Ds/anp method: A simplified group analytic network process with consensus reaching

Abstract

Analytic network process (ANP) is a significant multiple criteria decision making (MCDM) method. Although lots of efforts have been spent on improving the ANP, there still exist the four aspects of problems to be solved such as too many comparison times, unconsidering expert knowledge structure, ignoring consensus level of experts' group and ineffectively determining holistic information of the group. This study focuses on providing a simplified group ANP with consensus reaching named as DS/ANP method which incorporates the Dempster-Shafer theory of evidence (DS) with the ANP. An expert information extraction mechanism with the help of knowledge matrix and basic probability assignment function is introduced to simplify comparisons of group ANP and reflect expert knowledge structure. Then Shafer's discounting and Dempster's rule are both used to get the holistic information of the group, in which three levels of consensus indices (element level, cluster level, and holism level) are defined in terms of Jousselme distance. A group ANP method with consensus reaching and its corresponding algorithm are both established by following the principles of ANP. Finally, a numerical example is presented to make comparisons and discussions for the proposed method.