Generalized concavity in fuzzy optimization and decision analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Acad. Publ.
2002
|
| Series: | International series in operations research & management science
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 296 S. graph. Darst. |
| ISBN: | 0792374959 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV014550067 | ||
| 003 | DE-604 | ||
| 005 | 20030718 | ||
| 007 | t | ||
| 008 | 020709s2002 d||| |||| 00||| eng d | ||
| 020 | |a 0792374959 |9 0-7923-7495-9 | ||
| 035 | |a (OCoLC)47296245 | ||
| 035 | |a (DE-599)BVBBV014550067 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 | ||
| 050 | 0 | |a T57.95 | |
| 082 | 0 | |a 658.4/03 |2 21 | |
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 100 | 1 | |a Ramík, Jaroslav |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized concavity in fuzzy optimization and decision analysis |c Jaroslav Ramík ; Milan Vlach |
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2002 | |
| 300 | |a XIV, 296 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series in operations research & management science |v 41 | |
| 650 | 4 | |a Concave functions | |
| 650 | 4 | |a Decision making | |
| 650 | 4 | |a Fuzzy mathematics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 0 | 7 | |a Entscheidungsprozess |0 (DE-588)4121202-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fuzzy-Optimierung |0 (DE-588)4659945-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fuzzy-Optimierung |0 (DE-588)4659945-9 |D s |
| 689 | 0 | 1 | |a Entscheidungsprozess |0 (DE-588)4121202-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Vlach, Milan |e Verfasser |4 aut | |
| 830 | 0 | |a International series in operations research & management science |v 41 |w (DE-604)BV011630976 |9 41 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009893268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009893268 | ||
Record in the Search Index
| _version_ | 1804129328653402112 |
|---|---|
| adam_text | Contents
Preface xi
Acknowledgments xv
Part I Theory
1. PRELIMINARIES 5
2. GENERALIZED CONVEX SETS 11
2.1 Convex Sets 11
2.2 Starshaped Sets 12
2.3 Strongly Starshaped Sets 18
2.4 Co Starshaped Sets 20
2.5 Separation of Starshaped Sets 21
2.5.1 Separating Hyperplanes 22
2.5.2 Separation by a Family of Hyperplanes 24
2.5.3 Separation by a Family of Linear Functionals 26
2.5.4 Separation by a Cone 27
2.5.5 Separation of Starshaped Sets 31
2.6 Generalizations of Starshaped Sets 34
2.6.1 Path Connected Sets 34
2.6.2 Invex and Univex Sets 35
2.6.3 ^ Convex Sets 36
3. GENERALIZED CONCAVE FUNCTIONS 37
3.1 Concave and Quasiconcave Functions 37
3.2 Starshaped Functions 40
3.3 Further Generalizations of Concave Functions 46
3.3.1 Quasiconnected Functions 46
3.3.2 ( $, *I ) Concave Functions 50
3.4 Differentiable Functions 57
vi GENERALIZED CONCAVITY
3.4.1 Differentiable Quasiconcave Functions 57
3.4.2 Pseudoconcave Functions 59
3.4.3 Incave, Pseudoincave and Pseudounicave Functions 62
3.5 Constrained Optimization 66
4. TRIANGULAR NORMS AND T QUASICONCAVE FUNCTIONS 73
4.1 Triangular Norms and Conorms 73
4.2 Properties of Triangular Norms and Triangular Conorms 76
4.3 Representations of Triangular Norms and Triangular Conorms 79
4.4 Negations and De Morgan Triples 82
4.5 Domination of Triangular Norms 84
4.6 T Quasiconcave Functions 85
4.7 ( $, T) Concave Functions 95
4.8 Properties of ( $, T) Concave Functions 97
5. AGGREGATION OPERATORS 101
5.1 Introduction 101
5.2 Definition and Basic Properties 102
5.3 Continuity Properties 104
5.4 Averaging Aggregation Operators 106
5.4.1 Compensative Aggregation Operators 106
5.4.2 Order Statistic Aggregation Operators 108
5.4.3 Order Weighted Averaging Operators 108
5.5 Sugeno and Choquet Integrals 110
5.6 Other Aggregation Operators 113
5.7 Aggregation of Functions 114
6. FUZZY SETS 121
6.1 Introduction 121
6.2 Definition and Basic Properties 122
6.3 Operations with Fuzzy Sets 126
6.4 Extension Principle 127
6.5 Binary and Valued Relations 129
6.6 Fuzzy Relations 131
6.7 Fuzzy Extensions of Valued Relations 133
6.8 Fuzzy Quantities and Fuzzy Numbers 137
6.9 Fuzzy Extensions of Real Valued Functions 140
6.10 Higher Dimensional Fuzzy Quantities 145
6.11 Fuzzy Extensions of Valued Relations 150
Contents vii
Part II Applications
7. FUZZY MULTI CRITERIA DECISION MAKING 163
7.1 Introduction 163
7.2 Fuzzy Criteria 164
7.3 Pareto Optimal Decisions 166
7.4 Compromise Decisions 170
7.5 Generalized Compromise Decisions 173
7.6 Aggregation of Fuzzy Criteria 177
7.7 Extremal Properties 178
7.8 Application to Location Problem 179
7.9 Application in Engineering Design 186
8. FUZZY MATHEMATICAL PROGRAMMING 193
8.1 Introduction 193
8.2 Modelling Reality by Fuzzy Mathematical Programming 195
8.3 Mathematical Programming Problems with Parameters 195
8.4 Formulation of Fuzzy Mathematical Programming Problems 197
8.5 Feasible Solutions of FMP Problems 199
8.6 Properties of Feasible Solution 200
8.7 Optimal Solutions of the FMP Problem 208
9. FUZZY LINEAR PROGRAMMING 217
9.1 Introduction 217
9.2 Formulation of FLP problem 217
9.3 Properties of Feasible Solution 220
9.4 Properties of Optimal Solutions 223
9.5 Extended Addition in FLP 227
9.6 Duality 231
9.7 Special Models of FLP 235
9.7.1 Interval Linear Programming 235
9.7.2 Flexible Linear Programming 238
9.7.3 FLP Problems with Interactive Fuzzy Parameters 240
9.7.4 FLP Problems with Centered Parameters 242
9.8 Illustrative Examples 244
10. FUZZY SEQUENCING AND SCHEDULING 253
10.1 Introduction 253
10.2 Deterministic Models 254
10.3 Stochastic Models 259
10.4 Fuzzy Models 265
10.4.1 Fuzzy Due Dates 266
viii GENERALIZED CONCAVITY
10.4.2 Fuzzy Processing Times 268
10.4.3 Fuzzy Precedence 276
10.4.4 Concluding Remarks 281
|
| any_adam_object | 1 |
