The main goal of this paper is to explicate and explain connections between neoclassical analysis and fuzzy set theory. To this goal, we consider here fuzzy sets of derivatives and intuitionistic fuzzy sets of derivatives of real functions. Neoclassical analysis may be treated as a new direction...

The main goal of this work is the further development of neoclassical analysis, which extends the scope and results of the classical mathematical analysis by applying fuzzy concepts to conventional mathematical objects, such as functions, sequences, and derivatives. This allows us to reflect and...

The theory of hypernumbers is a novel approach in functional analysis aimed at the development of such mathematically correct technique, which allows operations with divergent integrals and series. Although, it resembles nonstandard analysis, there are several distinctions between these...

Mathematical models for artificial intelligence (AI) are considered. It is assumed that AI is realized on the base of computers. Computers are controlled by algorithms in the form of software. Consequently, it is natural to assume that AI has to be realized by algorithms and it is reasonable to...

People think that their counting is governed by the rules of the conventional arithmetic and that other kinds of arithmetic do not exist and cannot exist. It is demonstrated in this paper that this popular image of counting is incorrect. In many situations, we have to utilize different rules of...

Named sets is a basic mathematical structure, providing a unified foundations for mathematics and encompassing different generalizations of sets that are studied in mathematics and used in applications. The most important and popular of these generalizations are multisets and fuzzy sets. An...

Traditionally probability is considered as a function that takes values in the interval [0, 1]. However, researchers found that negative, as well as larger than 1 probabilities could be a useful tool in making financial modeling more exact and flexible. Here we show how larger than 1...