Pairwise Comparisons Method: theory and applications in decision making
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| Format: | Thesis Book |
| Language: | English |
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Cham
Springer
[2020]
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| Series: | Lecture Notes in Economics and Mathematical Systems
690 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 231 Seiten Illustrationen 23.5 cm x 15.5 cm |
| ISBN: | 9783030398903 |
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Record in the Search Index
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| adam_text | Contents Part I Pairwise Comparisons Method—Theory 1 Preliminaries................................................................................................... 1.1 Fuzzy Sets............................................................................................ 1.2 Extension Principle.............................................................................. 1.3 Binary Relations, Valued Relations, and FuzzyRelations............. 1.4 Fuzzy Quantities, Fuzzy Numbers, and Fuzzy Intervals................. 1.5 Matrices with Fuzzy Elements........................................................... 1.6 Abelian Linearly Ordered Groups.................................................... References........................................................................................................ 3 3 5 6 7 9 11 14 2 Pairwise Comparison Matrices in Decision-Making............................. 2.1 Historical Remarks.............................................................................. 2.2 State of the Art..................................................................................... 2.3 Problem Definition.............................................................................. 2.4 Multiplicative Pairwise Comparisons Matrices............................... 2.5 Methods for Deriving Priorities from Multiplicative Pairwise Comparison Matrices........................................................... 2.5.1 Eigenvector Method (EVM).................................................. 2.5.2 Arithmetic Mean Method (AMM)........................................
2.5.3 Least Squares Method (LSM)............................................... 2.5.4 Logarithmic Least Squares Method (LLSM)/Geometric Mean Method (GMM)........................................................... 2.5.5 Fuzzy Programming Method............................................... 2.6 Desirable Properties of the Priority Vector...................................... 2.7 Alternative Approach to Derivation of the PriorityVector............. 2.7.1 (Problem 0).............................................................................. 2.7.2 Transformation to (Problem є)............................................. 2.7.3 Solving (Problem ε)................................................................ 2.7.4 Illustrative Example................................................................ 17 17 18 19 20 23 24 26 28 29 33 34 40 40 41 42 45 XV
xvi Contents? 2.8 Additive Pairwise Comparison Matrices.......................................... 2.8.1 Deriving Priority Vector from Additive PCM.................. 2.9 Fuzzy Pairwise Comparison Matrices............................................... 2.9.1 Some Relations Between Fuzzy Pairwise Comparison Matrices............................................................. 2.9.2 Methods for Deriving Priorities fromPCF Matrices........... 2.10 Conclusion............................................................................................ References....................................................................................................... 3 Pairwise Comparisons Matrices on Alo-Groups in Decision-Making....................................................................................... 3.1 Unified Framework for Pairwise Comparisons Matrices over ALO-Groups................................................................ 3.1.1 Introduction.............................................................................. 3.1.2 Continuous Alo-Groups over a Real Interval..................... 3.1.3 Pairwise Comparison Matrices over a Divisible Alo-Group................................................................................ 3.2 Desirable Properties of the Priority Vector...................................... 3.3 Deriving Priority Vector by Solving an Optimization Problem................................................................................................ 3.3.1 Transformation to (©-Problem ε)........................................ 3.3.2 Solving
(©-Problem ε)........................................................... 3.4 Generalized Geometric Mean Method (GGMM)............................ 3.5 Measuring Consistency of PCM in Alo-Groups............................ 3.5.1 Multiplicative Alo-Group...................................................... 3.5.2 Measuring the Inconsistency of PCMs on Alo-Groups......................................................................... 3.6 Strong Transitive and Weak Consistent PCM................................. 3.6.1 Special Notation.................................................................... 3.6.2 ©-Transitive PCM.................................................................. 3.6.3 Weak-©-Consistent PCM...................................................... 3.6.4 Strong-©-Transitive PCM...................................................... 3.6.5 Examples ................................................................................ 3.7 Pairwise Comparison Matrix with Missing Elements..................... 3.7.1 Formulation of the Problem.................................................. 3.7.2 Missing Elements of Matrix.................................................. 3.7.3 Problem of Missing Elements in PC Matrices Based on Optimization........................................................... 3.7.4 Particular Cases of PC Matrices with Missing Elements................................................................................... 3.7.5 Case L = {(1,2), (2,3),· ··,(«— l,n)}............................ 3.7.6 Case L = {(1,2), (1,3), ■ · -, ( 1,
и)}...................................... 3.7.7 Incompleteness Index............................................................. 47 49 54 56 57 60 61 67 67 67 68 73 75 82 83 84 85 89 89 91 93 93 94 96 98 99 100 100 102 103 106 107 108 110
