Rank fusion meta-search engine algorithms can be used to merge web search results of multiple search engines. In this paper we introduce two variants of the Weighted Borda-Fuse algorithm. The first variant retrieves documents based on popularities of component engines. The second one is based on k user-defined toplist of component engines. In this research, experiments were performed on k={50,100,200} toplist with AND/OR combinations implemented on ‘UNIB Meta Fusion’ meta-search engine prototype which employed 3 out of 5 popular search engines. Both of our two algorithms outperformed other rank fusion algorithms (relevance score is upto 0.76 compare to Google that is 0.27, at P@10). The pseudo-relevance automatic judgement techniques involved are Reciprocal Rank, Borda Count, and Condorcet. The optimal setting was reached for queries with operator "AND" (degree 1) or "AND ... AND" (degree 2) with k=200. The ‘UNIB Meta Fusion’ meta-search engine system was built correctly
