40 International Conference in Mathematical Methods in Economics 2022
Indexes of Desirable Properties of a Pairwise Comparison
Matrix with Fuzzy Elements
D a v i d B a r t l 1
, Jaroslav Ramík2
Abstract. I n the A n a l y t i c H i e r a r c h y Process ( A H P ) , p a i r w i s e c o m p a r i s o n s are used t o q u a n t i f y the r e l a t i v e i m portance
o f the elements, i.e. the c r i t e r i a and/or alternatives. F u z z y elements are appropriate w h e n e v e r the decision
m a k e r is u n c e r t a i n about the v a l u e o f his/her e v a l u a t i o n o f the r e l a t i v e i m p o r t a n c e o f the e l e m e n t s i n q u e s t i o n . I n
this paper, w e deal w i t h the general case w h e n the e l e m e n t s o f the p a i r w i s e c o m p a r i s o n m a t r i x are f u z z y subsets
o f a n A b e l i a n l i n e a r l y o r d e r e d g r o u p ( a l o - g r o u p ) . W e t h e n propose s o m e desirable properties - consistency, i n t e n sity,
a n d coherence - o f the f u z z y p a i r w i s e c o m p a r i s o n m a t r i x a n d w e also propose indexes t o m e a s u r e these
desirable properties.
B a s e d o n these indexes, a n e w s o l u t i o n a l g o r i t h m t o find the p r i o r i t y v e c t o r s a t i s f y i n g these desirable properties
can b e f o r m u l a t e d .
Keywords: m u l t i - c r i t e r i a o p t i m i z a t i o n , A n a l y t i c H i e r a r c h y Process ( A H P ) , p a i r w i s e c o m p a r i s o n m a t r i x , f u z z y
elements, consistency, i n t e n s i t y , coherence, p r i o r i t y vector, a l o - g r o u p
J E L Classification: C 4 4 , C 6 5
AMS Classification: 9 0 C 2 9 , 9 0 C 7 0
Acknowledgements
T h i s research has been supported b y G A C R project N o . 2 1 - 0 3 0 8 5 S .
Contact:
1- S i l e s i a n U n i v e r s i t y i n O p a v a , S c h o o l o f B u s i n e s s A d m i n i s t r a t i o n i n Karviná, D e p a r t m e n t o f I n f o r m a t i c s a n d
M a t h e m a t i c s , Univerzitní náměstí 1 9 3 4 / 3 , 7 3 3 4 0 Karviná, Czechia, b a r t l @ o p f . s l u . c z
2 - S i l e s i a n U n i v e r s i t y i n O p a v a , S c h o o l o f B u s i n e s s A d m i n i s t r a t i o n i n Karviná, D e p a r t m e n t o f I n f o r m a t i c s a n d
M a t h e m a t i c s , Univerzitní náměstí 1 9 3 4 / 3 , 7 3 3 4 0 Karviná, Czechia, r a m i k @ o p f . s l u . c z
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