Implicative Filters

Chapter

Abstract

In 2001, Turunen [233] proposed the notions of implicative filters and Boolean filters (Boolean deductive systems) and proved that implicative filters are equivalent to Boolean filters in BL-algebras. Boolean filters are important filters, because the quotient algebras induced by Boolean filters are Boolean algebras. Jun and Ahn [132] provided several degrees in defining a fuzzy implicative filter. Meng [171] introduced the concept of implicative ideals in BCK-algebras and investigated the relationship of it with the concepts of positive implicative ideals and commutative ideals. Meng et al. [179] and Mostafa [182] fuzzified the concept of implicative ideals in BCK-algebras independently. Also, Xu and Qin [245] proposed the notions of implicative filters and fuzzy implicative filters of lattice implication algebras.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsMVGR College of EngineeringVizianagaramIndia

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