<p>A study of vector boson scattering in <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi><mml:mi>p</mml:mi></mml:math></inline-formula> collisions at a center-of-mass energy of 8 TeV is presented. The data sample corresponds to an integrated luminosity of <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>19.4</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:msup><mml:mrow><mml:mi>fb</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> collected with the CMS detector. Candidate events are selected with exactly two leptons of the same charge, two jets with large rapidity separation and high dijet mass, and moderate missing transverse energy. The signal region is expected to be dominated by electroweak same-sign <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>W</mml:mi></mml:mrow></mml:math></inline-formula>-boson pair production. The observation agrees with the standard model prediction. The observed significance is 2.0 standard deviations, where a significance of 3.1 standard deviations is expected based on the standard model. Cross section measurements for <inline-formula><mml:math display="inline"><mml:msup><mml:mi>W</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>W</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>W</mml:mi><mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:math></inline-formula> processes in the fiducial region are reported. Bounds on the structure of quartic vector-boson interactions are given in the framework of dimension-eight effective field theory operators, as well as limits on the production of doubly charged Higgs bosons.</p>