کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1703797 1519410 2014 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A simple formula to find the closest consistent matrix to a reciprocal matrix
ترجمه فارسی عنوان
یک فرمول ساده برای یافتن نزدیکترین ماتریس سازگار به یک ماتریس متقابل
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
چکیده انگلیسی

Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benítez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematical Modelling - Volume 38, Issues 15–16, 1 August 2014, Pages 3968–3974
نویسندگان
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