Rekha Srivastava

Fuzzy Hausdorff topological spaces

Abstract We introduce the notion of a fuzzy Hausdorff topological space and make a few observations to establish the appropriateness of this notion.

On fuzzy hausdorffness concepts

We continue our earlier work on fuzzy Hausdorffness [11] by relating our fuzzy Hausdorffness notion with those due to other authors.

On T 0 - and T 1 -fuzzy closure spaces

Abstract In this paper, we introduce subspace of a fuzzy closure space, sum of a family of pairwise disjoint fuzzy closure spaces and product of a family of fuzzy closure spaces, for the fuzzy closure spaces defined in Srivastava et al., 1994. We also introduce the notion of a T1-fuzzy closure space. We have studied here T0- (introduced earlier in Srivastava et al., 1994) and T1-fuzzy closure spaces in detail. Several results have been proved which establish the appropriateness of the definitions. In particular, we observe that T0 and T1 satisfy the hereditary, productive and projective properties and in addition, both are “good extensions” of the corresponding concepts in a closure space.

On separation axioms in a newly defined fuzzy topology

Abstract In [Fuzzy Sets and Systems 45 (1992) 79–82], Hazra et al. defined a fuzzy topology on a non-empty set in a new fashion. Here we introduce separation axioms and some allied notions in this new set-up and prove several results related to these notions.

On fuzzy T1-topological spaces

On etudie diverses relations entre les differentes definitions des espaces topologiques T 1 flous

Separation axioms in intuitionistic fuzzy topological spaces

In this paper we have studied separation axioms Ti, i = 0, 1, 2 in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functors B : IF-Top → BF-Top and D : BF-Top → IF-Top and observe that D is left adjoint to B.

On compactness in bifuzzy topological spaces

Abstract Compactness in a bifuzzy topological space has been studied earlier by Abd El-Monsef and Ramadan (Fuzzy Sets and Systems, 30, 1989, 165–174) and Safiya et al. (Fuzzy Sets and Systems, 62, 1994, 89–96) as generalizations of P-compactness or S-compactness in a bitopological space. In Section 2 of this note, we have obtained some interesting results related to PC-compactness introduced by Safiya et al. (Fuzzy Sets and Systems, 62, 1994, 89–96) as a concept parallelling that of P-compactness of bitopological spaces. Further, in Section 3 , we have introduced and studied B-compactness, B- α compactness in a bifuzzy topological space which are parallel to the notion of B-compactness in a bitopological space. We have also defied B-almost (B- α -almost) compactness in a bfts which is weaker than B-compactness (B- α -compactness). Several related results have been proved.

Representability of Fuzzy Biorders and Fuzzy Weak Orders

In this paper, we have studied representability of both fuzzy biorders and fuzzy weak orders. It has also been shown that union of a finite family of fuzzy weak orders with respect to a t-norm T is...

Fuzzy Soft Compact Topological Spaces

In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.

Fuzzy topologies generated by fuzzy relations

In this paper, we have introduced and studied fuzzy topologies generated by fuzzy relations. Several related results have been proved. In particular, we have obtained characterizations of a fuzzy topology generated by a fuzzy relation, a fuzzy topology generated by a fuzzy interval order, a preorderable fuzzy topology and an orderable fuzzy topology. We have also introduced and studied fuzzy bitopological spaces generated by fuzzy relations.