The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

In this paper we review four fuzzy extensions of the socalled tight pair of covering based rough set approximation operators. Furthermore, we propose two new extensions of the tight pair: for the first model, we apply the technique of representation by levels to define the approximation operators, while the second model is an intuitive extension of the crisp operators. For the six models, we st...

In order to train distance learning students the discernment abilio, teachers often suggest to them web courseware on some specific topics, such as a controversial social issues, with different view points. Traditional discriminating strategies based on simple keyword matching often lead to low accuracy of discrimination. This paper proposes a method called DRSA (Discriminating via Representati...

Early work on case based reasoning reported in the literature shows the importance of case base maintenance for successful practical systems. Different criteria to the maintenance task have been used for more than half a century. In this paper we present different sort out techniques for case base maintenance. All the sort out techniques proposed are based on the same principle: a Rough Sets co...

We often describe lives (or parts of lives) as meaningful or as not meaningful. It is also common to characterize them as more or less meaningful. Some lives, we tend to think, are more meaningful than others. But how then can one compare lives with respect to how much meaning they contain? Can one? This paper argues that (i) only a notion of rough equality can be used when comparing different ...

In this presentation we shall raise the following issues connected with the discourse of rough set theory: 1. indistinguishability 2. definition of a rough set 3. language dependency, the problem of referent 4. vagueness 5. abstraction 6. application-friendliness We shall argue that existing practices prevailing in rough set research fall short in addressing most of the issues. After almost fif...

In covering based rough sets, the neighborhood of an element is the intersection of all the covering blocks containing the element. All the neighborhoods form a new covering called a covering of neighborhoods. In the course of studying under what condition a covering of neighborhoods is a partition, the concept of repeat degree is proposed, with the help of which the issue is addressed. This pa...

This paper focuses on generalization of rough set model and rule induction. First a extension of rough set approximations is established on general granular structure, so that the rough set models on some special granular structures are meaningful. The new rough approximation operators are interpreted by topological terminology well. Conversely, by means of the new rough approximation operators...

We present a general rule induction algorithm based on sequential covering, suitable for variable consistency rough set approaches. This algorithm, called VC-DomLEM, can be used for both ordered and non-ordered data. In the case of ordered data, the rough set model employs dominance relation, and in the case of non-ordered data, it employs indiscernibility relation. VC-DomLEM generates a minima...