Hadith is the word, deeds, decrees and approval of Prophet Muhammad SAW which is used as the basis of Islamic Sharia law after the Qur'an. Currently there are many websites that provide information about the hadith to facilitate users in the process of learning hadith, such as Lidwa Pustaka website which is used to search the hadith of Indonesian translation or commonly known as Information Retrieval (IR).
Basically, IR provides a search box for users to include queries that reflect the user's information needs. The query entered by the user is matched with the index of the hadith document collection to find the hadith containing the query, which is then sorted (ranking) based on various methods or models. However, the writing of different synonyms or string variants in the hadith of Indonesian translation, such as “????????” (al-khomru) is written to be "khamar", "khamer", "khamr" or "minuman keras", making the process of searching the hadith less precise.
Therefore, this study aims to improve the Indonesian translation of hadith translation system, using query expansion approach and smoothing probability model, namely Jelinerk-Mercer Smoothing, Dirichlet Smoothing and Absolute Discounting Smoothing. The query expansion method can handle semantic searching process (synonym and string variant), while smoothing method can perform hadits search on partial matching user query and estimate the relevance of the hadith document by calculating the unseen word probability value of each word each hadith document against the query, thus avoiding zero probability for the retrieval process of the document. The use of query expansion and Dirichlet smoothing in this study resulted in the most optimal performance compared to the usual LSI, Cosine Similarity and probability methods (without smoothing), which is 62.54% for MAP ALL, 57.39% for MAP @ 30 and 76.59% for recall, this is because the query expansion can search semantically. Whereas the most optimal smoothing parameter setting is at ?: 500 for the Dirichlet Smoothing method