کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
390796 661303 2009 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Representation of preference relations on σ-algebras of nonatomic measure spaces: Convexity and continuity
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Representation of preference relations on σ-algebras of nonatomic measure spaces: Convexity and continuity
چکیده انگلیسی

The purpose of this paper is to show how preference relations on σ-algebras can be represented by means of nonadditive set functions that satisfy appropriate requirements of convexity and continuity on σ-algebras. To this end, we introduce convex combinations of measurable sets, and quasiconcave and concave functions on σ-algebras, which conform with the standard results in convex analysis. We formulate the convexity and the continuity axioms for preference relations on σ-algebras with a metric topology and show the existence of utility functions for convex continuous preference relations. We also show that monotone continuous preference relations are representable by fuzzy measures.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Fuzzy Sets and Systems - Volume 160, Issue 5, 1 March 2009, Pages 624-634