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

Jaroslav Ramík

International Journal of Mathematics in Operational Research, 2016, vol. 9, issue 4, 412-422

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. (search for similar items in EconPapers)
Date: 2016
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