In this study, using the neutrosophic soft definitions, we define some new concept such as the neutrosophic soft lattice, neutrosophic soft sublattice, complete neutrosophic soft lattice, modular neutrosophic soft lattice, distributive neutrosophic soft lattice, neutrosophic soft chain then we study the relationship and observe some common properties.

Soft set theory was introduced by Molodtsov in 1999 as a general mathematical tool for dealing with problems that contain uncertainty. In this paper, we define concept of fuzzy soft lattice, fuzzy soft sublattice, complete fuzzy soft lattice, modular fuzzy soft lattice, distributive fuzzy soft lattice, fuzzy soft chain and study their basic properties.

We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals K and E. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations ar...

This paper provides the definitions of co-basis and co-covering graph. Using these new notations, it deals with the relationship between concept lattices and co-covering graphs. Afterwards, it solves the relation between complete lattices and co-covering graphs, and further, obtains that for a complete lattice, there is a concept lattice isomorphic to it. Mathematics Subject Classification: 06A...

In this work we introduce the notion of fuzzy congruence relation on an ndgroupoid and study conditions on the nd-groupoid which guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.

In this paper, we define the concepts of fuzzy initial and final segments in an Almost Distributive Lattice (ADL) certain properties these are discussed. It is proved that set forms a complete lattice ADL A if only bounded distributive lattice.

A calyx (multiplicative lattice) is a complete lattice endowed with the structure of a monoid such that multiplication by an element is a left adjoint functor of complete lattices (equivalently, a left adjoint functor which preserves colimits). Calyxes are a generalization of the set of ideals of a ring, which form a complete lattice under intersection and summation; in conjunction with the nat...

We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices, but that the class of lattices embeddable into the local clone lattice is strictly larger than that: For example, the lattice M2ω is a sublattice of the loc...

We call a semigroup compactification T of a (discrete) semigroup S Boolean if the underlying space of T is zero-dimensional. The class of Boolean compactifications of S is a complete lattice, in a natural way. Motivated by Numakura’s theoerem, we prove that this lattice is isomorphic to the ideal lattice of the lattice of finite congruence relations of S. We describe in some detail the lattice ...

Let E be a Banach lattice and let M be a norm-closed and Dedekind σ-complete ideal of E. If E contains a lattice-isometric copy of ∞ , then E/M contains such a copy as well, or M contains a lattice copy of ∞. This is one of the consequences of more general results presented in this paper. 1. Introduction. Let E be a locally solid linear lattice (Riesz space), for example , a Banach lattice, let...