In this paper, we initiate to deal the concepts of ideals on rough sets. Also we introduce the notions Rough pivot set and semiring on the set of all rough sets for the given information system together with the operations praba Δ and praba ∇. We illustrate these concepts through examples.

Fuzzy logic is an effective tool to handle the ambiguity and uncertainty of real world systems. Also it has been successfully applied to a wide range of problems in different domains such as uncertainty and vagueness. In particular, medical diagnosis techniques have triggered many researchers in past decades. Sometimes, we may have vague concepts in medical system to analyze the diagnosis; such uncertainty can be dealt by using fuzzy sets. There are many methods to analyze the diseases in medical diagnosis such as fuzzy set, fuzzy inference system, fuzzy relation, fuzzy soft complement, fuzzy distance measure, intuitionistic fuzzy set and etc. In this paper, we discuss the aforementioned existing methods in fuzzy environment for medical diagnosis and also provide the direction for further research in medical applications.

In this review article, we have discussed about energy of a graph and energy of a fuzzy graph. Further we presented some standard results on these graphs. Since most real world networks such as communication networks, data organization, computational devices, the flow of computation, web graphs etc are directed graphs, we have analyzed energy of an intuitionistic fuzzy directed graph through real time example.