The aim of this paper is to introduce the concept generalized (Λ, α)-closed sets. Moreover, we investigate some characterizations Λα-T1/2 -spaces, α)-normal spaces and α)-regular by utilizing

This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).

Fuzzy sets theory has several applications in biomedicine. The dissimilarity of fuzzy sets is used for this purpose. In this paper, we present the generalized equation of the dissimilarity of fuzzy sets. This relation is based on the set theoretic point of view. The parameter of this generalized equation and also its relation to a recently introduced metric defined in fuzzy hypercube are discus...

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...