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Implicative Filters

In: A Course in BE-algebras

Author

Listed:
  • Sambasiva Rao Mukkamala

    (MVGR College of Engineering, Department of Mathematics)

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.

Suggested Citation

  • Sambasiva Rao Mukkamala, 2018. "Implicative Filters," Springer Books, in: A Course in BE-algebras, chapter 0, pages 383-411, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6838-6_14
    DOI: 10.1007/978-981-10-6838-6_14
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