相关论文: On the alternatives to the ideal mathematical poin…

The work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of…

Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…

From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set…

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…

Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and…

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…

The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…

Set-theoretical, physical, and intuitive notions of continuum are compared. It is shown that the independence of the continuum hypothesis determines status and properties of the set of intermediate cardinality. The intermediate set is a…

In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…

Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the…

An alternative mathematics based on qualitative plurality of finiteness is developed to make non-standard mathematics independent of infinite set theory. The vague concept "accessibility" is used coherently within finite set theory whose…

The hypothesis concerning the off-site continuum existence is investigated from the point of view of the mathematical theory of sets. The principles and methods of the mathematical description of the physical objects from different off-site…

Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis…

This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core…

In dealing with veracity of data analytics, fuzzy methods are more and more relying on probabilistic and statistical techniques to underpin their applicability. Conversely, standard statistical models usually disregard to take into account…

Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…

The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern…

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…

To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…