{"type":"ScholarlyArticle","title":"Plato's Cave in the Dempster-Shafer land--the Link between Pignistic and Plausibility Transformations","authors":[{"name":"Chunlai Zhou","slug":"chunlai-zhou","given":"Chunlai","family":"Zhou","affiliation":"DEKE(MOE) , Computer Science Dept. , Renmin University of China; State Key Lab of Computer Science , Institute of Software , Chinese Academy of Sciences"},{"name":"Biao Qin","slug":"biao-qin","given":"Biao","family":"Qin","affiliation":"DEKE(MOE) , Computer Science Dept. , Renmin University of China"},{"name":"Xiaoyong Du","slug":"xiaoyong-du","given":"Xiaoyong","family":"Du","affiliation":"DEKE(MOE) , Computer Science Dept. , Renmin University of China"}],"abstract":"In reasoning under uncertainty in AI, there are (at least) two useful and different ways of understanding beliefs: the first is as absolute belief or degree of belief in propositions and the second is as belief update or measure of change in belief.  Pignistic and plausibility transformations are two well-known probability transformations that map belief functions to probability functions in the Dempster-Shafer theory of evidence.  In this paper, we establish the link between pignistic and plausibility transformations by devising a belief-update framework for belief functions where  plausibility transformation works on belief update while pignistic transformation operates on absolute belief. In this framework, we define a new belief-update operator connecting the two transformations, and interpret the framework in a belief-function model of parametric statistical inference. As a metaphor, these two transformations projecting the belief-update framework for belief functions to that for probabilities  are likened to the fire projecting reality into shadows on the wall in Plato's cave.","doi":"10.24963/ijcai.2017/652","url":"https://ijcai.org/proceedings/2017/652","pdf":"https://ijcai.org/proceedings/2017/0652.pdf","markdown":"https://ijcai.org/proceedings/2017/652.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/652","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Uncertainty in AI","track":"Main track","number":652,"pages":{"first":4676,"last":4682},"keywords":["Uncertainty in AI: Uncertainty in AI","Uncertainty in AI: Uncertainty Representations"],"videos":[],"references":[{"position":1,"raw":"[Cobb and Shenoy, 2006] Barry Cobb and Prakash Shenoy. 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