by associating to each such $C^{*}$-algebra an element in the third cohomology group $\check{H}^{3} ( X , {\ensuremath{\mathbb{Z}}\xspace})$. By [@Dadarlat:Adv09 Theorem 5.2], if $X$ is zero-dimensional, then the section algebra of the continuous field of $C^{*}$-algebras studied by Dixmier and Douady are AF-algebras. Thus, by Elliott’s classification of AF-algebras [@af], they are classified by their $K_{0}$-groups.

Since $K$-theory has proven to be a very successful invariant for classifying $C^{*}$-algebras, it is natural to ask “to what extent does $K$-theory classify continuous fields of $C^{*}$-algebras with simple fibers that are classifiable via $K$-theory”. There has been recent progress in this direction, for example, Marius Dadarlat and Cornel Pasnicu in [@DadarlatPasnicu:JFA05] classified continuous fields of $C^{*}$-algebras over locally compact, metrizable, zero-dimensional spaces for which the fibers are purely infinite simple $C^{*}$-algebras. Partial results have also been obtained involving continuous fields of $C^{*}$-algebras over non-zero dimensional spaces (see [@DadarlatElliott:CMP07], [@DadarlatElliottNiu:CJM11], [@BentmanDadarlat:arXiv:1306.1691], and [@Bentman:arXiv:1308.2126]). In all of the above results, either all the fibers are purely infinite or all the fibers are AF-algebras.

In this paper, we consider the classification of $C^{*}$-algebras whose primitive ideal space is Hausdorff and fibers are of mixed type. In fact, we consider the classification problem for $C^{*}$-algebras whose 