Generalized Measure Theory View Full Text


Ontology type: schema:Book     


Book Info

DATE

2009

GENRE

Monograph

AUTHORS

Zhenyuan Wang , George J. Klir

PUBLISHER

Springer Nature

ABSTRACT

This 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. More... »

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-0-387-76852-6

DOI

http://dx.doi.org/10.1007/978-0-387-76852-6

ISBN

978-0-387-76851-9 | 978-0-387-76852-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046473572


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A.", 
          "id": "http://www.grid.ac/institutes/grid.266815.e", 
          "name": [
            "Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A."
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wang", 
        "givenName": "Zhenyuan", 
        "id": "sg:person.014741117732.20", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014741117732.20"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Thomas J. Watson School of Engineering, Department of  Systems Science &, Binghamton University, 13902, Binghamton, U.S.A.", 
          "id": "http://www.grid.ac/institutes/grid.264260.4", 
          "name": [
            "Thomas J. Watson School of Engineering, Department of  Systems Science &, Binghamton University, 13902, Binghamton, U.S.A."
          ], 
          "type": "Organization"
        }, 
        "familyName": "Klir", 
        "givenName": "George J.", 
        "id": "sg:person.07560122403.54", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07560122403.54"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2009", 
    "datePublishedReg": "2009-01-01", 
    "description": "This 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.", 
    "genre": "monograph", 
    "id": "sg:pub.10.1007/978-0-387-76852-6", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isbn": [
      "978-0-387-76851-9", 
      "978-0-387-76852-6"
    ], 
    "keywords": [
      "generalized measure theory", 
      "measure theory", 
      "nonadditive measures", 
      "classical measure theory", 
      "types of integrals", 
      "Department of Mathematics", 
      "mathematical areas", 
      "weaker requirement", 
      "mathematical analysis", 
      "nonlinear integrals", 
      "fuzzy systems", 
      "areas of science", 
      "imprecise probabilities", 
      "information theory", 
      "integration theory", 
      "integrals", 
      "soft computing", 
      "upper integral", 
      "new results", 
      "important new results", 
      "mathematics", 
      "Choquet integral", 
      "Sugeno integral", 
      "computer science", 
      "extensive bibliography", 
      "systems science", 
      "theory", 
      "Distinguished Professor", 
      "original results", 
      "numerous examples", 
      "current research interest", 
      "detailed treatment", 
      "probability", 
      "bibliographical notes", 
      "Binghamton University", 
      "realistic way", 
      "new concept", 
      "Klir", 
      "statistics", 
      "data mining", 
      "problem", 
      "class", 
      "preliminaries", 
      "key features", 
      "research interest", 
      "Wang", 
      "exposition", 
      "computing", 
      "science", 
      "wide range", 
      "requirements", 
      "concept", 
      "applications", 
      "system", 
      "note", 
      "chapter", 
      "engineering", 
      "additivity", 
      "graduate level", 
      "interest", 
      "measures", 
      "results", 
      "sound background", 
      "final chapter", 
      "types", 
      "way", 
      "authors", 
      "work", 
      "researchers", 
      "topic", 
      "analysis", 
      "comprehensive text", 
      "book", 
      "bibliography", 
      "mining", 
      "features", 
      "end", 
      "area", 
      "background", 
      "index", 
      "range", 
      "professors", 
      "University", 
      "levels", 
      "seminars", 
      "name", 
      "text", 
      "Nebraska", 
      "classroom", 
      "course", 
      "exercise", 
      "University of Nebraska", 
      "Department", 
      "Omaha", 
      "subject index", 
      "treatment", 
      "example", 
      "paper", 
      "method", 
      "new mathematical area", 
      "requirement of additivity", 
      "associated integration theory", 
      "Zhenyuan Wang", 
      "George J. Klir", 
      "J. Klir"
    ], 
    "name": "Generalized Measure Theory", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1046473572"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-0-387-76852-6"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-0-387-76852-6", 
      "https://app.dimensions.ai/details/publication/pub.1046473572"
    ], 
    "sdDataset": "books", 
    "sdDatePublished": "2021-11-01T18:45", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211101/entities/gbq_results/book/book_26.jsonl", 
    "type": "Book", 
    "url": "https://doi.org/10.1007/978-0-387-76852-6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-0-387-76852-6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-0-387-76852-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-0-387-76852-6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-0-387-76852-6'


 

This table displays all metadata directly associated to this object as RDF triples.

