Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

In generalized rough set covering reduction theory, it is necessary to find a new measure to knowledge and rough set because the upper and lower approximations of rough sets are determined by their covering reduction. In this paper, information entropy is introduced to discuss the rough entropy of knowledge and the roughness of rough set, based on generalized rough set covering reduction. A new...

Due to its constantly growing incidence, obesity is an increasingly serious social and medical problem. Available data on the use of novel oral anticoagulants in morbidly obese and obese patients are very limited. However, we tried to summarize the available knowledge on the use of anticoagulants in this subpopulation of patients in everyday clinical practice. Studies on the clinical use of ant...

OBJECTIVE To evaluate the current and ideal body weight perceptions of schoolchildren in relation to their actual body weight and socio-economic status (SES). DESIGN Baseline evaluation of schoolchildren from January 2008 to April 2008 as part of a 3-year longitudinal study. SETTING City and non-city locations, Karnataka State, South India. SUBJECTS Schoolchildren (n 1877) aged between 8 ...

Although the burgeoning discipline of welfare economics is based on essentially utilititarian principles, the foundations of utilitarianism have received little attention in recent years. This paper seeks to reopen the debate by drawing a distinction between Harsanyi’s two defences of utilitarianism, labeling the first a teleological or ideal-observer theory, and the second a nonteleological th...

Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering-based rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as subbase, neighborhood and separation axioms have bee...

The concept, rough truth, is first presented in rough logic. It is a logical value, and lies between truth and falsity. By combining rough logic with modal logic, rough validity of the rough axioms is studied in this paper, which has close links with the logical value: rough truth. Because an axiom of modal logic corresponds to a rough axiom, the study of this paper actually focuses on the anal...

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...