Convergence of powers of reciprocal fuzzy matrices

On the max-nilpotent t-norm powers of a fuzzy matrix

“…Various publications [3][4][5]7,[9][10][11][14][15][16]18,[25][26][27][28][29][30]32] evaluated the powers of a fuzzy matrix with max-min/maxproduct/lattice compositions and studied the relative properties or applications with these compositions in the literatures, however the limiting behavior of the powers of a fuzzy matrix depends on its composition. The above Fuzzy Algebras ([0, 1], max, ) are fairly general subclass of dioïds where addition is the maximum of two real numbers and is an arbitrary t-norm [13].…”

“…Thomason [32] first explored the powers of a fuzzy relation, demonstrating that the max-min powers of a fuzzy matrix [3,7,[9][10][11][17][18][19][20][21][22][23] either converge to an idempotent matrix or oscillate in a finite period. By contrast, the maxproduct powers of a fuzzy matrix demonstrate distinct behavior compared with max-min fuzzy matrices [2,30].…”

A transitivity analysis of bipartite rankings in pairwise multi-class classification

“…½0; 1 on a set X of data objects or alternatives, it has been shown that the notion of transitivity plays a crucial role in this context. We recall that the reciprocity property [14] expresses that for all ðx 1 ; x 2 Þ 2 X 2 it holds that Q ðx 1 ; x 2 Þ þ Q ðx 2 ; x 1 Þ ¼ 1:…”

Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix

“…He also showed that controllable fuzzy matrix oscillate with period equal 2. Nola [28] worked on the convergence of powers of reciprocal fuzzy matrices and deduced some properties. Kolodziejczyk [29] examined canonical form of s-transitive fuzzy matrix by using max-min transitive fuzzy matrix.…”