Generalized Almost Distributive Fuzzy Lattices
نویسندگان
چکیده
منابع مشابه
Generalized Almost Distributive Lattices-I
The concept of a GADL as a generalization of an ADL is introduced. Necessary and sufficient conditions for a GADL to become a distributive lattice and a GADL to become an ADL are obtained. We also study the maximal sets in a GADL and give equivalent conditions for a GADL to become a distributive lattice in terms of maximal
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Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [11] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Se...
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Necessary and sufficient conditions for a GADL to become an ADL are obtained interms of congruence relations and proved that every associative GADL is an ADL.
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A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.
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The concept of a closure operator ∇ in an ADL R was introduced. If ∇R is the set of all ∇−invariant elements of R, then the concepts of ∇R−ideal, ∇R−prime ideal are introduced. The interrelations between ∇R−prime ideal and minimal prime ideal of R are derived. If B is the Birkhoff centre of R, then a sufficient condition is derived for a B−ideal to be a minimal prime ideal of R. Mathematics Sub...
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ژورنال
عنوان ژورنال: International Journal of Computing Science and Applied Mathematics
سال: 2017
ISSN: 2477-5401
DOI: 10.12962/j24775401.v3i2.2884