Implicative Filters

Sambasiva Rao Mukkamala ()
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Sambasiva Rao Mukkamala: MVGR College of Engineering, Department of Mathematics

Chapter Chapter 14 in A Course in BE-algebras, 2018, pp 383-411 from Springer

Abstract: 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 algebrasQuotient algebra 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.

Date: 2018
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DOI: 10.1007/978-981-10-6838-6_14

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