The problem of extracting knowledge from decision tables in terms of functional dependencies is one of the important problems in knowledge discovery and data mining. Based on some results in relational database, in this paper we propose two algorithms. The first one is to find all reducts of a consistent decision table. The second is to infer functional dependencies from a consistent decision table. The second algorithm is based on the result of the first. We show that the time complexity of the two algorithms proposed is exponential in the number of attributes in the worst case.

A Method for Extracting Knowledge from Decision Tables in Terms of Functional Dependencies

Most decision support systems based on rough set theory are related to the minimal reduct calculation problem, which is NP-hard. This paper investigates the problem of searching for the set of useful attributes that occur in at least one reduct. By complement, this problem is equivalent to searching for the set of redundant attributes, i.e. the attributes that do not occur in any reducts of the given decision table. We show that the considered problem is equivalent to a Sperner system for relational data base system and prove that it can be solved in polynomial time. On the base of these theoretical results, we also propose two different algorithms for elimination of redundant attributes in decision tables.

Searching for Reductive Attributes in Decision Tables

Armstrong databases are a popular tool in example-based database design. An Armstrong database for a given constraint set Σ from a fixed constraint class $\mathcal Z$ satisfies precisely those constraints from $\mathcal Z$ that are logically implied by Σ. In this paper we study Armstrong data trees for functional dependencies for XML-encoded data in the context of a simple XML tree model reflecting the permitted parent-child relationships together with their frequencies.

On the existence of armstrong data trees for XML functional dependencies

Most decision support systems based on rough set theory are related to the minimal reduct calculation problem, which is NP-hard. This paper investigates the problem of searching for the set of useful attributes that occur in at least one reduct. By compliment, this problem is equivalent to searching for the set of redundant attributes, i.e. the attributes that do not occur in any reducts of the given decision table. We show that the considered problem is equivalent to a Sperner system for relational data base system and prove that it can be solved in polynomial time. On the base of these theoretical results, we also propose some algorithms for elimination of redundant attributes in decision tables.

On elimination of redundant attributes in decision tables

The relational data model was defined by Codd [3] in 1970. Functional dependencies and minimal keys are very important concepts in the relational data model. The dense families of database relations were introduced by Järvinen [5] (2001), who has characterized functional dependencies and minimal keys of relations in terms of dense families. The aim of this paper is to continue investigating some properties of dense families of database relations and their applications. We give necessary and sufficient conditions for an arbitrary family to be R− dense. We prove that for a given relation R the equality set ER is an R−dense family. We also propose an effective algorithm finding all minimal keys of a given relation R. Finally, some related problems are also studied in this paper. Tóm tắt. Mô h̀ınh dũ. liê.u quan hê. du .o. . c dè̂ xuất bo . ’ i Codd [3] vào năm 1970. Phu. thuô.c hàm và khoá tối tiê’u là nhũ.ng khái niê.m rất quan tro.ng trong mô h̀ınh dũ . liê.u quan hê.. Ho. trù mâ.t cu’a quan hê. trong co . so. ’ dũ. liê.u du .o. . c gió .i thiê.u bo . ’ i Järvinen [5] (2001). Järvinen dă.c tru .ng phu. thuô.c hàm và khoá tối tiê’u cu’a quan hê. theo quan diê’m ho. trù mâ.t. Mu.c tiêu bài báo là tiếp tu. c nghiên cú.u mô.t số t́ınh chất cu’a ho. trù mâ.t cu’a quan hê., và ú .ng du.ng cu’a nó. Chúng tôi du .a ra mô.t số diè̂u kiê.n cà̂n và du’ dê’ mô.t ho. bất kỳ là ho. R− trù mâ.t. Chúng tôi chú.ng minh rà̆ng vó.i mô.t quan hê. cho tru .́o.c R tâ.p bà̆ng nhau ER là mô.t ho. R− trù mâ.t. Chúng tôi cũng du.a ra mô.t thuâ.t toán hiê.u qua’ t̀ım tất ca’ các khoá tối tiê’u cu’a quan hê. cho tru .́o.c R. Cuối cùng mô.t số vấn dè̂ liên quan cũng du.o. . c nghiên cú .u trong bài báo này.

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On the dense families of database relations

The strong dependency has been introduced and axiomatized in [2], [3], [4], [5]. The aim of this paper is to investigate on Armstrong relations for strong dependencies. We give a necessary and sufficient condition for an abitrary relation to be Armstrong relation of a given strong scheme. We also give an effective algorithm finding a relation υ such that υ is Armstrong relation of a given strong scheme G = (U, S) (i.e. Sr = S, where Sr is a full family of strong dependencies of r, and Sis a set of all strong dependencies that can be derived from S by the system of axioms). We estimate this algorithm. We show that the time complexity of this algorithm is polynomial in |U| and |S|.

On armstrong relations for strong dependencies

The dense families of database relations were introduced by Jarvinen [7] The aim of this paper is to investigate some new properties of dense families of database relations, and their applications That is, we characterize functional dependencies and minimal keys in terms of dense families We give a necessary and sufficient condition for an abitrary family to be R-- dense family We prove that with a given relation R the equality set ER is an R-dense family whose size is at most m(m-1)/2, where m is the number of tuples in R We also prove that the set of all minimal keys of relation R is the transversal hypergraph of the complement of the equality set ER We give an effective algorithm finding all minimal keys of a given relation R We aslo give an algorithm which from a given relation R finds a cover of functional dependencies that holds in R The complexity of these algorithms is also esimated

Some results related to dense families of database relations

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On armstrong relations for strong dependencies

Some results related to dense families of database relations