165 TRIPLES      21 PREDICATES      130 URIs      123 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-0-387-76852-6 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N38d2b1bf4a1f403aa00eb3223e1880ca
4 schema:datePublished 2009
5 schema:datePublishedReg 2009-01-01
6 schema:description This 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.
7 schema:genre monograph
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isbn 978-0-387-76851-9
11 978-0-387-76852-6
12 schema:keywords Binghamton University
13 Choquet integral
14 Department
15 Department of Mathematics
16 Distinguished Professor
17 George J. Klir
18 J. Klir
19 Klir
20 Nebraska
21 Omaha
22 Sugeno integral
23 University
24 University of Nebraska
25 Wang
26 Zhenyuan Wang
27 additivity
28 analysis
29 applications
30 area
31 areas of science
32 associated integration theory
33 authors
34 background
35 bibliographical notes
36 bibliography
37 book
38 chapter
39 class
40 classical measure theory
41 classroom
42 comprehensive text
43 computer science
44 computing
45 concept
46 course
47 current research interest
48 data mining
49 detailed treatment
50 end
51 engineering
52 example
53 exercise
54 exposition
55 extensive bibliography
56 features
57 final chapter
58 fuzzy systems
59 generalized measure theory
60 graduate level
61 important new results
62 imprecise probabilities
63 index
64 information theory
65 integrals
66 integration theory
67 interest
68 key features
69 levels
70 mathematical analysis
71 mathematical areas
72 mathematics
73 measure theory
74 measures
75 method
76 mining
77 name
78 new concept
79 new mathematical area
80 new results
81 nonadditive measures
82 nonlinear integrals
83 note
84 numerous examples
85 original results
86 paper
87 preliminaries
88 probability
89 problem
90 professors
91 range
92 realistic way
93 requirement of additivity
94 requirements
95 research interest
96 researchers
97 results
98 science
99 seminars
100 soft computing
101 sound background
102 statistics
103 subject index
104 system
105 systems science
106 text
107 theory
108 topic
109 treatment
110 types
111 types of integrals
112 upper integral
113 way
114 weaker requirement
115 wide range
116 work
117 schema:name Generalized Measure Theory
118 schema:productId Nc2d857a6f3354b2a872f682d9377680f
119 Nf450302e133c4a7db555e3029d64836b
120 schema:publisher N63c4aa4b447d4808a762001ef63a32fd
121 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046473572
122 https://doi.org/10.1007/978-0-387-76852-6
123 schema:sdDatePublished 2021-11-01T18:45
124 schema:sdLicense https://scigraph.springernature.com/explorer/license/
125 schema:sdPublisher N70b1a7d798da409ea8ea6bc480c0d4f0
126 schema:url https://doi.org/10.1007/978-0-387-76852-6
127 sgo:license sg:explorer/license/
128 sgo:sdDataset books
129 rdf:type schema:Book
130 N0a481fff0b2f482886b4ae3b95e3a812 rdf:first sg:person.07560122403.54
131 rdf:rest rdf:nil
132 N38d2b1bf4a1f403aa00eb3223e1880ca rdf:first sg:person.014741117732.20
133 rdf:rest N0a481fff0b2f482886b4ae3b95e3a812
134 N63c4aa4b447d4808a762001ef63a32fd schema:name Springer Nature
135 rdf:type schema:Organisation
136 N70b1a7d798da409ea8ea6bc480c0d4f0 schema:name Springer Nature - SN SciGraph project
137 rdf:type schema:Organization
138 Nc2d857a6f3354b2a872f682d9377680f schema:name doi
139 schema:value 10.1007/978-0-387-76852-6
140 rdf:type schema:PropertyValue
141 Nf450302e133c4a7db555e3029d64836b schema:name dimensions_id
142 schema:value pub.1046473572
143 rdf:type schema:PropertyValue
144 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
145 schema:name Mathematical Sciences
146 rdf:type schema:DefinedTerm
147 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
148 schema:name Pure Mathematics
149 rdf:type schema:DefinedTerm
150 sg:person.014741117732.20 schema:affiliation grid-institutes:grid.266815.e
151 schema:familyName Wang
152 schema:givenName Zhenyuan
153 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014741117732.20
154 rdf:type schema:Person
155 sg:person.07560122403.54 schema:affiliation grid-institutes:grid.264260.4
156 schema:familyName Klir
157 schema:givenName George J.
158 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07560122403.54
159 rdf:type schema:Person
160 grid-institutes:grid.264260.4 schema:alternateName Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, 13902, Binghamton, U.S.A.
161 schema:name Thomas J. Watson School of Engineering, Department of Systems Science &, Binghamton University, 13902, Binghamton, U.S.A.
162 rdf:type schema:Organization
163 grid-institutes:grid.266815.e schema:alternateName Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A.
164 schema:name Department of Mathematics, University of Nebraska at Omaha, Dodge St. 6001, 68182, Omaha, U.S.A.
165 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...