Probabilistic approaches have been applied to the theory of rough set in several forms, including decision-theoretic analysis, variable precision analysis, and information-theoretic analysis. Based on rough membership functions and rough inclusion functions, we revisit probabilistic rough set approximation operators and present a critical review of existing studies. Intuitively, they are define...

Domain Theory and Rough Set Theory are relatively independent but have much close relationship worthy of further investigation. In this paper, we propose the notion of (orientated) lower concept formula (for short, lcf) of relational information systems and study the order-theoretic properties of the derived lcf systems. Particularly, we show that every orientated lcf system is an algebraic lat...

In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which l...

One of the main concepts in grey system theory is how systems should be controlled under incomplete or lack of information situation. Grey number denoting an uncertain value is described in real interval from this concept. In this paper, we introduce the real formal concept analysis based on grey-rough set theory by using grey numbers, instead of binary values. We propose, to extend the notion ...

Decision theoretic framework has been helpful in providing a better understanding of classification models. In particular, decision theoretic interpretations of different types of the binary rough set classification model have led to the refinement of these models. This study extends the decision theoretic rough set model to supervised and unsupervised multi-category problems. The proposed fram...

We develop two algebraic semantics for bitten rough set theory ([19]) over similarity spaces and their abstract granular versions. Connections with choice based generalized rough semantics developed in [15] by the present author and general cover based rough set theories are also considered.

The graded rough set and multi-granulation rough set are two significant generalized rough set models which be constructed on the indiscernibility relation. They solve the issues that the degree of overlap between the equivalence class and basic set in different view points of quantitative information. The purpose of this study is that research the good points of graded rough set in the multi-g...

Rough Set Theory, proposed in 1982 by Zdzislaw Pawlak, is in a state of constant development. Its methodology is concerned with the classification and analysis of imprecise, uncertain or incomplete information and knowledge, and of is considered one of the first non-statistical approaches in data analysis (Pawlak, 1982). The fundamental concept behind Rough Set Theory is the approximation of lo...

The framework for decision value oriented decomposition of data tables is stated with examples of its applications to partially generalized reasoning. Operation of synthesis of information is introduced for distributed decision tables. Theoretical foundations are built on the basis of the main factors of quality of reasoning, by referring to rough set, Dempster-Shafer and statistical theories.

In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of ’relative ability of subsets of approximation spaces to approximate’. The eventual algebraic semantics is developed via many deep results in convexity in ordered structures. A new variation of rough set th...