On the Menelaus and Ceva 6-Figures in the Fibered Projective Planes

Abstract

The fibered versions of Menelaus and Ceva 6-figures in the fibered projective plane are given and the conditions to the fibered versions of Menelaus and Ceva 6-figures in the fibered projective plane with base plane, that is, projective plane, are determined.

On the intuitionistic fuzzy projective Menelaus and Ceva's conditions

“…Then the three intersection IF points (c 1 ; De…nition 10. ( see [6]) Let FP be a …bered projective plane with base plane P. Choose three f points (a i ; i ); i 2 f1; 2; 3g in FP with non collinear base points and the other three f points (b k ; k ); k 2 f1; 2; 3gwith (b k ; k ) 2 (ha i ; a j i ; i^ j ) for i 6 = j 6 = k; fi; j; kg = f1; 2; 3g. If the f points (b k ; k ) are f collinear, the con…guration that consists of these six f points is called an f Menelaus 6 …gure.…”

“…(see [7]) Suppose we have an intuitionistic fuzzy projective plane IFP with Pappian base plane P. Choose two di¤ erent lines L 1 and L 2 in P. Choose two triples of IF points (a i ; i ; 0 i ) and (b i ; i ; 0 i ) with a i on L 1 and b i on L 2 ; i = 1; 2; 3 and such that no three of the base points a 1 , a 2 ; b 1 ; b 2 are collinear. Then the three intersection IF points (c 1 ; 1 ; 0 [6]) Let FP be a …bered projective plane with base plane P. Choose three f points (a i ; i ); i 2 f1; 2; 3g in FP with non collinear base points and the other three f points (b k ; k ); k 2 f1; 2; 3gwith (b k ; k ) 2 (ha i ; a j i ; i^ j ) for i 6 = j 6 = k; fi; j; kg = f1; 2; 3g. If the f points (b k ; k ) are f collinear, the con…guration that consists of these six f points is called an f Menelaus 6 …gure.…”

“…In these geometry, the points and lines of the base geometry mostly have multiple degrees of membership. The …bered version of Menelaus and Ceva's 6-…gures was studied in [6].…”