By Zhenyuan Wang, George J. Klir (auth.)
This complete textual content examines the rather new mathematical sector of generalized degree idea. This sector expands classical degree idea by way of leaving behind the requirement of additivity and changing it with a variety of weaker specifications. each one of those weaker necessities characterizes a category of nonadditive measures. This leads to new suggestions and techniques that let us to house many difficulties in a extra sensible method. for instance, it permits us to paintings with obscure probabilities.
The exposition of generalized degree thought unfolds systematically. It starts off with preliminaries and new innovations, via an in depth therapy of significant new effects relating to a variety of different types of nonadditive measures and the linked integration idea. The latter consists of different types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and reduce and higher integrals. the entire issues are encouraged by means of various examples, culminating in a last bankruptcy on functions of generalized degree theory.
Some key positive aspects of the e-book contain: many workouts on the finish of every bankruptcy in addition to suitable historic and bibliographical notes, an intensive bibliography, and identify and topic indices. The paintings is acceptable for a school room atmosphere on the graduate point in classes or seminars in utilized arithmetic, laptop technology, engineering, and a few components of technological know-how. a legitimate heritage in mathematical research is needed. because the booklet comprises many unique effects through the authors, it is going to additionally attract researchers operating within the rising quarter of generalized degree theory.
About the Authors:
Zhenyuan Wang is at present a Professor within the division of arithmetic of college of Nebraska at Omaha. His examine pursuits were within the parts of nonadditive measures, nonlinear integrals, likelihood and information, and information mining. He has released one publication and plenty of papers in those areas.
George J. Klir is at the moment a special Professor of structures technology at Binghamton collage (SUNY at Binghamton). He has released 29 books and good over three hundred papers in a variety of components. His present learn pursuits are basically within the parts of fuzzy structures, smooth computing, and generalized info theory.