Published in last 50 years
In this paper, we introduced concept of fuzzy homotopy lifting property, fuzzy fiber structure is introduced. Also, the definition of the fuzzy lifting function and some theorems in a fuzzy topological space are discussed.
This paper introduces a new fuzzy structure named “fuzzy primal.” Then, it studies the essential properties and discusses their basic operations. By applying the q-neighborhood system in a primal fuzzy topological space and the Łukasiewicz disjunction, we establish a fuzzy operator (·) ⋄ on the family of all fuzzy sets, followed by its core characterizations. Next, we use (·) ⋄ to investigate a further fuzzy operator denoted by Cl⋄. To determine a new fuzzy topology from the existing one, the earlier fuzzy operators are explored. Such a new fuzzy topology is called primal fuzzy topology. Various properties of primal fuzzy topologies are found. Among others, the structure of a fuzzy base that generates a primal fuzzy topology. Furthermore, the concept of compatibility between fuzzy primals and fuzzy topologies is introduced, and some equivalent conditions to that concept are examined. It is shown that if a fuzzy primal is compatible with a fuzzy topology, then the fuzzy base that produces the primal fuzzy topology is itself a fuzzy topology.
In this paper, we introduce the concept of fuzzy δ-ideal continuous, fuzzy θ-ideal continuous, fuzzy strongly δ-ideal continuous and fuzzy almost ideal continuous mappings in fuzzy ideal topological spaces given the definition of Sostak. In addition, we study some properties between them.
In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy F<sub>σ</sub>- sets in a fuzzy Baire-separated space. Conditions under which fuzzy topological spaces become fuzzy Baire-separated spaces are established. Fuzzy nowhere dense sets are fuzzy closed sets in fuzzy nodec spaces and subsequently a question will arise. Which fuzzy topological spaces [other than fuzzy hyperconnected spaces, fuzzy globally disconnected spaces] have fuzzy closed sets with fuzzy nowhere denseness? For this, fuzzy topological spaces having fuzzy closed sets with fuzzy nowhere denseness are identified in this paper. It is verified that fuzzy ultraconnected spaces are non fuzzy Baire -separated spaces. The means, by which fuzzy weakly Baire space become fuzzy Baire -separated spaces and in turn fuzzy Baire - separated spaces become fuzzy seminormal spaces, are obtained. There are scope in this paper for exploring the inter-relations between fuzzy Baire spaces and Baire -separated spaces.
The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their neighborhood structure in bipolar fuzzy supra topological spaces. Then, we consider another important structure, “quasi-coincident”, in the case of bipolar fuzzy points and bipolar fuzzy sets. Then, we introduce the corresponding neighborhood structure called “Q-neighborhood system” by using the quasi-coincident relations. Furthermore, we also investigate the characterization of bipolar fuzzy supra topological space in terms of quasi-neighborhoods. Finally, we present a new method to solve medical diagnosis problems by using the bipolar fuzzy score function.
Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.
<abstract><p>In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.</p></abstract>
In this article, the concept of fuzzy hypersoft δ (resp. semi, pre, δ semi δ pre)-separation axioms in fuzzy hypersoft topological spaces are introduced by developing fuzzy hypersoft δ (resp. semi, pre, δ semi δ pre)-neighbourhood with respect to fuzzy hypersoft points. Also, the properties and relations between fuzzy hypersoft δ (resp. semi, pre, δ semi δ pre)- Ti- spaces (i = 0, 1, 2, 3, 4) are discussed.
<abstract><p>In this paper, we first introduced the concept of $ r $-fuzzy soft $ \beta $-closed sets in fuzzy soft topological spaces based on the sense of Šostak and investigated some properties of them. Also, we defined the closure and interior operators with respect to the classes of $ r $-fuzzy soft $ \beta $-closed and $ r $-fuzzy soft $ \beta $-open sets and studied some of their properties. Moreover, the concept of $ r $-fuzzy soft $ \beta $-connected sets was introduced and characterized with the help of fuzzy soft $ \beta $-closure operators. Thereafter, some properties of a fuzzy soft $ \beta $-continuity were studied. Also, we introduced and studied the concepts of fuzzy soft almost (weakly) $ \beta $-continuous functions, which are weaker forms of a fuzzy soft $ \beta $-continuity. The relationships between these classes of functions were specified with the help of some illustrative examples. Finally, we explored new types of fuzzy soft functions called fuzzy soft $ \beta $-irresolute (strongly $ \beta $-irresolute, $ \beta $-irresolute open, $ \beta $-irresolute closed, and $ \beta $-irresolute homeomorphism) functions and discussed some properties of them. Also, we showed that fuzzy soft strongly $ \beta $-irresolute $ \Rightarrow $ fuzzy soft $ \beta $-irresolute $ \Rightarrow $ fuzzy soft $ \beta $-continuity, but the converse may not be true.</p></abstract>
This research aims to define and investigate the properties of Nano fuzzy Z-open explicitly sets defined in Nano fuzzy topological spaces. Also, there is an attempt to define Nano fuzzy Z-closure Nano fuzzy Z-interior in Nano fuzzy topological spaces. The work has grown by incorporating Nano fuzzy δ open sets, Nano fuzzy δ semi-open sets, Nano fuzzy δ semi-open sets, and Nano fuzzy δ pre-open sets. Also, the work has been concluded with a numerical application of the Nano fuzzy score function in the medical field (to check the proper diagnosis of disease and drug combinations given to the patient).
