Applied Interval Analysis

This book is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of engineering problems. Guaranteed means here that inner and outer approximations of the sets of interest are obtained, which can be made as precise as desired, at the cost of increasing the computational effort. It thus becomes possible to achieve tasks still thought by many to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequality or all global optimizers of possibly multi-modal criteria.The basic methodology is explained as simply as possible, in a concrete and readily applicable way, with a large number of figures and illustrative examples.

At the core of many engineering problems is the solution of sets of equa­ tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un­ knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed.

by Walter N. Osborne (Author)
This book begins by presenting a method for Interval Analysis based on simple statistical tools applied on a space of Gaussian variables in Chapter One.

Authors: Li, Deng-Feng
Establishes a series of formulas, methods and properties of commonly used interval-valued solutions of interval-valued cooperative games
Presents improvements to modern interval-valued game theory and methods, including new linear programming models that surpass traditional and fuzzy optimizations
Proposes innovative game methods for interactive management problems with interval-valued data
Designed for readers across various disciplines