Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements

@inproceedings{32052,
   author = {Ramík, Jaroslav},
   address = {Praha, CZ},
   booktitle = {36-th International Conference Mathematical Methods in Economics 2018},
   keywords = {ranking alternatives; pairwise comparisons matrix; analytic hierarchy process; consistency},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Praha, CZ},
   isbn = {978-80-7378-372-3},
   pages = {457-462},
   publisher = {Silesian Univeristy in Opava, SBA Karviná},
   title = {Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements},
   year = {2018}
}

TY  - JOUR
ID  - 32052
AU  - Ramík, Jaroslav
PY  - 2018
TI  - Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements
PB  - Silesian Univeristy in Opava, SBA Karviná
CY  - Praha, CZ
SN  - 9788073783723
KW  - ranking alternatives
KW  - pairwise comparisons matrix
KW  - analytic hierarchy process
KW  - consistency
N2  - In this paper we deal with Preference Order Preservation (POP) condition of pairwise comparisons (PC) matrix with fuzzy elements. Fuzzy elements are appropriate whenever the decision maker (DM) is uncertain about the value of his/her evaluation of the relative importance of elements in question, or, when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. We formulate the problem in a general setting investigating pairwise comparisons matrices with fuzzy elements from Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive or fuzzy approaches. Then we propose new order preservation concept based on alpha-cuts. We define the concept of consistency of PC matrix with fuzzy elements (PCF matrices), generalize the concept of the preference order preservation condition (POP condition) to PCF matrices defining weak POP and strong POP condition and derive sufficient conditions for POP condition to be met. Finally, we discuss a numerical example in order to illustrate the proposed concepts and properties.
ER  - 

RAMÍK, Jaroslav. Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements. Online. In \textit{36-th International Conference Mathematical Methods in Economics 2018}. Praha, CZ: Silesian Univeristy in Opava, SBA Karviná, 2018. s.~457-462. ISBN~978-80-7378-372-3. [citováno 2024-04-24]