Fuzzy preference matrix with missing elements and its application to ranking of alternatives

A fuzzy preference matrix is the result of pairwise comparison a powerful method in multi-criteria optimization. When comparing two elements, the decision maker assigns the value between 0 and 1 to any pair of alternatives representing the element of the fuzzy preference matrix. Here, we investigate relations between transitivity and consistency of fuzzy preference matrices and multiplicative preference ones. The obtained results are applied to situations where some elements of the fuzzy preference matrix are missing. We propose a new method for completing fuzzy matrix with missing elements called the extension of the fuzzy preference matrix. We investigate some important particular cases of fuzzy preference matrix with missing elements. Consequently, by the eigenvector of the transformed matrix we obtain the corresponding priority vector. Illustrative numerical examples are supplemented.