Orderings of Fuzzy Sets Based on Fuzzy Orderings. Part I: The Basic Approach.
Orderings of Fuzzy Sets Based on Fuzzy Orderings Part II: Generalizations.
Ordinal indices in Banach spaces.
Ordinal remainders of classical ψ-spaces
Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain of infinite subsets of ω, there exists , an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain , hence a ψ-space with Stone-Čech remainder...
Ordinal ultrafilters versus P-hierarchy
An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.
Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension
We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is -complete and that the set of Cauchy problems which locally have a unique solution is -complete. We prove that the set of Cauchy problems which have a global solution is -complete...
Orthogonal partitions
Outer measure on boolean algebras
Ovchinnikov's automorphisms revisited.
In [6] an approach to the representation of synonyms and antonyms via the automorphisms of the De Morgan Algebra [0,1]X was suggested. In [3], Ovchinnikov established a representation theorem for automorphisms of the function's complete and completely distributive lattice [0,1]X with the pointwise extension of Min and Max operations in [0,1]. Ovchinnikov results are now inmediately generalized by using a positive t-norm T and its dual eta-dual t-conorm T*. These results are applied to study the...
Overtaker binary relations on complete completely distributive lattices related to the level sets of the L-Fuzzy sets.
The class of overtaker binary relations associated with the order in a lattice is defined and used to generalize the representations of L-fuzzy sets by means of level sets or fuzzy points.
OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making
A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual...
OWA weights determination by means of linear functions.