Naturalness and Interpretability of Graphical Representations of Fuzzy Numbers (#2011)

Authors

Ramos Pozo, Luis Enrique

Pisco Jordán, Juan Carlos

Townsend Hinostroza, Danaé Jacqueline

Abstract

In this research, an experimental evaluation of the naturalness and interpretability using fuzzy numbers in an everyday university context was carried out. Four graphical representations of fuzzy numbers (triangular, trapezoidal, Gaussian and L-R) were evaluated in linguistic expressions such as "around _" and "greater than _" to determine the most natural ones in that context. In addition, two forms were designed with simple arithmetic operations and imprecise linguistic expressions. In this way we were able to evaluate whether the results obtained through mathematical operations with fuzzy numbers proposed by different authors resemble the mental calculations that university students would perform. A sample of 44 students was used, the results reflected that the expressions "around _" and "close to _" are better represented with the Gaussian form; trapezoidal representations are associated with expressions such as "between _ and _" and "not less than _" and better represent results of addition and subtraction operations; while the L-R representation is more natural when obtaining results in multiplications.