Topological structures on classes I.
Topological Structures On Classes II
Topological structures on classes II.
Topologically invariant σ-ideals on Euclidean spaces
We study and classify topologically invariant σ-ideals with an analytic base on Euclidean spaces, and evaluate the cardinal characteristics of such ideals.
Totally proper forcing and the Moore-Mrówka problem
We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of ZFC + CH in which countably tight compact spaces are sequential-we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets
In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...
Towards the properties of fuzzy multiplication for fuzzy numbers
In this paper, by using a new representation of fuzzy numbers, namely the ecart-representation, we investigate the possibility to consider such multiplication between fuzzy numbers that is fully distributive. The algebraic and topological properties of the obtained semiring are studied making a comparison with the properties of the existing fuzzy multiplication operations. The properties of the generated fuzzy power are investigated.
Towers of measurable functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
Trajectories and natural numbers
Transfinite inductions producing coanalytic sets
A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that consistently there exists an uncountable coanalytic subset of the plane that intersects every C¹ curve in a countable set.
Transitive closures of binary relations. I.
Transitive closures of binary relations II.
Transitive closures of binary relations. III.
Transitive closures of binary relations. IV.
Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum
Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...
Transitive Properties of Ideals on Generalized Cantor Spaces
We compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we show that there exists a null set such that for every null set we can find such that A ∪ (A+x) cannot be covered by any translation of B.
Transitive ternary relations and quasiorderings
Trees, inverse systems, and valuated vector spaces
Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals.
The addition of fuzzy intervals based on a triangular norm T is studied. It is shown that the addition based on a t-norm T weaker than the Lukasiewicz t-norm TL acts on linear fuzzy intervals just as the TL-based addition. Some examples are given.
Turning Borel sets into clopen sets effectively
We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show that under some conditions the emerging parameters can be chosen in a hyperarithmetical way and using this we obtain some uniformity results.