| author | Ramík, Jaroslav Vlach, Milan |
| author_facet | Ramík, Jaroslav Vlach, Milan |
| author_role | aut aut |
| author_sort | Ramík, Jaroslav |
| author_variant | j r jr m v mv |
| building | Verbundindex |
| bvnumber | BV014550067 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.95 |
| callnumber-search | T57.95 |
| callnumber-sort | T 257.95 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)47296245 (DE-599)BVBBV014550067 |
| dewey-full | 658.4/03 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.4/03 |
| dewey-search | 658.4/03 |
| dewey-sort | 3658.4 13 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01762nam a2200445 cb4500</leader><controlfield tag="001">BV014550067</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20030718 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020709s2002 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792374959</subfield><subfield code="9">0-7923-7495-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)47296245</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014550067</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">T57.95</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">658.4/03</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 870</subfield><subfield code="0">(DE-625)143265:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ramík, Jaroslav</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized concavity in fuzzy optimization and decision analysis</subfield><subfield code="c">Jaroslav Ramík ; Milan Vlach</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston [u.a.]</subfield><subfield code="b">Kluwer Acad. Publ.</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 296 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">International series in operations research & management science</subfield><subfield code="v">41</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Concave functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Decision making</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fuzzy mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Entscheidungsprozess</subfield><subfield code="0">(DE-588)4121202-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fuzzy-Optimierung</subfield><subfield code="0">(DE-588)4659945-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fuzzy-Optimierung</subfield><subfield code="0">(DE-588)4659945-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Entscheidungsprozess</subfield><subfield code="0">(DE-588)4121202-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vlach, Milan</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">International series in operations research & management science</subfield><subfield code="v">41</subfield><subfield code="w">(DE-604)BV011630976</subfield><subfield code="9">41</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009893268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009893268</subfield></datafield></record></collection> |
| id | DE-604.BV014550067 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:24Z |
| institution | BVB |
| isbn | 0792374959 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009893268 |
| oclc_num | 47296245 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIV, 296 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Ramík, Jaroslav Verfasser aut Generalized concavity in fuzzy optimization and decision analysis Jaroslav Ramík ; Milan Vlach Boston [u.a.] Kluwer Acad. Publ. 2002 XIV, 296 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 41 Concave functions Decision making Fuzzy mathematics Mathematical optimization Entscheidungsprozess (DE-588)4121202-2 gnd rswk-swf Fuzzy-Optimierung (DE-588)4659945-9 gnd rswk-swf Fuzzy-Optimierung (DE-588)4659945-9 s Entscheidungsprozess (DE-588)4121202-2 s DE-604 Vlach, Milan Verfasser aut International series in operations research & management science 41 (DE-604)BV011630976 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009893268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramík, Jaroslav Vlach, Milan Generalized concavity in fuzzy optimization and decision analysis International series in operations research & management science Concave functions Decision making Fuzzy mathematics Mathematical optimization Entscheidungsprozess (DE-588)4121202-2 gnd Fuzzy-Optimierung (DE-588)4659945-9 gnd |
| subject_GND | (DE-588)4121202-2 (DE-588)4659945-9 |
| title | Generalized concavity in fuzzy optimization and decision analysis |
| title_auth | Generalized concavity in fuzzy optimization and decision analysis |
| title_exact_search | Generalized concavity in fuzzy optimization and decision analysis |
| title_full | Generalized concavity in fuzzy optimization and decision analysis Jaroslav Ramík ; Milan Vlach |
| title_fullStr | Generalized concavity in fuzzy optimization and decision analysis Jaroslav Ramík ; Milan Vlach |
| title_full_unstemmed | Generalized concavity in fuzzy optimization and decision analysis Jaroslav Ramík ; Milan Vlach |
| title_short | Generalized concavity in fuzzy optimization and decision analysis |
| title_sort | generalized concavity in fuzzy optimization and decision analysis |
| topic | Concave functions Decision making Fuzzy mathematics Mathematical optimization Entscheidungsprozess (DE-588)4121202-2 gnd Fuzzy-Optimierung (DE-588)4659945-9 gnd |
| topic_facet | Concave functions Decision making Fuzzy mathematics Mathematical optimization Entscheidungsprozess Fuzzy-Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009893268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011630976 |
| work_keys_str_mv | AT ramikjaroslav generalizedconcavityinfuzzyoptimizationanddecisionanalysis AT vlachmilan generalizedconcavityinfuzzyoptimizationanddecisionanalysis |