Forcings which preserve large cardinals
Fragments of strong compactness, families of partitions and ideal extensions
We investigate some natural combinatorial principles related to the notion of mild ineffability, and use them to obtain new characterizations of mild ineffable and weakly compact cardinals. We also show that one of these principles may be satisfied by a successor cardinal. Finally, we establish a version for of the canonical Ramsey theorem for pairs.
Fraïssé structures and a conjecture of Furstenberg
We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference between , the Samuel compactification, and , the enveloping semigroup of the universal minimal flow. We resolve Furstenberg’s problem for several automorphism groups and give a detailed study in the case of , leading us to define and investigate several new types...
Free -products of lattices. I
Free -products of lattices. II
Free Power or Width of some Kinds of Mathematical Structures
From an alternative model of rough sets to fuzzy sets
From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions
Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired...
Function spaces and application to fuzzy analysis
Functions Equivalent to Borel Measurable Ones
Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.
Functions having stationary constant sets
Functions of Baire class one
Let K be a compact metric space. A real-valued function on K is said to be of Baire class one (Baire-1) if it is the pointwise limit of a sequence of continuous functions. We study two well known ordinal indices of Baire-1 functions, the oscillation index β and the convergence index γ. It is shown that these two indices are fully compatible in the following sense: a Baire-1 function f satisfies for some countable ordinals ξ₁ and ξ₂ if and only if there exists a sequence (fₙ) of Baire-1 functions...
Fundamentals of a mathematical theory of fuzzy sets
Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.
Fuzziness and fuzzy equality
Fuzzy BCI-subalgebras with interval-valued membership functions.
Fuzzy Boolean algebras and Łukasiewicz logic.
Fuzzy concepts defined via residuated maps
Fuzzy data in statistics
The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data...
Fuzzy distances
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to are dealt with in detail.