On Fuzzy Regularly Closed Filters in Michálek Fuzzy Topological Space

C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itself. In 1975, Michálek presented a functional definition of ordinary topology and later developed fuzzy topology as a distinct extension of this idea, setting it apart from Chang’s approach. While there has been significant research on Chang’s fuzzy topology, Michálek’s version has not received as much attention. This paper introduces the concept of fuzzy regularly closed filters, or FRCM filters, within Michálek’s fuzzy topological space and explores some properties of FRCM ultrafilters.

Fuzzy Topology Based on Residuated Lattice-Valued Logic

We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.

Pythagorean m-polar fuzzy topology with TOPSIS approach in exploring most effectual method for curing from COVID-19

The corona virus disease 2019(COVID-19)has emerged as a fatal virus.This deadly virus has taken the whole world into clutches and many people have embraced death due to this invincible bug.The death toll is rising with every tick of time.The aspiration behind this article is to discover the preventive measure that should be taken to cope with this intangible enemy.We study the prime notions of novel sort of topology accredited Pythagorean m-polar fuzzy topology along with its prime attributes.We slightly amend the well-acknowledged multi-criteria decision analysis tool TOPSIS(Technique for Order of Preference by Similarity to Ideal Solution)to befit the proposed multi-criteria group decision making(MCGDM)problem of exploring the most effective method for curing from COVID-19 employing the proposed model.

Relative N-compactness in L-fuzzy Topological Spaces

The concept of relative N-compactness is defined and characterized in terms ofnets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy setsand the relative N-compactness is L-good extension. Some connections between the N-compactness and the relative N-compactness are investigated. It is also proved that inducedrelative N-compact spaces are productive, and the product of finite relative compact sets isrelative compact.

Intuitionistic Fuzzy α-Generalized Closed Sets in Terms of Minimal Structure Spaces

In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.

T_2 Separation Subsets and T_2 Separateness in L-fuzzy Topological Spaces

The concept of α-CT2 separation L-fuzzy subsets in L-fuzzy topological spaces is presented by taking the stratiform structure of L-fuzzy subsets as the point of departure,and its basic characterizations and some topological properties are discussed,and the relation between it and other separateness is exposed,and the action is studied of α-CT2 separateness in N-compact spaces and N-paracompact spaces.

An Introduction to Fuzzy Topological Spaces

Topology has enormous applications on fuzzy set. An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article. In this research, first we have classified the fuzzy sets and topological spaces, and then we have made relation between elements of them. For expediency, with mathematical view few basic definitions about crisp set and fuzzy set have been recalled. Then we have discussed about topological spaces. Finally, in the last section, the fuzzy topological spaces which is our main object we have developed the relation between fuzzy sets and topological spaces. Moreover, this article has been concluded with the examination of some of its properties and certain relationships among the closure of these spaces.

Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces

In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated.

Separation Properties of Bitopological Space

In this paper we study a bitopological space with a fuzzy topological space,and examine the relation between various fuzzy and bitopological separation axioms.

On Felbin-type Fuzzy 2-normed Spacesand Its Fuzzy I-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.

FUZZY PRETOPOLOGICALSPACES, AN EXTENSIONALTOPOLOGICAL EXTENSION OF FTS

The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.

Lower and Upper Fuzzy Topological Subhypergroups

This paper provides a new connection between algebraic hyperstructures and fuzzy sets. More specifically, using both properties of fuzzy topological spaces and those of fuzzy subhypergroups, we define the notions of lower （upper） fuzzy topological subhypergroups of a hypergroup endowed with a fuzzy topology. Some results concerning the image and the inverse image of a lower （upper） topological subhypergroup under a very good homomorphism of hypergroups （endowed with fuzzy topologies） are pointed out.