We study the Bianchi type-V string cosmological model with bulk viscosity in <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy="false">)</mo></math> theory of gravity by considering a special form and linearly varying deceleration parameter. This is an extension of the earlier work of Naidu et al., 2013, where they have constructed the model by considering a constant deceleration parameter. Here we find that the cosmic strings do not survive in both models. In addition we study some physical and kinematical properties of both models. We observe that in one of our models these properties are identical to the model obtained by Naidu et al., 2013, and in the...