second part covers methods and assessment techniques. A good introduction to the nature of multiobjective decision problems, various scales of measurement, elementary decision analysis, and optimality conditions in mathematical programming is provided in Chapters 1 and 2. Both the value function theory and the utility theory are discussed in Chapter 3. The former deals with decisions under certainty and the latter with decisions under uncertainty. Vector optimization theory is covered in Chapter 4 - a strong chapter.

The assessment procedures for multiattribute utility and the ELECTRE method are contained in Chapter 5. Various methods for generating noninferior or Pareto-optimal solutions in mathematical programming formulation are covered in Chapter 6.

Chapter 7 covers several interactive and noninteractive procedures for multiobjective mathematical programming. In interactive methods the algorithm progresses by seeking some information from the decision maker. In noninteractive methods either all information about the decision maker’s preferences is quantified prior to the implementation of the method (e.g., goal programming) or a complete set of efficient solutions is generated. The surrogate worth tradeoff method and several of its extensions are discussed in Chapter 8. Finally, in Chapter 9 a comparative evaluation is provided.

Overall, the book is up-to-date with respect to the developments in the field by 1980. Numerous references provided in the book should help the reader in obtaining greater details in a specific area of interest.

The book is divided into two parts. The first part covers the theory and the second part covers methods and assessment techniques. A good introduction to the nature of multiobjective decision problems, various scales of measurement, elementary decision analysis, and optimality conditions in mathematical programming is provided in Chapters 1 and 2. Both the value function theory and the utility theory are discussed in Chapter 3. The former deals with decisions under certainty and the latter with decisions under uncertainty. Vector optimization theory is covered in Chapter 4 - a strong chapter.

The assessment procedures for multiattribute utility and the ELECTRE method are contained in Chapter 5. Various methods for generating noninferior or Pareto-optimal solutions in mathematical programming formulation are covered in Chapter 6.

Chapter 7 covers several interactive and noninteractive procedures for multiobjective mathematical programming. In interactive methods the algorithm progresses by seeking some information from the decision maker. In noninteractive methods either all information about the decision maker’s preferences is quantified prior to the implementation of the method (e.g., goal programming) or a complete set of efficient solutions is generated. The surrogate worth tradeoff method and several of its extensions are discussed in Chapter 8. Finally, in Chapter 9 a comparative evaluation is provided.

Overall, the book is up-to-date with respect to the developments in the field by 1980. Numerous references provided in the book should help the reader in obtaining greater details in a specific area of interest.

### MSC:

91B16 | Utility theory |

91B06 | Decision theory |

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 |