Characterizations of MV-Algebras Based on the Theory of Falling Shadows

الملخص EN

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧ -fuzzy (implicative) ideal is proposed in MV-algebras.

The relationships between falling fuzzy (implicative) ideals and T -fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧ -fuzzy (implicative) ideal are provided.

Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them.

The product ⊛ and the up product ⊚ operations on falling shadows and the upset of a falling shadow are established, by which T -fuzzy ideals are investigated based on probability spaces.