The purpose of this study is to introduce the concept of homeomorphism via βm – closed set and study its behavior and properties in double fuzzy topological spaces. This objective is achieved through the definitions of df- βm continuous functions and df- βm closed functions. The results of this study represent important relationships and proofs, in addition to providing some necessary examples.
The intuitionistic fuzzy sets, in which the elements of the universe have their membership and non-membership degrees in [0, 1], is a generalization of Zadeh’s fuzzy set. In this paper intuitionistic fuzzy sets are used as tools for assessment and decision making. This is useful in cases where one is not sure about the suitability of the linguistic characterizations assigned to each element of the universal set. Further, it is described how the notions of convergence, continuity, compactness, and of Hausdorff topological space are extended to intuitionistic fuzzy topological spaces. Applications illustrating our results are also presented.
Generalized fuzzy open sets are playing a vital role in the study of fuzzy topological space as well as that of fuzzy bitopological space since its inception. More often, it is reported that fuzzy closed sets are always included in the family of generalized fuzzy closed sets. Very recently, it has appeared that fuzzy γ∗ -open sets are incomparable with fuzzy open sets. This paper aims to present three different kinds of fuzzy generalized closed sets in the light of fuzzy γ∗ -open set and associated closure operators with the terminologies- generalized fuzzy γ∗ -closed set, γ∗ -generalized fuzzy closed set and γ∗ -generalized fuzzy γ∗-closed set and it is found that the relation between any two concepts is not necessarily linear. Also, the interrelationships among them are established along with suitable counter examples which are properly placed to make the paper self-sufficient.
In this article, mixed fuzzy topology and its topological properties have been studied. Mixed fuzzy topology is defined with the help of quasi-coincidence and closure of a fuzzy set in one of the fuzzy topologies. Thus, a new fuzzy topology is generated from the given two fuzzy topologies. This new fuzzy topology may or may not contain the topological properties of the parent topologies. This study identifies some topological properties that are carried to the mixed fuzzy topology from the given parent fuzzy topologies and some other properties which are not carried to the mixed fuzzy topology. Here a base for mixed fuzzy topology from the bases of the given parent topologies is constructed. Considering the regularity of one of the parent topologies mixed fuzzy topology is investigated. Hausdorff’s properties of mixed fuzzy topological spaces are also discussed. It is now of general interest to know which properties are carried to the mixed topology and which are not. A few of these are being tried to answer here in this paper.
On Some New Forms of Fsgb-Continuous Mappings in Fuzzy Topological Spaces.
In a fuzzy topological space, this article introduces fuzzy locally minimal open, fuzzy s-mean open sets at certain fuzzy points. Additionally, several of those fuzzy open sets attributes are expanded. Fuzzy mean open sets are weaker than the fuzzy s-mean open. We note that for each of its fuzzy points, a fuzzy minimum open is a fuzzy locally minimal open set.
In this article, we give defines about fuzzy pseudo norm module space and fuzzy metric module space which induces by this space. Complete metric space was proved. Also we are defining fuzzy topological module space which induces by fuzzy metric module space.
Fuzzy wg**- Connectedness in Fuzzy Topological Spaces
The aim of the present paper is to introduce two classes of open mappings using intuitionistic fuzzy supra open sets and semi-supra open sets in intuitionistic fuzzy supra topological spaces. It is nothing but, the image of intuitionistic fuzzy supra open set (resp. supra open) is intuitionistic fuzzy semi-supra closed set (resp. supra closed) in co-domain space. Moreover , a few of their significant properties have been studied. A necessary and sufficient condition for intuitionistic fuzzy supra contra semi-open mapping has been derived in terms of semi-supra closure and semi-supra interior. Also, the class of intuitionistic fuzzy supra contra open mappings is properly contained in that of intuitionistic fuzzy supra contra semi-open mappings has been investigated. Suitable examples have been given to establish that the reversible implications are lacking in general. A notion of intuitionistic fuzzy supra contra semi-homeomorphism has been defined and characterized.
In present of this paper, new classes of generalized fuzzy continuous functions called fuzzy -continuous functions and fuzzy -irresolute continuous functions are defined and studied. Also, several examples are given.