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Fuzzy topological concepts via ideals and grills
Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.2
In this paper, we have introduced various types of $r$-fuzzy ideal continuity based on a fuzzy ideal ${\mathcal{I}}$ on a fuzzy topological space $(X, \tau)$. According to various types of $r$-fuzzy ideal openness, many implications between these types of $r$-fuzzy ideal continuity are illustrated. Fuzzy ideal openness and fuzzy ideal $\beta$-continuity are the core of these types of continuity. Fuzzy grills are investigated, and it is shown that studying concepts in view of fuzzy ideals is equivalent to studying the same concepts in view of fuzzy grills.
Generalized upper and lower continuous multifunctions
Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.3
In this paper, we introduce the concept of fuzzy $(\alpha, \beta, \theta, \delta, I)$-continuous multifunctions. There is a unification of several characterizations and properties of some types of modifications of upper and lower semi-continuous multifunctions. We deduce a generalized form of upper and lower continuous multifunctions, namely upper and lower $\eta \eta^{*}$-continuous multifunctions.
Maximal and minimal neighborhoods of rough fuzzy sets
Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.2
It has a comment on two patterns of generalizations of the roughness of some fuzzy set. The authors in 2022, based on the minimal neighborhoods of rough fuzzy sets, introduced a generalization of rough fuzzy sets. This paper will be used maximal neighborhoods in defining a new generalization of rough fuzzy sets in a pattern similar to this generalization introduced by the authors in 2022. Mainly, it is shown that the new boundary region set computed using maximal neighborhoods does not depend on that set computed using minimal neighborhoods as given by the authors in 2022. As an application, it is shown that the connectedness of rough fuzzy topological spaces could be defined using maximal neighborhoods. Still, this connectedness is not related to the connectedness expressed by the authors in 2022 using minimal neighborhoods.
Initial fuzzy soft closure structures
Ali N. Koam,Ismail Ibedou,S. E. Abbas 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.17 No.2
In this paper, we introduce the notions of fuzzy soft interior spaces and fuzzy soft closure spaces. In particular, we prove the existence of initial fuzzy soft interior structures and initial fuzzy soft closure structures. From this fact, the category FSC is a topological category over SET.