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**Theory and practice of uncertain programming.**
*(English)*
Zbl 1029.90084

Studies in Fuzziness and Soft Computing. 102. Heidelberg: Physica-Verlag. xiv, 388 p. EUR 74.95/net; $ 102.00; £52.50; sFr 124.50 (2002).

Real-life decisions are usually made in the state of uncertainty (randomness, fuzziness, roughness, etc.). How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas and various applications in transportation problem, inventory system, feed mixture problem, production process, water supply problem, facility location and allocation, capital budgeting, topological optimization, vehicle routing problem, redundancy optimization, critical path problem, and parallel machine scheduling.

Numerous intelligent algorithms such as genetic algorithm, neural network, simulated annealing, and tabu search have been developed by researchers of different backgrounds. A natural idea is to integrate these intelligent algorithms to produce more effective and powerful hybrid intelligent algorithms. In order to solve uncertain programming models, a spectrum of hybrid intelligent algorithms are documented in this book.

Part I, Fundamentals, offers the basic concepts of mathematical programming, genetic algorithms and neural networks.

Part II, Stochastic Programming, lists various methods of generating random numbers, and deals with the law of large numbers, stochastic simulation, expected value model, chance-constrained programming, dependent-chance programming, hybrid intelligent algorithms, and applications in various decision problems.

Part III, Fuzzy Programming, introduces possibility space, fuzzy variable, possibility measure, necessity measure, credibility measure, expected value operator, fuzzy simulation, and fuzzy programming theory.

Part IV, Rough Programming, is devoted to rough space, rough variable, trust measure, expected value operator, rough simulation, and rough programming. As a byproduct, interval programming is also discussed.

Part V, Fuzzy Random Programming, deals with fuzzy random variable, expected value operator, chance measure, fuzzy random simulation, and fuzzy random programming.

Part VI, Random Fuzzy Programming, discusses random fuzzy variable, expected value operator, chance measure, random fuzzy simulation, and random fuzzy programming.

In Part VII, General Principle, a spectrum of multifold uncertain variables is proposed, and an uncertain programming theory is sketched.

Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.

Numerous intelligent algorithms such as genetic algorithm, neural network, simulated annealing, and tabu search have been developed by researchers of different backgrounds. A natural idea is to integrate these intelligent algorithms to produce more effective and powerful hybrid intelligent algorithms. In order to solve uncertain programming models, a spectrum of hybrid intelligent algorithms are documented in this book.

Part I, Fundamentals, offers the basic concepts of mathematical programming, genetic algorithms and neural networks.

Part II, Stochastic Programming, lists various methods of generating random numbers, and deals with the law of large numbers, stochastic simulation, expected value model, chance-constrained programming, dependent-chance programming, hybrid intelligent algorithms, and applications in various decision problems.

Part III, Fuzzy Programming, introduces possibility space, fuzzy variable, possibility measure, necessity measure, credibility measure, expected value operator, fuzzy simulation, and fuzzy programming theory.

Part IV, Rough Programming, is devoted to rough space, rough variable, trust measure, expected value operator, rough simulation, and rough programming. As a byproduct, interval programming is also discussed.

Part V, Fuzzy Random Programming, deals with fuzzy random variable, expected value operator, chance measure, fuzzy random simulation, and fuzzy random programming.

Part VI, Random Fuzzy Programming, discusses random fuzzy variable, expected value operator, chance measure, random fuzzy simulation, and random fuzzy programming.

In Part VII, General Principle, a spectrum of multifold uncertain variables is proposed, and an uncertain programming theory is sketched.

Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.

Reviewer: Nikolay Yakovlevich Tikhonenko (Odessa)

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

90C90 | Applications of mathematical programming |

90B05 | Inventory, storage, reservoirs |

90B06 | Transportation, logistics and supply chain management |

90B30 | Production models |

90B20 | Traffic problems in operations research |

90B35 | Deterministic scheduling theory in operations research |

68T37 | Reasoning under uncertainty in the context of artificial intelligence |