Strict Consistency in Pairwise Comparisons Matrix With Fuzzy Elements

@inbook{35988,
   author = {Ramík, Jaroslav},
   address = {Cham, Switzerland},
   booktitle = {Intelligent Decision Technologies 2017 - Smart Innovation, Systems and Technologies},
   keywords = {ranking alternatives; pairwise comparisons matrix; reciprocity; consistency; alo-group},
   howpublished = {paměťový nosič},
   language = {eng},
   location = {Cham, Switzerland},
   isbn = {978-3-319-59420-0},
   pages = {1-10},
   publisher = {Springer International AG},
   title = {Strict Consistency in Pairwise Comparisons Matrix With Fuzzy Elements},
   year = {2017}
}

TY  - CHAP
ID  - 35988
AU  - Ramík, Jaroslav
PY  - 2017
TI  - Strict Consistency in Pairwise Comparisons Matrix With Fuzzy Elements
VL  - neuveden
PB  - Springer International AG
CY  - Cham, Switzerland
SN  - 9783319594200
KW  - ranking alternatives
KW  - pairwise comparisons matrix
KW  - reciprocity
KW  - consistency
KW  - alo-group
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 sucient 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. Strict Consistency in Pairwise Comparisons Matrix With Fuzzy Elements. In \textit{Intelligent Decision Technologies 2017 - Smart Innovation, Systems and Technologies}. Cham, Switzerland: Springer International AG. s.~1-10. ISBN~978-3-319-59420-0. 2017.