Contents З§ 39 incompleteness—Conclusions............................................................ What Is the Best Evaluation Method for Pairwise Comparisons: A Case Study............................................................. 3.9.1 Introduction to Case Study.................................................... 3.9.2 Three Evaluation Systems .................................................... 3.9.3 The Experiment....................................................................... 3.9.4 Results of the Experiment.................................................... 3.9.5 Discussion and Conclusions................................................. References....................................................................................................... 4 Pairwise Comparisons Matrices with Fuzzy and Intuitionistic Fuzzy Elements in Decision-Making........................................................ 4.1 Introduction......................................................................................... 4.2 Preliminaries ....................................................................................... 4.3 FPC Matrices, Reciprocity, and Consistency................................... 4.4 Desirable Properties of the Priority Vector...................................... 4.5 Priority Vectors................................................................................... 4.6 Measuring Inconsistency of FPC Matrices...................................... 4.7 Pairwise Comparisons Matrices with Intuitionistic Fuzzy
Elements.............................................................................................. 4.7.1 Introduction.............................................................................. 4.7.2 Preliminaries........................................................................... 4.7.3 Pairwise Comparison Matrices with Elements Being Intuitionistic Fuzzy Intervals...................................... 4.7.4 IFPC Matrices, Reciprocity, and Consistency ................... 4.7.5 Priority Vectors of IFPC Matrices........................................ 4.7.6 Measuring Inconsistency of IFPC Matrices........................ 4.8 Conclusion............................................................................................ References........................................................................................................ 5 Stochastic Approaches to Pairwise Comparisons Matrices in Decision-Making....................................................................................... 5.1 Introduction......................................................................................... 5.2 Basic Models....................................................................................... 5.3 Linear Models..................................................................................... 5.3.1 Thurstone-Mosteller Model................................................. 5.3.2 Bradley-Terry Model............................................................. 5.3.3 Logarithmic Least Squares and the Normal
Distribution.............................................................................. 5.4 Direct Approaches.............................................................................. 5.4.1 The Kullback-Leibler Distance............................................. 5.5 Conclusion............................................................................................ References........................................................................................................ xvii Ill 112 112 112 116 119 121 121 125 125 127 129 139 144 147 150 150 152 154 156 161 164 167 168 171 171 172 173 175 176 177 179 181 183 184
xviii Part II 6 7 Conto Pairwise Comparisons Method—Applications in Decision Making Applications in Decision-Making: Analytic Hierarchy Process—AHP Revisited.............................................................................. 6.1 Introduction......................................................................................... 6.2 Applications of AHP........................................................................... 6.3 Establishing Priorities......................................................................... 6.3.1 Normalization of Criteria...................................................... 6.3.2 Basic Scale.............................................................................. 6.3.3 Calculation of Weights from the Matrix of Pairwise Comparisons...................................................... 6.3.4 Consistency of a PCM........................................................... 6.4 Synthesis.............................................................................................. 6.5 Case Study: Optimal Choice of a Passenger Car............................ 6.6 AHP Procedure: Seven Steps in Decision-Making........................ 6.7 Case Study: Optimal Choice of a Passenger Car—Continuation from Sect. 6.5.................................................... References....................................................................................................... Applications in Practical Decision-Making Methods: PROMETHEE andTOPSIS........................................................................ 7.1 Introduction to
PROMETHEE........................................................... 7.2 Formulation of the Problem................................................................ 7.3 Preference Functions........................................................................... 7.4 Case Study: Optimal Choice of Personal Computer..................... 7.5 Introduction to TOPSIS Method...................................................... 7.6 Description of the TOPSIS Method................................................. 7.7 The Algorithm..................................................................................... 7.8 Application of TOPSIS: An Example............................................... 7.9 Conclusion of Applications of PCMs in Practical Decision-Making Problems................................................................ References........................................................................................................ Index 18c 18Ç 19Q 19՛ 194. 195« 195 19՜ 19! 20Q 201 207 210 213 213 214 215 219 220 221 224 225 227 228 229
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Contents Part I Pairwise Comparisons Method—Theory 1 Preliminaries. 1.1 Fuzzy Sets. 1.2 Extension Principle. 1.3 Binary Relations, Valued Relations, and FuzzyRelations. 1.4 Fuzzy Quantities, Fuzzy Numbers, and Fuzzy Intervals. 1.5 Matrices with Fuzzy Elements. 1.6 Abelian Linearly Ordered Groups. References. 3 3 5 6 7 9 11 14 2 Pairwise Comparison Matrices in Decision-Making. 2.1 Historical Remarks. 2.2 State of the Art. 2.3 Problem Definition. 2.4 Multiplicative Pairwise Comparisons Matrices. 2.5 Methods for Deriving Priorities from Multiplicative Pairwise Comparison Matrices. 2.5.1 Eigenvector Method (EVM). 2.5.2 Arithmetic Mean Method (AMM).
