Fuzzy Graphs are having numerous applications in problems like Network analysis, Clustering, Pattern Recognition and Neural Networks. The analysis of properties of fuzzy graphs has facilitated the study of many complicated networks like Internet. In this paper we study the structures of complement of many important fuzzy graphs such as Fuzzy cycles, Blocks etc. The complement of fuzzy graphs wi...

Algebraic structures and lattice structures of rough sets are basic and important topics in rough sets theory. In this paper we pointed out that a basic problem had been overlooked, that is the closeness of union and intersection operations of rough approximation pairs, i.e. (lower approximation, upper approximation). We present that the union and intersection operations of rough approximation ...

This paper is aimed at constructing a topology on fuzzy hypersoft sets. The concepts of topology, open(closed) sets, interior, closure, base and subspace are also introduced here some important theorems have been established.

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...

We introduce a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...

The class of ω-closed subsets of a space (X ,τ) was defined to introduce ω-closed functions. The aim of this paper is to introduce and study the class of gω-closed sets. This class of sets is finer than g-closed sets and ω-closed sets. We study the fundamental properties of this class of sets. In the space (X ,τω), the concepts closed set, g-closed set, and gω-closed set coincide. Further, we i...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as de1ned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to...

Fuzziness is not a priori an obvious concept and demands some explanation. “Fuzziness” is what Black (NF 1937) calls “vagueness” when he distinguishes it from “generality” and from “ambiguity.” Generalizing refers to the application of a symbol to a multiplicity of objects in the field of reference, ambiguity to the association of a finite number of alternative meanings having the same phonetic...