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.

The study of Sierpiński triangle network and extended Sierpiński graph is quite interesting in the field of fractal networks. In nature, fractal networks (FN) and silicate structure networks (Sio4) play vital roles and in architecture to analyze the dimension of the above-mentioned FN and Sio4 networks it is necessary to identify the number of copies of the network. In this paper, we introduced a silicate triangle fractal network (Sin) which is a planar fractal and it is created using a related sequence of graphs named (Sin)n≥0, where n is the nth level of silicate triangle fractal network. We analyze the topological indices (TI) of the silicate triangle fractal network Sin graph and compare the calculated topological indices to the number of copies of silicate structure (Sio4) in each iteration of Sin for a sequence of a graph.