Implicative Almost Distributive Lattice

Alaba, Berhanu Assaye; Alamneh, Mihret; Munie, Tilahun Mekonnen

doi:10.12962/j24775401.v4i1.2999

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“…The concept of an Almost Distributive Lattice (ADL) was introduced in 1981 by U. M. Swamy and G. C. Rao [7] as a common abstraction to most of the existing ring theoretic and lattice theoretic generalization of Boolean algebra. Berhanu Assaye, Mihret Alamneh and Tilahun Mekonnen [8] introduced the concept of Implicative Almost Distributive Lattices (IADLs) as a generalization of implicative algebra in the class of ADLs. We proved some properties and equivalence condition in an implicative almost distributive lattice.…”

Section: Introductionmentioning

confidence: 99%

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Alaba¹,

Alamneh²,

Munie³

2018

IJCSAM

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Section: Introductionmentioning

confidence: 99%

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Alaba¹,

Alamneh²,

Munie³

2018

IJCSAM

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Weak LI-ideals in implicative almost distributive lattices

Munie

2021

Eth J Sci & Technol

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In the field of many valued logic, lattice valued logic (especially ideals) plays an important role. Nowadays, lattice valued logic is becoming a research area. Researchers introduced weak LI-ideals of lattice implication algebra. Furthermore, other scholars researched LI-ideals of implicative almost distributive lattice. Therefore, the target of this paper was to investigate new development on the extension of LI-ideal theories and properties in implicative almost distributive lattice. So, in this paper, the notion of weak LI-ideals and maximal weak LI- ideals of implicative almost distributive lattice are defined. The properties of weak LI- ideals in implicative almost distributive lattice are studied and several characterizations of weak LI-ideals are given. Relationship between weak LI-ideals and weak filters are explored. Hence, the extension properties of weak LI-ideal of lattice implication algebra to that of weak LI-ideal of implicative almost distributive lattice were shown.

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Implicative Almost Distributive Lattice

Cited by 2 publications

References 2 publications

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Weak LI-ideals in implicative almost distributive lattices

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