Some Properties and the Distributivity of the (p,q)-superlattice
نویسندگان
چکیده
We consider a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined as follows: a P ∨ b = a ∨ b ∨ P , a Q ∧ b = a ∧ b ∧Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. We explore some properties of (L, P ∨, Q ∧) with special attention to various types of P ∨ and Q ∧ distributivity. AMS Subject Classification: 06B99, 06D99.
منابع مشابه
An Investigation of the Properties of the (p, Q)-superlattice
The (P,Q)-superlattice is a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined as follows: a P ∨ b . = a ∨ b ∨ P , a Q ∧ b . = a ∧ b ∧ Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. We examine the properties of the sets a P ∨ b and a Q ∧ b in connection to the properties of P,Q. Especial...
متن کاملThe Structure of the (P, Q)-Superlattice and Order Related Properties
In a previous work we have introduced the (P,Q)-superlattice, a hyperstructure of the form (L, P ∨, Q ∧). Here (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined by a P ∨b . = a∨b∨P , a Q ∧b . = a∧b∧Q; when the sets P,Q ⊆ L satisfy appropriate conditions (L, P ∨, Q ∧) is a superlattice. In this work we continue the investigation of (P,Q)superlattice and consider the structure of ...
متن کاملSome Representation Results for (P, Q)-Superlattices
On the the lattice (L,∨,∧) we construct the hyperoperations P ∨, Q ∧ as follows: a P ∨ b = a ∨ b ∨ P , a Q ∧ b = a∧ b∧Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. In this paper we give two representation results for (P,Q)-superlattices. The first result is an analog of the [1] representation result. The second result gives necessary and sufficient...
متن کاملOn the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...
متن کاملON ($epsilon, epsilon vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...
متن کامل