In Information mining and Knowledge discovery Techniques area, frequent pattern having important role, Frequent patterns are patterns that come out in data set recurrently. Itemsets that occur frequent are patterns or items like Itemsets, substructure, or subsequences. Frequent weighted Itemset characterize associations frequently holding in information in which items may weight contrarily. Still, in some contexts, e.g., when the need is to minimize a certain cost function, determining infrequent information associations is more curious than mining frequent ones. This paper tackles the issue of determining infrequent and weighted Itemsets, i.e. Infrequent weighted item set determine item sets whose frequency of occurrence in the analyzed data is less than or equal to a maximum threshold. To determine infrequent weighted item set, two algorithms are naked infrequent weighted item set (IWI) and Minimal infrequent item set (MIWI). In this study is motivated on the infrequent weighted item sets, as of transactional weighted data sets to address IWI support quantity is defined as a weighted frequency of occurrence of an item set in the examined data. Occurrence weights resulting from the weights related with items in each transaction and applying a given cost function.