{"title":"Metric and Latticial Medians","authors":"O. Hudry, B. Leclerc, B. Monjardet, J. Barthélemy","doi":"10.1002/9780470611876.CH20","DOIUrl":"https://doi.org/10.1002/9780470611876.CH20","url":null,"abstract":"This paper presents the -linked- notions of metric and latticial medians and it explains what is the median procedure for the consensus problems, in particular in the case of the aggregation of linear orders. First we consider the medians of a v-tuple of arbitrary or particular binary relations.. Then we study in depth the difficult (in fact NP-difficult) problem of finding the median orders of a profile of linear orders. More generally, we consider the medians of v-tuples of elements of a semilattice and we describe the median semilattices, i.e. the semilattices were medians are easily computable.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116843294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Aggregation Functions for Decision Making","authors":"J. Marichal","doi":"10.1002/9780470611876.ch17","DOIUrl":"https://doi.org/10.1002/9780470611876.ch17","url":null,"abstract":"Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are widely used in many well-known disciplines such as statistics, economics, finance, and computer science. In this paper we confine ourselves to the use of aggregation functions in decision making.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125714733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Decision under Uncertainty: The Classical Models","authors":"A. Chateauneuf, M. Cohen, J. Jaffray","doi":"10.1002/9780470611876.CH9","DOIUrl":"https://doi.org/10.1002/9780470611876.CH9","url":null,"abstract":"This chapiter of a collective book is dedicated to classical decision models under uncertainty, i.e. under situations where events do not have \"objective\" probabilities with which the Decision Marker agrees. We present successively the two main theories, their axiomatic, the interpretation and the justification of their axioms and their main properties : first, the general model of Subjective Expected Utility due to Savage (Savage, 1954), second, the Anscombe-Aumann (1963) theory, in a different framework. Both theories enforce the universal use of a probabilistic representation. We then discuss this issue in connection with the experimental result known as the Ellsberg paradox.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129950983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Decision under Risk: The Classical Expected Utility Model","authors":"A. Chateauneuf, M. Cohen, J. Tallon","doi":"10.1002/9780470611876.CH8","DOIUrl":"https://doi.org/10.1002/9780470611876.CH8","url":null,"abstract":"This chapter of a collective book aims at presenting the basics of decision making under risk. We first define notions of risk and increasing risk and recall definitions and classifications (that are valid independently of any representation) of behavior under risk. We then review the classical model of expected utility due to von Neumann and Morgenstern andd its main properties. Issues raised by this model are then discussed and two models generalizing the expected utility model are briefly discussed.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128640801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Logical Representation of Preferences","authors":"J. Lang","doi":"10.1002/9780470611876.CH7","DOIUrl":"https://doi.org/10.1002/9780470611876.CH7","url":null,"abstract":"The specification of a decision making problem includes the agent's preferences on the available alternatives. We have to distinguish between preference modeling, which consists of choosing a mathematical model for preferences and studying its properties, from preference representation (or specification), which consists of choosing a language for expressing, storing and processing an agent's preferences efficiently. A third important problem is preference elicitation, which consists of interacting with the agent in order to acquire enough information about their preferences.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131733973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Social Choice Theory and Multicriteria Decision Aiding","authors":"D. Bouyssou, T. Marchant, P. Perny","doi":"10.1002/9780470611876.CH19","DOIUrl":"https://doi.org/10.1002/9780470611876.CH19","url":null,"abstract":"The aim of this chapter is to present some important results in Social Choice Theory in a simple way and to discuss their relevance for multicriteria decision aiding. Using some classical examples of voting problems, we will show some fundamental difficulties arising when aggregating preferences. We will then present some theoretical results that can help us better understand the nature of these difficulties. We will then try to analyze the consequences of these results for multicriteria decision aiding. A long references list will help the interested reader to deepen his understanding of these questions.","PeriodicalId":112888,"journal":{"name":"Decision-making Process","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126916855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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