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

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  • Jaroslav Ramík

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.

Suggested Citation

  • Jaroslav Ramík, 2016. "Incomplete preference matrix on Alo-group and its application to ranking of alternatives," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(4), pages 412-422.
    • Handle: RePEc:ids:ijmore:v:9:y:2016:i:4:p:412-422
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