Symmetric triangular approximations of fuzzy numbers under a general condition and properties

Abstract

We consider the set $\mathcal {P}$ of real parameters associated to a fuzzy number, in a general form which includes the most important characteristics already introduced for fuzzy numbers. We find the set $\mathcal {P}_{\mathrm{s}}\subset \mathcal {P}$ with the property that for any given fuzzy number there exists at least a symmetric triangular fuzzy number which preserves a fixed parameter $p\in \mathcal {P}$. We compute the symmetric triangular approximation of a fuzzy number which preserves the parameter $p\in \mathcal {P }_{\mathrm{s}}$. The uniqueness is an immediate consequence; therefore, an approximation operator is obtained. The properties of scale and translation invariance, additivity and continuity of this operator are studied. Some applications related with value and expected value, as important parameters, are given too.