Some recent results provide su,cient conditions for complete lattices of closure operators on complete lattices, ordered pointwise, to be pseudocomplemented. This paper gives results of pseudocomplementation in the more general setting of closure operators on mere posets. The following result is 0rst proved: closure operators on a meet-continuous meet-semilattice form a pseudocomplemented compl...

We argue that closure operators are fundamental tools for the study of relationships between order structures and their sequence representations. We also propose and analyse a closure operator for interval order structures.

We continue the work of Blok and Jónsson by developing the theory of structural closure operators and introducing the notion of a representation between them. Similarities and equivalences of Blok-Jónsson turn out to be bijective representations and bijective structural representations, respectively. We obtain a characterization for representations induced by a transformer. In order to obtain a...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators σ, encountered in economics and social theory, and closure operators φ, encountered in discrete geometry and data mining. Be...

For closure operators Γ and ∆ on the same set X, we say that ∆ is a weak (resp. strong) extension of Γ if Cl(X, Γ) is a complete meet-subsemilattice (resp. complete sublattice) of Cl(X, ∆). This context is used to describe describe the extensions of a finite lattice that preserve various properties.

In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...

We explore how fixed-point operators can be designed to interact and be composed to form autonomic control mechanisms. We depart from the idea that an operator is idempotent only for the states that it assures, and define a more general concept in which acceptable states are a superset of assurable states. This modified definition permits operators to make arbitrary choices that are later chang...

We propose a framework for managing resources via convergent operators. Operators represent their need for a resource to a designated resource closure operator that manages the resource. We evaluate a specific design for a resource closure operator by simulation and demonstrate that the operator achieves a near-optimal balance between cost and value without using any model of the relationship b...

In analogy with the relation between closure operators in presheaf toposes and Grothendieck topologies, we identify the structure in a category with finite limits that corresponds to universal closure operators in its regular and exact completions. The study of separated objects in exact completions will then allow us to give conceptual proofs of local cartesian closure of different categories ...