New Approach: Tabular Fuzzy Arithmetic of the LR Type by Jomatopfe

Abstract

This paper presents a fuzzy approach of LR types, also called LR-type tabular fuzzy arithmetic capable of handling or computing simultaneously the kernels and supports of trapezoidal fuzzy numbers, instead of doing it separately (Advantage of this approach) in order to minimize the tedious steps of alpha-cut based approaches. On the theoretical level, the aim of this article is to explain in a concise and clear manner some basic concepts of fuzzy logic that seem to continue to complicate authors and readers (researchers) in this field, given the important place of this theory in Artificial Intelligence today. Some user interfaces have been created in this article, with the python language, in order to automatically calculate certain results; and especially to minimize the calculation time, in particular of membership degrees, kernels and supports. Trapezoidal fuzzy numbers are transformed into LR form in order to allow a comparative study between the alpha-cut approach with the Jomatopfe LR-type tabular fuzzy arithmetic presented in this paper. We successfully demonstrated the transition from the trapezoidal fuzzy form to the LR type form and vice versa. After a comparative study between the alpha-cut approach and the tabular fuzzy arithmetic of the LR type, Jomatopfe's LR type arithmetic significantly reduced the complexity of the calculation processes compared to classical methods, which require distinct steps for each element. This fuzzy tabular altimetry is not to be confused with other fuzzy tables operations on membership degrees.