Existence of Fixed Points in Fuzzy Strong b-Metric Spaces

Kanwal, Shazia; Kattan, Doha A.; Perveen, Saba; Islam, Sahidul; Shagari, Mohammed Shehu

doi:10.1155/2022/2582192

Cited by 6 publications

(3 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sitara et al [36] proposed q-rung picture fuzzy (q-RPF) graph structures and numerous significant results for modeling with q-RPF graph. Kanwal et al [37] proposed the existence of fixed points in fuzzy strong b-metric spaces, and Kanwal and Azam [38] gave the notion of common fixed points of IFS maps for Meir-Keeler type contractions. Many AOs for different extensions of fuzzy sets are proposed in [39,40].…”

Section: Introductionmentioning

confidence: 99%

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Riaz

Farid

Alblowi

et al. 2022

Journal of Function Spaces

View full text Add to dashboard Cite

A q -rung orthopair fuzzy set (q-ROFS) is a robust approach for fuzzy modeling, computational intelligence, and multicriteria decision-making (MCDM) problems. The aim of this paper is to study the topological structure on q-ROFSs and define the idea of q -rung orthopair fuzzy topology (q-ROF topology). The characterization of q-ROF α -continuous mappings between q-ROF topological spaces and q-ROF connectedness is investigated. Some relationships of different types of q -rung orthopair fuzzy connectedness are also investigated. Additionally, the “ q -rung orthopair fuzzy weighted product model” (q-ROF WPM) is developed for MCDM of a hierarchical healthcare system. Due to limited and insufficient resources, a hierarchical healthcare system (HHS) is very effective to deal with the increasing problems of healthcare. Recognizing the stage of a disease with the symptoms, ranking the critical condition of patients, and referring patients to feasible hospitals are key features of HHS. A HHS will provide healthcare services in three levels, a primary health centers for initial stage of disease, secondary hospitals for secondary stage of disease, and tertiary hospital for the third-order stage. A numerical example is illustrated to demonstrate the efficiency of q-ROF WPM and advantages of HHS.

show abstract

Section: Introductionmentioning

confidence: 99%

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Riaz

Farid

Alblowi

et al. 2022

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…Then, Öner showed that every "open" ball in a fuzzy strong b-metric space is an open set. Since then, fuzzy strong b-metric spaces have received the attention of some researchers (see, e.g., [33][34][35]).…”

Section: Definitionmentioning

confidence: 99%

Concerning Fuzzy b-Metric Spaces †

Romaguera

2023

Mathematics

View full text Add to dashboard Cite

In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Nădăban presented a notion of a fuzzy b-metric space that is slightly different from the one given by Hussain et al., and explored some of its topological properties. Related to Nădăban’s study, Sedghi and Shobe, Saadati, and Šostak independently conducted investigations in articles published in 2012, 2015, and 2018, respectively, about another class of spaces that Sedgi and Shobe called b-fuzzy metric spaces, Saadati, fuzzy metric type spaces, and Šostak, fuzzy k-metric spaces. The main contributions of our paper are the following: First, we propose a notion of fuzzy b-metric space that encompasses and unifies the aforementioned types of spaces. Our approach, which is based on Gabriec’s notion of a fuzzy metric space, allows us to simultaneously cover two interesting classes of spaces, namely, the 01-fuzzy b-metric spaces and the K-stationary fuzzy b-metric spaces. Second, we show that each fuzzy b-metric space, in our sense, admits uniformity with a countable base. From this fact, we derive, among other consequences, that the topology induced by means of its “open” balls is metrizable. Finally, we obtain a characterization of complete fuzzy b-metric spaces with the help of a fixed point result which is also proved here. In support of our approach, several examples, including an application to a type of difference equations, are discussed.

show abstract

“…Ishtiaq et al [17] derived several FP results in generalizations of FMSs. In fuzzy strong b-metric spaces, Shazia et al [18] identified FPs for a number of nonlinear contraction mappings. In 2004, Park [19] used the idea of intuitionistic FSs, continuous t-norm (CTN), and continuous t-conorm (CTCN) to established intuitionistic fuzzy metric spaces (IFMSs) as a generalization of FMSs.…”

Section: Introduction and Prelimainariesmentioning

confidence: 99%

New Fixed Point Results in Neutrosophic b-Metric Spaces With Application

Saeed¹,

Ishtiaq²,

Kattan³

et al. 2023

Int. J. Anal. Appl.

View full text Add to dashboard Cite

In this manuscript, we establish the notion of neutrosophic b-metric spaces as a generalization of fuzzy b-metric spaces, intuitionistic fuzzy b-metric spaces and neutrosophic metric spaces in which three symmetric properties plays an important role for membership, non-membership and neutral functions as well we derive some common fixed point and coincident point results for contraction mappings. Also, we provide several non-trivial examples with graphical views of neutrosophic b-metric spaces and contraction mappings by using computational techniques. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to test the validity of the main result.

show abstract

Existence of Fixed Points in Fuzzy Strong b-Metric Spaces

Cited by 6 publications

References 19 publications

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Concerning Fuzzy b-Metric Spaces †

New Fixed Point Results in Neutrosophic b-Metric Spaces With Application

Contact Info

Product

Resources

About

Existence of Fixed Points in Fuzzy Strong b-Metric Spaces

Cited by 6 publications

References 19 publications

Novel Concepts of q -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Novel Concepts of q -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Concerning Fuzzy b-Metric Spaces †

New Fixed Point Results in Neutrosophic b-Metric Spaces With Application

Contact Info

Product

Resources

About

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making

Novel Concepts of $q$ -Rung Orthopair Fuzzy Topology and WPM Approach for Multicriteria Decision-Making