000			04367nam a22004575i 4500
001			978-0-387-76852-6
003			DE-He213
005			20250710084025.0
007			cr nn 008mamaa
008			110413s2009 xxu| s |||| 0|eng d
020			_a9780387768526 _a99780387768526
024	7		_a10.1007/978-0-387-76852-6 _2doi
082	0	4	_a515.42 _223
100	1		_aWang, Zhenyuan. _eauthor.
245	1	0	_aGeneralized Measure Theory _h[recurso electrónico] / _cby Zhenyuan Wang, George J. Klir.
264		1	_aBoston, MA : _bSpringer US, _c2009.
300			_aXVI, 384p. 50 illus., 25 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aIFSR International Series on Systems Science and Engineering, _x1574-0463 ; _v25
505	0		_aPreliminaries -- Basic Ideas of Generalized Measure Theory -- Special Areas of Generalized Measure Theory -- Extensions -- Structural Characteristics for Set Functions -- Measurable Functions on Monotone Measure Spaces -- Integration -- Sugeno Integrals -- Pan-Integrals -- Choquet Integrals -- Upper and Lower Integrals -- Constructing General Measures -- Fuzzification of Generalized Measures and the Choquet Integral -- Applications of Generalized Measure Theory.
520			_aThis comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weaker requirements. Each of these weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to work with imprecise probabilities. The exposition of generalized measure theory unfolds systematically. It begins with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory. About the Authors: Zhenyuan Wang is currently a Professor in the Department of Mathematics of University of Nebraska at Omaha. His research interests have been in the areas of nonadditive measures, nonlinear integrals, probability and statistics, and data mining. He has published one book and many papers in these areas. George J. Klir is currently a Distinguished Professor of Systems Science at Binghamton University (SUNY at Binghamton). He has published 29 books and well over 300 papers in a wide range of areas. His current research interests are primarily in the areas of fuzzy systems, soft computing, and generalized information theory.
650		0	_aMATHEMATICS.
650		0	_aSYSTEMS THEORY.
650		0	_aLOGIC, SYMBOLIC AND MATHEMATICAL.
650	1	4	_aMATHEMATICS.
650	2	4	_aMEASURE AND INTEGRATION.
650	2	4	_aMATHEMATICAL LOGIC AND FOUNDATIONS.
650	2	4	_aSYSTEMS THEORY, CONTROL.
700	1		_aKlir, George J. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387768519
830		0	_aIFSR International Series on Systems Science and Engineering, _x1574-0463 ; _v25
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-76852-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c58840 _d58840