We give an algorithm solving combined word problems (over non-necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth–Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both co...

In a rough set approach to knowledge discovery problems, a set of rules is generated basing on training data using a notion of reduct. Because a problem of finding short reducts is NP-hard, we have to use several approximation techniques. A covering approach to the problem of generating rules based on information system is presented in this article. A new, efficient algorithm for finding local ...

We give an algorithm solving combined word problems (over non necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth-Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both co...

This paper critically analyzes reduct construction methods at two levels. At a high level, one can abstract commonalities from the existing algorithms, and classify them into three basic groups based on the underlying control structures. At a low level, by adopting different heuristics or fitness functions for attribute selection, one is able to derive most of the existing algorithms. The analy...

Since there may exist many relative reducts for a decision table, some attributes that are very important from the viewpoint of human experts may fail to be included in relative reduct(s) computed by certain reduction algorithms. In this paper we present the concepts of M-relative reduct and core where M is a user specified attribute set to deal with this problem. M-relative reducts and cores c...

This is a survey of a recent work done by the three authors, in which an analysis of geometric properties of a structure relative to a reduct is initiated. In particular, definable groups and fields in this context are considered. In a relatively 1-based theory every group is definably isogenous to a subgroup of a group definable in the reduct. For relatively CM-trivial theories (which encompas...

This paper focuses on rough set theory which provides mathematical foundations of set-theoretical approximation for concepts, as well as reasoning about data. Also presented in this paper is the concept of relative reducts which is one of the most important notions for rule generation based on rough set theory. In this paper, from the viewpoint of approximation, the authors introduce an evaluat...

We prove that the value group of field transseries is isomorphic to additive reduct field.

This paper presents a novel data mining approach for fault diagnosis of turbine-generator units. The proposed rough set theory based approach generates the diagnosis rules from inconsistent and redundant information using genetic algorithm and process of rule generalization. In this paper, a fault diagnosis decision table is obtained from discretization of continuous symptom attributes in the d...

In any information system, the reducts are useful in classifying data. Janusz Starzyk developed an algorithm for computing reducts using strong equivalence and the law of expansion on the data. However, implementation of this algorithm is cumbersome for huge volume of data. This paper deals with a technique for obtaining the reduct of the entire system by partitioning it into two with respect t...