We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

This technical report summarized facts from the basic theory of generalized closure spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs. 1. Set-Valued Set-Functions 1.1. Closure, Interior, Neighborhood, and Convergent. In this section, which in part generalizes the results o...

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on...

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

We study the numerical solution of the problem minX≥0 ‖BX−c‖2, where X ∈ Sm is a symmetric square matrix, and B : Sm → R is a linear operator, such that B∗B is invertible. With ρ the desired fractional duality gap, we prove O( √ m log ρ−1) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints, however not d...

In this paper, we introduce the concepts of r-semigeneralized fuzzy closed sets, r-semi-generalized fuzzy open sets, rsemi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.

Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geome...

As general concepts of sup-hesitant fuzzy right (resp., left, interior, two-sided) ideals semigroups, the sup+α-hesitant and sup-β-hesitant are introduced their properties investigated. Then, established by sets, Łukasiewicz anti-fuzzy Pythagorean hesitant hybrid interval-valued sets cubic sets. Finally, we characterize which is intra-regular, completely regular, simple semigroups or another ty...

We formulate an infinitary proof system for transitive closure logic, which is the logic obtained by augmenting first-order logics with a transitive closure operator. Our system is an infinite descent-style counterpart to the existing (explicit induction) proof system for the logic. We show that, as for similar systems for first order logic with inductive definitions, our infinitary system is c...

This paper addresses the following general problem of tree regular model-checking: decide whether R * (L) ∩ L p = ∅ where R * is the reflexive and transitive closure of a successor relation induced by a term rewriting system R, and L and L p are both regular tree languages. We develop an automatic approximation-based technique to handle this – undecidable in general – problem in most practical ...