Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...

we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja’s conjecture. As a consequence, we show that each of the spaces c0 and `1 has a subspace which has the AP but fails to have the strong AP.

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over function field complex or real curve that refines weak (and known cohomological obstructions to it) by incorporating an condition in Euclidean topology. We prove is stable birational invariant, compatible with fibrations, satisfies descent under torsors linear groups. Its validit...