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2015 | 10 | 124-140

Article title

Incomplete Preference Matrix on Alo-Group and Its Application to Ranking of Alternatives



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Pairwise comparison is a powerful method in multi-criteria optimiza- tion. When comparing two elements, the decision maker assigns a value from the given scale which is an Abelian linearly ordered group (Alo- group) of the real line to any pair of alternatives representing an element of the preference matrix (P-matrix). Both non-fuzzy and fuzzy mul- tiplicative and additive preference matrices are generalized. Then we focus on situations where some elements of the P-matrix are missing. We propose a general method for completing fuzzy matrix with missing elements, called the extension of the P-matrix, and investigate some im- portant particular cases of fuzzy preference matrix with missing elements. Eight illustrative numerical examples are included.






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