The so-called measure of approximation quality plays an important role in many applications of rough set based data analysis. In this chapter, we provide an overview on various extensions of approximation quality based on rough-fuzzy and fuzzy-rough sets, along with highlighting their potential applications as well as future directions for research in the topic.

As medical images contain uncertainties, there are difficulties in classification of images into homogeneous regions. Fuzzy sets, rough sets and the combination of fuzzy and rough sets plays a prominent role in formalizing uncertainty, vagueness, and incompleteness in diagnosis. Development of hybrid approaches for the segmentation of the magnetic resonance imaging (MRI) with the ability of com...

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

In this paper, we discuss some basic properties of rough intuitionistic fuzzy set in semigroup. Intuitionistic fuzzy analogues of some results concerning rough semiprime (semiprimary) ideals in semigroup are obtained. 2010 AMS Classification: 03E72, 03F55, 06B10.

In this paper we define rough intuitionistic fuzzy sets (analogous to the definition of rough fuzzy sets introduced by Dubois and Prade [8] ) and study their properties. Some propositions in this notion are proved.

Rough set theory is one of important tools of soft computing, and rough approximations are the essential elements in rough set models. However, the existing fuzzy rough set model for set-valued data, which is directly constructed based on a kind of similarity relation, fail to explicitly define fuzzy rough approximations. To solve this issue, in this paper, we propose two types of fuzzy rough a...

Attribute selection is one of the important problems encountered in pattern recognition, machine learning, data mining, and bioinformatics. It refers to the problem of selecting those input attributes or features that are most effective to predict the sample categories. In this regard, rough set theory has been shown to be successful for selecting relevant and nonredundant attributes from a giv...

Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we intr...

In this paper, a different approach to extract the threshold value β of Variable Precision Rough Set (VPRS) applied to continuous information systems is presented. This study combines the Fuzzy Set and Rough Fuzzy Set (RFS) theories to determine the β value of VPRS. The β value was determined by the Fuzzy C-means and relevant Fuzzy theories, for the reason that errors of system classification c...