Vadnyov D. Formalization methods of fuzzy values representations based on specific sequences of prime numbers

The thesis is devoted to constructive methods of fuzzy numbers formalization development, processing fuzzy data new algorithms development, research of software and approaches for solving current interest tasks for processing fuzzy information with uncertain conditions. It contains analysis of special sequences of prime numbers and their properties and definitions of operations on defined sequences. An algorithm to approximate an arbitrary rational number with usage of elements from given prime number sequence is proposed. Set of non-negative rational numbers represented as two elements from given sequences ratio is reviewed. Representation method for fuzzy integers and real numbers revealed. A method of formalization of the process of fuzzy discrete system states membership functions dynamics is developed. The obtained results are allowed to prove the technique of using triangular fuzzy numbers as intervals, the boundaries of which are selected from the elements of specific prime numbers sequences.