Fuzzy Sets of Strong, Weak, and Conditional Derivatives

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 in fuzzy set theory, in which fuzzy concepts are applied to conventional mathematical objects, such as functions, sequences, and derivatives. This allows us to reflect and model vagueness and uncertainty of our knowledge, which results from imprecision of measurement and inaccuracy of computation.In the second part of this paper, going after introduction, we give some basic definitions of neoclassical analysis. Then, in the third part of this paper, we construct a fuzzy extension for the classical theory of differentiation in the context of computational mathematics. It is done in the second part of this paper, going after introduction. Two kinds of fuzzy derivatives of real functions are considered: weak and strong ones. Strong fuzzy derivatives are similar to ordinary derivatives of real functions, being their fuzzy generalizations. Weak fuzzy derivatives generate a new concept of a weak derivative even in a classical case when we assume complete precision. In comparison with previous works, here fuzzy derivatives are relativized, becoming conditional derivatives. In the fourth part of this paper, we construct fuzzy sets of derivatives and intuitionistic fuzzy sets of derivatives of real functions and study their properties