Methods of Expert Information Formalization Based on Complete Orthogonal Semantic Spaces

Abstract

Let us consider tolerance and unimodal (L − R)-numbers with membership functions

$$ \mu_{\tilde{A}}(x)=\left\{ \begin{array}{cc} L \left(\frac{a_{1}-x}{a_L}\right), & {\ \ \ 0 \leq \frac{a_{1}-x}{a_L} \leq 1; a_{L} > 0;} \\ R\left(\frac{x-a_2}{a_R}\right), & {\ \ \ 0\leq\frac{x-a_2}{a_R}\leq 1; a_R > 0;} \\ 1, & {\ \ \ \frac{a_1-x}{a_L}< 0 \cap \frac{x-a_2}{a_R}< 0;} \\ 0, & {\ \ \ \frac{a_1-x}{a_L}> 1 \cup \frac{x-a_2}{a_R}> 1} \\ \end{array} \right. $$