$$\boldsymbol{q}$$-Rung Orthopair Fuzzy Topological Spaces

Türkarslan, Ezgi; Ünver, Mehmet; Olgun, Murat

doi:10.1134/s1995080221020219

Cited by 17 publications

(15 citation statements)

References 14 publications

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“…Turkarslan et al [21] proposed the idea of q-ROF topological spaces as a generalization of Pythagorean fuzzy topological spaces [19,20]. Definition 6 (see [21]). Let X ≠ ∅ be a set and £τ be a family of q-ROF subsets of X.…”

Section: Q-rof Topologymentioning

confidence: 99%

“…Olgun et al [19] and Öztürk and Yolcu [20] proposed the notion of "Pythagorean fuzzy topology and Pythagorean fuzzy topological spaces." Turkarslan et al [21] proposed some results of "q-rung orthopair fuzzy topological spaces", and Charisma and Ajay [22] gave the idea of "Pythagorean fuzzy α-continuity." Haydar gave the notion of connectedness for Pythagorean fuzzy topological space [23].…”

Section: Introductionmentioning

confidence: 99%

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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

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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.

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Section: Q-rof Topologymentioning

confidence: 99%

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

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show abstract

“…Cheng [29] proposed the idea of fuzzy topological space and extended some basic terms related to topology. Olgun [30] et al proposed the idea of a q-rung orthopair fuzzy topological space (q-ROF z TS) and discussed continuity between two q-ROF z TSs.…”

Section: Q-rof Z Ts Induced By Rrmentioning

confidence: 99%

Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making

2021

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Yager recently introduced the q-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of q-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a q-rung orthopair fuzzy set to search out the accuracy of a q-rung orthopair fuzzy set, and we defined two types of q-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough q-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of q-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for q-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision.

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“…He defined the main topological concepts via this space such as continuity, compactness, connectedness, and separation axioms. Recently, Turkarslan et al [36] have familiarized a q-rung orthopair fuzzy topological space and studied some its properties. Recently, Ameen et al [16] have initiated the concept of infra-fuzzy topological structures and explored main features.…”

Section: Introductionmentioning

confidence: 99%

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

Al-shami¹,

Ibrahim²,

Mhemdi³

et al. 2022

IJFIS

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One of the most useful expansions of fuzzy sets for coping with information uncertainties is the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novel extension of fuzzy sets called n th power root fuzzy set (briefly, nPR-fuzzy set) and elucidate their relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rung orthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets as well as study their various features. Furthermore, we familiarize the concept of nPR-fuzzy topology and investigate the basic aspects of this topology. In addition, we define separated nPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, we study and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish T 0 and T 1 in nPR-fuzzy topologies and discover the links between them.

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$$\boldsymbol{q}$$-Rung Orthopair Fuzzy Topological Spaces

Cited by 17 publications

References 14 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

Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

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$$\boldsymbol{q}$$-Rung Orthopair Fuzzy Topological Spaces

Cited by 17 publications

References 14 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

Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

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Product

Resources

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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