We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if $\left|X\right|={\kappa }^{\omega }=2^{\kappa }$ for some cardinal κ.

The focus is put on the application of fuzzy sets and Dempster-Shafer theory in assessing the nature and extent of uncertainty in the response of $M$ models that model the same phenomenon and depend on fuzzy input data. Dempster-Shafer theory uses a weighted family of fixed sets called the focal elements to evaluate the relationship between an arbitrarily chosen set and the focal elements. It is proposed to create at least $M$ weighted focal elements on the basis of 1) the responses to fuzzy inputs...