Pythagorean fuzzy topological spaces

Olgun, Murat; Ünver, Mehmet; Yardımcı, Şeyhmus

doi:10.1007/s40747-019-0095-2

Cited by 33 publications

(19 citation statements)

References 36 publications

(34 reference statements)

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“…Coker [30] pioneered intuitionistic fuzzy topology. Olgun [31] expanded on this concept by introducing Pythagorean fuzzy topology. Topological structures on fuzzy soft sets [32] and cubic m-polar fuzzy sets [33] have robust applications in decision-making.…”

Section: Introductionmentioning

confidence: 99%

Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management

Riaz

Akmal

Almalki

et al. 2022

Mathematical Problems in Engineering

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The concept of the cubic intuitionistic fuzzy set is an effective hybrid model for modeling uncertainties with an intuitionistic fuzzy set and an interval-valued intuitionistic fuzzy set, simultaneously. The primary objective of this study is to develop a topological structure on cubic intuitionistic fuzzy sets with P-order and R-order as well as to define some fundamental characteristics and significant results with illustrations. Taking advantage of topological data analysis with cubic intuitionistic information, novel multicriteria group decision-making methods are developed for an uncertain supply chain management. Algorithms 1 and 2 are proposed for extensions of the weighted product model and the choice value method towards a cubic intuitionistic fuzzy environment, respectively. A comparative analysis is also given to discuss the validity and advantages of the proposed techniques.

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Section: Introductionmentioning

confidence: 99%

Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management

Riaz

Akmal

Almalki

et al. 2022

Mathematical Problems in Engineering

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“…Çoker [13] subsequently initiated a study of intuitionistic fuzzy topological spaces. Recently, Olgun et al [14] presented the concept of Pythagorean fuzzy topological spaces and Ibrahim [15] defined the concept of Fermatean fuzzy topological spaces.…”

Section: Introductionmentioning

confidence: 99%

(3, 2)‐Fuzzy Sets and Their Applications to Topology and Optimal Choices

Ibrahim

Al-shami

Elbarbary

2021

Computational Intelligence and Neuroscience

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The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

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“…Thivagar et al presented the idea of nanotopology neutrosophic units in [23]. [24] introduced the Pythagorean fuzzy topological space by following Chang. By making a fusion of the concepts Pythagorean topological space and nanotopological space, Pythagorean nanotopological spaces (PNTSs) were developed in [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Nanogeneralized Closed Sets with Application in Decision-Making

Ajay

Charisma

Petaratip

et al. 2021

Journal of Function Spaces

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Topology is studying the objects which are considered to be equal if they may also be continually deformed through other shapes as bending and twisting without tearing or glueing them. Topology is similar in geometrical structures and quantitatively equivalent. Nanotopology is the study of set. The main goal of this article is to propose the idea of generalized closed sets in Pythagorean nanotopological spaces. In addition, the concept of semigeneralized closed sets is also defined, and their properties are investigated. An application to MADM using Pythagorean nanotopology has been proposed and illustrated using a numerical example.

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Pythagorean fuzzy topological spaces

Cited by 33 publications

References 36 publications

Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management

Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management

(3, 2)‐Fuzzy Sets and Their Applications to Topology and Optimal Choices

Pythagorean Nanogeneralized Closed Sets with Application in Decision-Making

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