Possibility for decision. A possibilistic approach to real life decisions.

*(English)*Zbl 1227.91002
Studies in Fuzziness and Soft Computing 270. Berlin: Springer (ISBN 978-3-642-22641-0/hbk; 978-3-642-22642-7/ebook). xi, 249 p. (2011).

The monograph is devoted to investigating possibility distributions and their usage in decision making under uncertain information. The book is divided into 9 chapters. After a general introduction and outline of the organization of the material contained in the book in Chapter 1, the authors introduce in Chapter 2 the concepts of fuzzy set, extension principle, averaging operator, and compare possibility and probability distributions. The next chapter is devoted to a detailed study of properties of possibility distributions, their extensions, and related topics as e.g. possibilistic mean value, variance, covariance or possibilistic correlation coefficient. The introduced concepts are illustrated by examples. Chapter 4 investigates the concept of ordered weighted averaging (OWA) operators. Known properties as well as some new results concerning OWA operators are presented. Examples of using these operators for multicriteria decision making in settlement modeling under various budget restrictions demonstrate the applicability of the theoretical results. None, fixed, flexible, and fuzzy budget constraints are considered. Probabilistic distribution is further used in Chapter 5 to model strategic decisions in situations with fuzzy real options.

The main ideas concerning decisions about closing production plants are explained under various additional real world conditions. Applications of possibilistic concepts to portfolio selection, risk assessment in grid computing, and knowledge mobilization are presented in Chapters 6–8. The last chapter of the book discusses advantages of applying the possibilistic approach to designing mobile value services. A long list of related references (364 items) and an index conclude the book.

The main ideas concerning decisions about closing production plants are explained under various additional real world conditions. Applications of possibilistic concepts to portfolio selection, risk assessment in grid computing, and knowledge mobilization are presented in Chapters 6–8. The last chapter of the book discusses advantages of applying the possibilistic approach to designing mobile value services. A long list of related references (364 items) and an index conclude the book.

Reviewer: Karel Zimmermann (Praha)

##### MSC:

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

91B06 | Decision theory |

60A86 | Fuzzy probability |

90C29 | Multi-objective and goal programming |

91G50 | Corporate finance (dividends, real options, etc.) |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

91G10 | Portfolio theory |