2.5.3 Least Squares Method (LSM). 2.5.4 Logarithmic Least Squares Method (LLSM)/Geometric Mean Method (GMM). 2.5.5 Fuzzy Programming Method. 2.6 Desirable Properties of the Priority Vector. 2.7 Alternative Approach to Derivation of the PriorityVector. 2.7.1 (Problem 0). 2.7.2 Transformation to (Problem є). 2.7.3 Solving (Problem ε). 2.7.4 Illustrative Example. 17 17 18 19 20 23 24 26 28 29 33 34 40 40 41 42 45 XV
xvi Contents? 2.8 Additive Pairwise Comparison Matrices. 2.8.1 Deriving Priority Vector from Additive PCM. 2.9 Fuzzy Pairwise Comparison Matrices. 2.9.1 Some Relations Between Fuzzy Pairwise Comparison Matrices. 2.9.2 Methods for Deriving Priorities fromPCF Matrices. 2.10 Conclusion. References. 3 Pairwise Comparisons Matrices on Alo-Groups in Decision-Making. 3.1 Unified Framework for Pairwise Comparisons Matrices over ALO-Groups. 3.1.1 Introduction. 3.1.2 Continuous Alo-Groups over a Real Interval. 3.1.3 Pairwise Comparison Matrices over a Divisible Alo-Group. 3.2 Desirable Properties of the Priority Vector. 3.3 Deriving Priority Vector by Solving an Optimization Problem. 3.3.1 Transformation to (©-Problem ε). 3.3.2 Solving
(©-Problem ε). 3.4 Generalized Geometric Mean Method (GGMM). 3.5 Measuring Consistency of PCM in Alo-Groups. 3.5.1 Multiplicative Alo-Group. 3.5.2 Measuring the Inconsistency of PCMs on Alo-Groups. 3.6 Strong Transitive and Weak Consistent PCM. 3.6.1 Special Notation. 3.6.2 ©-Transitive PCM. 3.6.3 Weak-©-Consistent PCM. 3.6.4 Strong-©-Transitive PCM. 3.6.5 Examples . 3.7 Pairwise Comparison Matrix with Missing Elements. 3.7.1 Formulation of the Problem. 3.7.2 Missing Elements of Matrix. 3.7.3 Problem of Missing Elements in PC Matrices Based on Optimization. 3.7.4 Particular Cases of PC Matrices with Missing Elements. 3.7.5 Case L = {(1,2), (2,3),· ··,(«— l,n)}. 3.7.6 Case L = {(1,2), (1,3), ■ · -, ( 1,
и)}. 3.7.7 Incompleteness Index. 47 49 54 56 57 60 61 67 67 67 68 73 75 82 83 84 85 89 89 91 93 93 94 96 98 99 100 100 102 103 106 107 108 110
Contents З§ 39 incompleteness—Conclusions. What Is the Best Evaluation Method for Pairwise Comparisons: A Case Study. 3.9.1 Introduction to Case Study. 3.9.2 Three Evaluation Systems . 3.9.3 The Experiment. 3.9.4 Results of the Experiment. 3.9.5 Discussion and Conclusions. References. 4 Pairwise Comparisons Matrices with Fuzzy and Intuitionistic Fuzzy Elements in Decision-Making. 4.1 Introduction. 4.2 Preliminaries . 4.3 FPC Matrices, Reciprocity, and Consistency. 4.4 Desirable Properties of the Priority Vector. 4.5 Priority Vectors. 4.6 Measuring Inconsistency of FPC Matrices. 4.7 Pairwise Comparisons Matrices with Intuitionistic Fuzzy
Elements. 4.7.1 Introduction. 4.7.2 Preliminaries. 4.7.3 Pairwise Comparison Matrices with Elements Being Intuitionistic Fuzzy Intervals. 4.7.4 IFPC Matrices, Reciprocity, and Consistency . 4.7.5 Priority Vectors of IFPC Matrices. 4.7.6 Measuring Inconsistency of IFPC Matrices. 4.8 Conclusion. References. 5 Stochastic Approaches to Pairwise Comparisons Matrices in Decision-Making. 5.1 Introduction. 5.2 Basic Models. 5.3 Linear Models. 5.3.1 Thurstone-Mosteller Model. 5.3.2 Bradley-Terry Model. 5.3.3 Logarithmic Least Squares and the Normal
Distribution. 5.4 Direct Approaches. 5.4.1 The Kullback-Leibler Distance. 5.5 Conclusion. References. xvii Ill 112 112 112 116 119 121 121 125 125 127 129 139 144 147 150 150 152 154 156 161 164 167 168 171 171 172 173 175 176 177 179 181 183 184
