Condition of Order Preservation in Pairwise Comparisons Matrix

@inproceedings{32053,
   author = {Ramík, Jaroslav},
   address = {Cham, Switzerland},
   booktitle = {International Conference on Intelligent Decision Technologies},
   keywords = {ranking alternatives; pairwise comparisons matrix; analytic hierarchy process; consistency},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Cham, Switzerland},
   isbn = {978-3-319-59420-0},
   pages = {283-292},
   publisher = {Springer},
   title = {Condition of Order Preservation in Pairwise Comparisons Matrix},
   year = {2018}
}

TY  - JOUR
ID  - 32053
AU  - Ramík, Jaroslav
PY  - 2018
TI  - Condition of Order Preservation in Pairwise Comparisons Matrix
PB  - Springer
CY  - Cham, Switzerland
SN  - 9783319594200
KW  - ranking alternatives
KW  - pairwise comparisons matrix
KW  - analytic hierarchy process
KW  - consistency
N2  - This paper forms both theoretical and practical innovation basis for decision making process in micro and macro economics. The decision making problem considered here is to rank n alternatives from the best to the worst, using the information given by the decision maker(s) in the form of an n×n pairwise comparisons matrix. Here, we deal with pairwise comparisons matrices with fuzzy elements. Fuzzy elements of the pairwise comparisons matrix are applied whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of elements in question. We investigate pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group) over a real interval which is a generalization of traditional multiplicative or additive approaches. The concept of reciprocity and consistency of pairwise comparisons matrices with fuzzy elements is well known. Here, we extend these concepts, namely to the strict as well as strong consistency of pairwise comparisons matrices with fuzzy elements (PCF matrices). We derive the necessary and sufficient conditions for strict/strong consistency and investigate their properties as well as some consequences to the problem of ranking the alternatives. Illustrating examples are presented and discussed.
ER  - 

RAMÍK, Jaroslav. Condition of Order Preservation in Pairwise Comparisons Matrix. In \textit{International Conference on Intelligent Decision Technologies}. Cham, Switzerland: Springer. s.~283-292, 6 s. ISBN~978-3-319-59420-0. 2018.