Detection of Fuzzy Association Rules by Fuzzy Transforms

Table 1

Schema of a dataset.

	𝑋1	⋯	𝑋𝑖	⋯	𝑋𝑟
𝑂1	𝑝11	⋯	𝑝1𝑖	⋯	𝑝1𝑟
⋮	⋮	⋮	⋮	⋮	⋮
𝑂𝑗	𝑝𝑗1	⋯	𝑝𝑗𝑖	⋯	𝑝𝑗𝑟
⋮	⋮	⋮	⋮	⋮	⋮
𝑂𝑚	𝑝𝑚1	⋯	𝑝𝑚𝑖	⋯	𝑝𝑚𝑟

X = {𝑋₁,…,𝑋_𝑖,…,𝑋_𝑟} is the set of the attributes and 𝑂={𝑂₁,𝑂₂,…,O_𝑚} is the set of the objects or instances in the dataset. A value p_𝑗𝑖 belonging to the domain of the attribute 𝑋_𝑖 is called an item and a set of items is called an itemset. An association rule is represented as a directional dependence between sets of attributes in the dataset. It is indicated with an expression of the type 𝑆→𝑇, where 𝑆, 𝑇 are sets of attributes. The implication operator means that if all the items in S exist in an object, then all the items in T are also in the object with a high probability [2].