xviii Part II 6 7 Conto Pairwise Comparisons Method—Applications in Decision Making Applications in Decision-Making: Analytic Hierarchy Process—AHP Revisited. 6.1 Introduction. 6.2 Applications of AHP. 6.3 Establishing Priorities. 6.3.1 Normalization of Criteria. 6.3.2 Basic Scale. 6.3.3 Calculation of Weights from the Matrix of Pairwise Comparisons. 6.3.4 Consistency of a PCM. 6.4 Synthesis. 6.5 Case Study: Optimal Choice of a Passenger Car. 6.6 AHP Procedure: Seven Steps in Decision-Making. 6.7 Case Study: Optimal Choice of a Passenger Car—Continuation from Sect. 6.5. References. Applications in Practical Decision-Making Methods: PROMETHEE andTOPSIS. 7.1 Introduction to
PROMETHEE. 7.2 Formulation of the Problem. 7.3 Preference Functions. 7.4 Case Study: Optimal Choice of Personal Computer. 7.5 Introduction to TOPSIS Method. 7.6 Description of the TOPSIS Method. 7.7 The Algorithm. 7.8 Application of TOPSIS: An Example. 7.9 Conclusion of Applications of PCMs in Practical Decision-Making Problems. References. Index 18c 18Ç 19Q 19՛ 194. 195« 195 19՜ 19! 20Q 201' 207 210 213 213 214 215 219 220 221 224 225 227 228 229 |
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| series2 | Lecture Notes in Economics and Mathematical Systems |
| spelling | Ramík, Jaroslav Verfasser (DE-588)1066606587 aut Pairwise Comparisons Method theory and applications in decision making Jaroslav Ramík Cham Springer [2020] XVIII, 231 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Economics and Mathematical Systems 690 Dissertation Universität Bielefeld 2017 Spieltheorie (DE-588)4056243-8 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Entscheidung (DE-588)4014904-3 gnd rswk-swf Entscheidungsfindung (DE-588)4113446-1 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Entscheidung (DE-588)4014904-3 s Entscheidungstheorie (DE-588)4138606-1 s Operations Research (DE-588)4043586-6 s DE-604 Spieltheorie (DE-588)4056243-8 s Entscheidungsfindung (DE-588)4113446-1 s 1\p DE-604 Lecture Notes in Economics and Mathematical Systems 690 (DE-604)BV000000036 690 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032044987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ramík, Jaroslav Pairwise Comparisons Method theory and applications in decision making Lecture Notes in Economics and Mathematical Systems Spieltheorie (DE-588)4056243-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Entscheidung (DE-588)4014904-3 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4138606-1 (DE-588)4014904-3 (DE-588)4113446-1 (DE-588)4043586-6 (DE-588)4113937-9 |
| title | Pairwise Comparisons Method theory and applications in decision making |
| title_auth | Pairwise Comparisons Method theory and applications in decision making |
| title_exact_search | Pairwise Comparisons Method theory and applications in decision making |
| title_exact_search_txtP | Pairwise Comparisons Method theory and applications in decision making |
| title_full | Pairwise Comparisons Method theory and applications in decision making Jaroslav Ramík |
| title_fullStr | Pairwise Comparisons Method theory and applications in decision making Jaroslav Ramík |
| title_full_unstemmed | Pairwise Comparisons Method theory and applications in decision making Jaroslav Ramík |
| title_short | Pairwise Comparisons Method |
| title_sort | pairwise comparisons method theory and applications in decision making |
| title_sub | theory and applications in decision making |
| topic | Spieltheorie (DE-588)4056243-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Entscheidung (DE-588)4014904-3 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Spieltheorie Entscheidungstheorie Entscheidung Entscheidungsfindung Operations Research Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032044987&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT ramikjaroslav pairwisecomparisonsmethodtheoryandapplicationsindecisionmaking |