Characterizations of MV-algebras based on the theory of falling shadows.

ScientificWorldJournal

School of Mathematics, Northwest University, Xi'an 710127, China.

Published: June 2015

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.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4167447PMC
http://dx.doi.org/10.1155/2014/951796DOI Listing

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