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Granular-Relational Data Mining by Piotr Hońko

By Piotr Hońko

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E. an extended attribute-value language) compared with a relational one, but they are able to preserve expressiveness of their relational counterparts. The remaining of the chapter is organized as follows. 2 introduces relational information granules. 4 develop a compound information system and constrained compound information system, respectively. 5 investigates the consistency and completeness of the approach. 6 provides concluding remarks. © Springer International Publishing AG 2017 P. 2 Information Granules This section introduces a granular computing based framework which is constructed based on definitions from [83].

Let B0 amount}. We obtain simB0 ((purchase(B, A, C, 1, _), 2), (purchase(B, A, C, 1, _), 1 (o2 ) = {purchase(B, A, _, 1)) = 1/2. Consider also different generalizations rltgen 1 {1, 3}, _))} and rltgen (o3 ) = {purchase(B, A, _, 4, _))}. Let B0 = {prod_id}. 20 we obtain simB0 (purchase(B, A, C, {1, 3}, _), purchase(B, A, C, 4, _)) = sim({1, 3}, {4}) = 0. 25. Customer 2 bought two products, whereas customer 3—one. 5. 25. 3 The measure can be used for sets of positive numbers only. 48 5 Rough-Granular Computing Let attributes age and income be generalized as follows age1 = {25-30}, age2 = {30-35}, age3 = {36-40}, inc1 = {1500-2000}, inc2 = {2500-3000}.

Firstly, two general definitions of the syntax and semantics of the language are introduced. Let L be a language such that the syntax and semantics of an atomic formula α ∈ L and its negation ¬α ∈ L are defined. 4 Symbolic values are abbreviated to their first letters. g. the granule (30, {3, 4}) from column age corresponds to the granule ((age, 30), {3, 4}). 54 6 Compound Information Systems Fig. 4 (Syntax and semantics of L) The syntax and semantics of the language L are defined recursively by those of α ∈ L and ¬α ∈ L, and by 1.

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