Hi Koji,
strictly talking about TF-IDF ( and BM25 which is an evolution of that
approach) I would say it is a weighting function/numerical statistic that
can be used for ranking functions and is based on probabilistic concepts (
such as IDF) but it is not a probabilistic function[1].
Indeed a BM25 score for a term is not assured to be 0<x<1

Furthermore Lucene and Solr adds a lot on top of the BM25 similarity (
including different kind of boost( document, field and query time boost,
norms, coord ) so they use probabilistic concepts but they are not
probabilistic search engine.

[1]
http://math.stackexchange.com/questions/610165/prove-that-the-bm25-scoring-function-is-probabilistic



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Alessandro Benedetti
Search Consultant, R&D Software Engineer, Director
Sease Ltd. - www.sease.io
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