Algebra of trapezoidal fuzzy numbers for fuzzy information processing

Existing approaches to the implementation of fuzzy calculations have several significant problems that restrain practical applications of the fuzzy sets theory to the solutions of many control and decisionmaking tasks. In our previous research, we proposed the algebra of double component numbers that solves the aforementioned problems for fuzzy triangular numbers. In this paper, we extend the algebra of double component numbers to the trapezoidal fuzzy numbers, explore its properties and compare it with other approaches.