In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated with it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set that we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied. Keywords: Interval-valued intuitionistic fuzzy set, interval-valued intuitionistic fuzzy topology, fuzzy topology, homeomorphism, compactness

© 2021 – IOS Press.

DOI: 10.3233/JIFS-202757

The concepts of ij -δ-semi closed and ij -δ-semi open sets in bitopological spaces are introduced and studied. Also, the notions of    sets and    sets are investigated. Furthermore, a new closure operator called  on the bitopological space  is defined and associated topology   is given.

@2021 by the authors.

http://doi.org/10.26637/mjm0903/008

In this paper, we define r-L-fuzzy closed convex sets and r-L-fuzzy closed neighbourhoods in an (L, M)-fuzzy topology (L, M)-fuzzy convexity spaces. Also, r-L-fuzzy neighbourhood separation properties rL-FNS_i were studied where . In addition, we also study the invariance or otherwise of these separation properties under subspace and product. @FMI

@ 2021 Research Institute for Basic Science, Wonkwang University

http://www.afmi.or.kr

 https://doi.org/10.30948/afmi.2021.21.1.93

In this paper, we point out that the proof of Theorem 2.4(5), Proposition 2.6(1) and Proposition 2.8(1) in the paper titled ”On (L, M)-fuzzy convex structures” (Filomat 33(13): 4151-4163, 2019) are not true in general. Then, we give three correct proofs of these results.

@ 2021 Faculty of Sciences and Mathematics, University of NIŠ, Serbia.

http://www.pmf.ni.ac.rs/filomat

Different from the separation axioms in the framework of (L, M)-fuzzy convex spaces defined by Liang et al. (2019). In this paper, we give some new investigations on separation axioms in (L, M)-fuzzy convex structures by L-fuzzy hull operators and r-L-fuzzy biconvex. We introduce the concepts of r-LFS_i spaces where  , and obtain various properties. In particular, we discuss the invariance of these separation properties under subspace and product.

DOI:10.3233/JIFS-200340

© 2021 – IOS Press.                                                 

In this paper, we introduce the concepts of delta generalized closed, generalized delta closed and delta star generalized closed sets in bitopological spaces and study some of its properties and its relations with other types of closed sets. Also, we study some properties of weak forms of separation axioms.

© 2021 Pushpa Publishing House, Prayagraj, India.

http://www.pphmj.com

http://dx.doi.org/10.17654/UM014010013

In this paper, we will define an L-fuzzifying preuniform structure based on way below relation (or L-fuzzifying preuniform structure) and study their properties. Also, the concept of interior and closure operators in L-fuzzifying setting were established. Furthermore, the relation between L-fuzzifying preuniform and L-fuzzifying topology were explained.

The aim of this paper is to present and make a preliminary study of a new -fuzzy (K, E)-soft topology  from old -fuzzy (K, E)-soft topology T  via L-fuzzy (K, E)-soft grill G  induced by L-fuzzy soft operators     .

© 2020 Pushpa Publishing House, Prayagraj, India

http://dx.doi.org/10.17654/FS025010058

This paper defines a new class of L-fuzzy sets called r-L-fuzzy biconvex sets in (L; M)-fuzzy convex structures (X; C); where C is an (L; M)-fuzzy convexity on X; and some of their properties were studied. In addition, we introduce (L; M)-fuzzy topological convexity space and study some of its properties. Finally, we introduce locally (L; M)-fuzzy topology (L; M)-fuzzy convexity space and study some of its properties.

@ Faculty of Sciences and Mathematics, University of NIŠ, Serbia.

https://doi.org/10.2298/FIL1913151S