A splitting theorem for ℱ-products
A stabilization property and its applications in the theory of sections
A stabilization property and its applications in theory of sections
A stochastic model of choice.
An approach to choice function theory is suggested which is probabilistic and non-deterministic. In the framework of this approach fuzzy choice functions are introduced and a number of necessary and sufficient conditions for a fuzzy choice function to be a fuzzy rational choice function of a certain type are established.
A strong boundedness result for separable Rosenthal compacta
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
A strongly non-Ramsey uncountable graph
It is consistent that there exists a graph X of cardinality such that every graph has an edge coloring with colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).
A supplement to Gottwald's note on fuzzy cardinals
A theorem for basis operators over intuitionistic fuzzy sets.
The concept of s-basis operators over intuitionistic fuzzy sets is introduced and all 2-, 3-, 4- basis operators are listed.
A theorem on almost disjoint sets
A Theorem on Directed Quasi-Ordered Sets and Some Remarks
A theorem on polarised partition relations for singular cardinals
A theorem on supports in the theory of semisets
A Theorem which is Equivalent to the Axiom of Choice.
A theoretical comparison of disco and CADIAG-II-like systems for medical diagnoses
In this paper a fuzzy relation-based framework is shown to be suitable to describe not only knowledge-based medical systems, explicitly using fuzzy approaches, but other ways of knowledge representation and processing. A particular example, the practically tested medical expert system Disco, is investigated from this point of view. The system is described in the fuzzy relation-based framework and compared with CADIAG-II-like systems that are a “pattern” for computer-assisted diagnosis systems based...
A theoretical development of distance measure for intuitionistic fuzzy numbers.
A topological application of flat morasses
We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
A topology generated by eventually different functions
A T-partial order obtained from T-norms
A partial order on a bounded lattice is called t-order if it is defined by means of the t-norm on . It is obtained that for a t-norm on a bounded lattice the relation iff for some is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of and a complete lattice on the subset of all elements of which are the supremum of a subset of atoms.
A tree axiom.
A tree -base for without cofinal branches
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.