Ebook: Semiorders: Properties, Representations, Applications

Semiorder is probably one of the most frequently ordered structures in science. It naturally appears in fields like psychometrics, economics, decision sciences, linguistics and archaeology. It explicitly takes into account the inevitable imprecisions of scientific instruments by allowing the replacement of precise numbers by intervals. The purpose of this book is to dissect this structure and to study its fundamental properties. The main subjects treated are the numerical representations of semiorders, the generalizations of the concept to valued relations, the aggregation of semiorders and their basic role in a general theoretical framework for multicriteria decision-aid methods.
Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.

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Semiorder is probably one of the most frequently ordered structures in science. It naturally appears in fields like psychometrics, economics, decision sciences, linguistics and archaeology. It explicitly takes into account the inevitable imprecisions of scientific instruments by allowing the replacement of precise numbers by intervals. The purpose of this book is to dissect this structure and to study its fundamental properties. The main subjects treated are the numerical representations of semiorders, the generalizations of the concept to valued relations, the aggregation of semiorders and their basic role in a general theoretical framework for multicriteria decision-aid methods.
Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.

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Semiorder is probably one of the most frequently ordered structures in science. It naturally appears in fields like psychometrics, economics, decision sciences, linguistics and archaeology. It explicitly takes into account the inevitable imprecisions of scientific instruments by allowing the replacement of precise numbers by intervals. The purpose of this book is to dissect this structure and to study its fundamental properties. The main subjects treated are the numerical representations of semiorders, the generalizations of the concept to valued relations, the aggregation of semiorders and their basic role in a general theoretical framework for multicriteria decision-aid methods.
Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-6
First Presentation of the Basic Concepts....Pages 7-18
Historical Review and Applications....Pages 19-48
Basic Concepts and Definitions....Pages 49-70
Minimal Representations....Pages 71-102
Valued Semiorders....Pages 103-123
Aggregation of Semiorders....Pages 125-165
Miscellaneous....Pages 167-172
Conclusion....Pages 173-174
Back Matter....Pages 175-190

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Semiorder is probably one of the most frequently ordered structures in science. It naturally appears in fields like psychometrics, economics, decision sciences, linguistics and archaeology. It explicitly takes into account the inevitable imprecisions of scientific instruments by allowing the replacement of precise numbers by intervals. The purpose of this book is to dissect this structure and to study its fundamental properties. The main subjects treated are the numerical representations of semiorders, the generalizations of the concept to valued relations, the aggregation of semiorders and their basic role in a general theoretical framework for multicriteria decision-aid methods.
Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-6
First Presentation of the Basic Concepts....Pages 7-18
Historical Review and Applications....Pages 19-48
Basic Concepts and Definitions....Pages 49-70
Minimal Representations....Pages 71-102
Valued Semiorders....Pages 103-123
Aggregation of Semiorders....Pages 125-165
Miscellaneous....Pages 167-172
Conclusion....Pages 173-174
Back Matter....Pages 175-190
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