## Uncertain ProgrammingAn up-to-date, authoritative, comprehensive look at optimization theory in uncertain environments Real-life management decisions, such as buy/sell decisions in the stock market, are almost always made in uncertain environments. Is it possible to make model decision problems to fit these circumstances? Once constructed, can these models be solved? In Uncertain Programming, Baoding Liu answers both of these questions in the affirmative and goes on to lay a solid foundation for optimization in generally uncertain environments. Uncertain Programming describes the basic concepts of mathematical programming, provides a genetic algorithm for optimization problems, and introduces the techniques of stochastic and fuzzy simulation. After examining some basic results of expected value models, the book moves on to explore chance-constrained programming with stochastic parameters and illustrate applications of chance-constrained programming models. Dr. Liu discusses dependent-chance programming in stochastic environments and extends both chance-constrained and dependent-chance programming from stochastic to fuzzy environments. He then constructs a theoretical framework for fuzzy programming with fuzzy rather than crisp decisions. This remarkable and revolutionary book: * Lays a foundation for optimization theory in uncertain environments * Provides a unifying principle for dealing with stochastic and fuzzy programming * Incorporates the most recent developments in the field * Emphasizes modeling ideas, evolutionary computation, and applications of uncertain programming Uncertain Programming is a reliable, authoritative, and eye-opening guide for researchers and engineers in operations research, management science, business management, information and systems science, and computer science. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Stochastic Simulation and Fuzzy Simulation | 45 |

Expected Value Models | 71 |

ChanceConstrained Programming | 81 |

Copyright | |

9 other sections not shown

### Common terms and phrases

a-level set CCGP CCP models chance constraint chance functions chance-constrained programming confidence levels convex crisp vector crossover DCGP decision components decision system decision vector denoted dependent-chance programming deterministic deviation for goal distributed variable event expected value models feasible set fi(x function f(x fuzzy chromosomes fuzzy decision fuzzy set fuzzy simulation fuzzy simulation-based genetic fuzzy vector given number goal constraints goal programming hypercube induced constraints integer programming law of large maximal maximax models membership functions minimax minimized Nash equilibrium negative deviation nonlinear programming normally distributed numbers with membership objective function objective values optimal solution popsize positive deviation priority j assigned priority level probability density function programming models random variable respectively set of fuzzy simulation-based genetic algorithm single-objective Step stochastic programming stochastic simulation stochastic simulation-based genetic stochastic vector target of goal trapezoidal fuzzy number uncertain environment uncertain programming weighting factor corresponding