scholarly journals On Generalized Transitive Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Jing Jiang ◽  
Lan Shu ◽  
Xinan Tian
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Canonical Form ◽  
Transitive Closure ◽  
Fuzzy Algebra

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. Some properties of compositions of incline matrices are also given, and a new transitive incline matrix is constructed from given incline matrices. Finally, the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references.

Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices

2017 ◽  
pp. 132-152
Author(s):  
Debashree Manna
Keyword(s):  
Vector Space ◽  
Distributive Lattice ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Algebra ◽  
Definition Of ◽  
Interval Valued

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0, 1]. Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs.

scholarly journals De Morgan Functions and Free De Morgan Algebras

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Yu. M. Movsisyan ◽  
V. A. Aslanyan ◽  
Alex Manoogian
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Boolean Functions ◽  
Bounded Lattice ◽  
De Morgan Algebra ◽  
Bounded Distributive Lattice ◽  
Monotone Boolean Functions ◽  
Free Generators ◽  
De Morgan Algebras

AbstractIt is commonly known that the free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free bounded distributive lattice on n free generators is isomorphic to the bounded lattice of monotone Boolean functions of n variables. In this paper, we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. This is a solution of the problem suggested by B. I. Plotkin.

scholarly journals On the order scale of a uniform space

1983 ◽  
Vol 34 (2) ◽  
pp. 248-257 ◽  
Author(s):  
D. C. Kent
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Closed Subspace ◽  
Uniform Space ◽  
Order Topology ◽  
Totally Bounded ◽  
Samuel Compactification ◽  
Closed Image ◽  
Atomic Boolean Algebra

AbstractThe order topology is compact and T2 in both the scale and retracted scale of any uniform space (S, U). if (S, U) is T2 and totally bounded, the Samuel compactification associated with (S, U) can be obtained by uniformly embedding (S, U) in its order retracted scale (that is, the retracted scale with its order topology). This implies that every compact T2 space is both a closed subspace of a complete, infinitely distributive lattice in its order topology, and also a continuous, closed image of a closed subspace of a complete atomic Boolean algebra in its order topology.

On the Triple Characterization for Stone Algebras

1975 ◽  
Vol 27 (4) ◽  
pp. 852-859 ◽  
Author(s):  
Raymond Balbes
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Stone Algebra ◽  
Injective Hulls

In [1], C. C. Chen and G. Grâtzer developed a method for studying Stone algebras by associating with each Stone algebra L, a uniquely determined triple (C(L), D(L), ɸ (L)), consisting of a Boolean algebra C(L), a distributive lattice D(L), and a connecting map ɸ(L). This approach has been successfully exploited by various investigators to determine properties of Stone algebras (e.g. H. Lakser [9] characterized the injective hulls of Stone algebras by means of this technique). The present paper is a continuation of this program.

The Boolean Algebra of Regular Open Sets

1953 ◽  
Vol 5 ◽  
pp. 95-100 ◽  
Author(s):  
R. S. Pierce
Keyword(s):  
Boolean Algebra ◽  
Topological Space ◽  
Distributive Lattice ◽  
Homomorphic Image ◽  
Continuous Functions ◽  
Completely Regular ◽  
Regular Open ◽  
Quasi Ordering

Let S be a completely regular topological space. Let C(S) denote the set of bounded, real-valued, continuous functions on 5. It is well known that C(S) forms a distributive lattice under the ordinary pointwise joins and meets. For any distributive lattice L and any ideal I⊆L, a quasi-ordering of L can be defined as follows : f⊇g if, for all h ∈ L, f ∩ h ∈ I implies g ∩ h ∈ I. If equivalent elements under this quasi-ordering are identified, a homomorphic image of L is obtained.

Sign in / Sign up

Export Citation Format

Share Document