Fuzzy Set Theory and Rough Set Theory are the most popular mathematical tools for dealing with uncertainties. During past decades, these set theories are being applied successfully in several areas for solving many complex tasks. This paper is concerned with the application of hybrid Fuzzy-Rough set based approach for feature subset selection. Keywords— Fuzzy set theory, Rough Set theory, Fuzzy...

Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and...

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, a-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, de®nability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. ...

Classification based on fuzzy logic techniques can handle uncertainty to a certain extent as it provides only the fuzzy membership of an element in a set. This paper implements the extension of fuzzy logic: Neutrosophic logic to handle indeterminacy, uncertainty effectively. Classification is done on various techniques based on Neutrosophic logic i.e. Neutrosophic soft set, rough Neutrosophic s...

Fuzzy rule interpolation is an important technique for performing inferences with sparse rule bases. Even when given observations have no overlap with the antecedent values of any rule, fuzzy rule interpolation may still derive a conclusion. Nevertheless, fuzzy rule interpolation can only handle fuzziness but not roughness. Rough set theory is a useful tool to deal with incomplete knowledge, wh...

Rough fuzzy sets are an effective mathematical analysis tool to deal with vagueness and uncertainty in the area of machine learning and decision analysis. Fuzzy information systems and fuzzy objective information systems exit in many applications and knowledge reduction in them can’t be implemented by reduction methods in Pawlak information systems. Therefore, this paper provides a model for ru...

In this paper, we discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron – as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 that rough inclusions (which represent a h...

Medical image segmentation plays a vital role in image processing due to the catering needs of the medical images in automating, delineating anatomical structures and diagnosis. Very often the medical images contain uncertain, vague, and incomplete data definition. The concepts of lower and upper approximations of rough sets effectively handle this data. In this paper, rough sets based clusteri...

Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract f...