کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4931792 | 1433263 | 2016 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Primary facets of order polytopes
ترجمه فارسی عنوان
جنبه های اولیه چند منظوره سفارش
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کلمات کلیدی
نیمه مدرن، نیمه صوتی چند جمله ای، سفارش چندساله، نابرابری تعریف فاکتور،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all order relations of a chosen type. The five prominent types of order relations are linear orders, weak orders, semiorders, interval orders and partial orders. For each of them, the problem of finding a complete, workable characterization of the vectors of probabilities is crucial-but it is reputably inaccessible. Under a geometric reformulation, the problem asks for a linear description of a convex polytope whose vertices are known. As for any convex polytope, a shortest linear description comprises one linear inequality per facet. Getting all of the facet-defining inequalities of any of the five order polytopes seems presently out of reach. Here we search for the facet-defining inequalities which we call primary because their coefficients take only the values â1, 0 or 1. We provide a classification of all primary, facet-defining inequalities of three of the five order polytopes. Moreover, we elaborate on the intricacy of the primary facet-defining inequalities of the linear order and the weak order polytopes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Psychology - Volume 75, December 2016, Pages 231-245
Journal: Journal of Mathematical Psychology - Volume 75, December 2016, Pages 231-245
نویسندگان
Jean-Paul Doignon, Selim Rexhep,