Title: Incomplete preference matrix on Alo-group and its application to ranking of alternatives

Authors: Jaroslav Ramík

Addresses: School of Business Administration, Silesian University, Karvina CZ 73340, Czech Republic

Abstract: A preference matrix is the result of pairwise comparison a powerful method in multi-criteria optimisation. When comparing two elements, the decision maker assigns the value from a given scale which is an Abelian linearly ordered group (Alo-group) of the real line to any pair of alternatives representing the element of the preference matrix (P-matrix). We generalise the well known multiplicative and additive preference matrices, and also multiplicative and additive fuzzy preference ones. Then we focus on situations where some elements of the P-matrix are missing. We propose a general method for completing P-matrix with missing elements called the extension of the P-matrix. We investigate some important particular case of fuzzy P-matrix with missing elements. Two illustrative numerical examples are supplemented.

Keywords: multicriteria optimisation; pairwise comparison; preference matrix; incomplete matrix; Alo-group; Abelian linearly ordered group; alternatives ranking; fuzzy P-matrix; missing elements.

DOI: 10.1504/IJMOR.2016.079805

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.4, pp.412 - 422

Received: 23 Dec 2014
Accepted: 06 Mar 2015

Published online: 23 Sep 2016 *

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