کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
326099 541924 2016 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Characterization of geodesics in the small in multidimensional psychological spaces
ترجمه فارسی عنوان
خواص ژئودزیک ها در فضاهای کوچک روانی چند بعدی
کلمات کلیدی
مقیاس گذاری چند بعدی؛ غیر محدب ؛ نابرابری مثلث
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی


• We characterized geodesics in the small in multidimensional psychological spaces.
• The distance measure in the small does not fulfill the triangle inequality.
• The geodesics in the small can be obtained from sets of tangent vectors with sum v.
• There exists one and only one F-face for each direction v.

Dzhafarov and Colonius (1999) proposed a theory of subjective Fechnerian distances in a continuous stimulus space of arbitrary dimensionality, where each stimulus is associated with a psychometric function that determines probabilities with which it is discriminated from its infinitesimally close neighboring stimuli. In their theory, the Finslerian metric function FF(x,v) plays a central role, where x is a point of a manifold MM and v∈TxM∖{0} is a nonzero vector in the tangent space at x. Dzhafarov and Colonius (2001) proved that if the Finslerian metric function FF(x,v) is not convex in the direction of a tangent vector v at x, then there exist polygonal arcs from x to x+vs, with s>0s>0 sufficiently small, called Fechnerian geodesic arcs in the small for v at x, whose psychometric length is strictly less than that of the straight line segment from x to x+vs. In their paper, the authors pointed out that: “it is important to investigate the problem of Fechnerian geodesics in the small, that is, the existence and properties of an allowable path connecting x to y=x+vs, whose psychometric length tends to the Fechnerian distance G(x,x+vs) as s→0+s→0+.” Consequently, the principal aim of our paper is to characterize the Fechnerian geodesic arcs in the small. We prove that the Fechnerian geodesic arcs in the small for v at x can be obtained from sets HH of tangent vectors at x, provided that: (a) the sum of the vectors in HH is equal to v, (b) the rays in the directions of the vectors of HH pass through extreme points of only one face Cx(v) of the convex closure of the indicatrix of FF at x, and (c) the ray in the direction of v intersects the relative interior of Cx(v). Also, we prove that the Fechnerian geodesic arcs in the small for v at x determine totally their corresponding face Cx(v).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Psychology - Volume 70, February 2016, Pages 12–20
نویسندگان
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