An algebraic approach to the study of market
baskets

Abstract. The paper focuses on the algebraic representation of market basket model. It is shown in this paper that the methods offered by the new approach are effective in analyzing the problems concerning the customer's market baskets. The results of the previous studies in discovering the frequent market baskets and the association rules between market baskets, as well as the definition of the constraints of market baskets are summarized. By using these methods the logical structure of the sets of market baskets is analysed and the complexity of the market baskets is determined. In this formalism this paper shows also that the algebraic model of market baskets is quite suitable for solving the problems concerning the market basket's classification. The operations on classifications are discussed. A new concept of neighborhood between market baskets is introduced and their properties are studied in this paper. It should be remarked that in this algebraic model the customers and the transactions can be identified by their market baskets. This implies that the results that hold for market baskets hold also for customers and transactions. The logical and algebraic methods that have been used to study the frequent market baskets, the association rules between market baskets and the constraints of market baskets here appear to be efficient tools in the study of the customer's classification.