Term weighting for document ranking and retrieval has been an important research topic in information retrieval for decades. We propose a novel term weighting method based on a hypothesis that a term's role in accumulated retrieval sessions in the past affects its general importance regardless. It utilizes availability of past retrieval results consisting of the queries that contain a particular term, retrieved documents, and their relevance judgments. A term's evidential weight, as we propose in this paper, depends on the degree to which the mean frequency values for the relevant and non-relevant document distributions in the past are different. More precisely, it takes into account the rankings and similarity values of the relevant and non-relevant documents. Our experimental result using standard test collections shows that the proposed term weighting scheme improves conventional TF*IDF and language model based schemes. It indicates that evidential term weights bring in a new aspect of term importance and complement the collection statistics based on TF*IDF. We also show how the proposed term weighting scheme based on the notion of evidential weights are related to the well-known weighting schemes based on language modeling and probabilistic models. (C) 2012 Elsevier Ltd. All rights reserved.