Pythagorean fuzzy points and applications in pattern recognition and Pythagorean fuzzy topologies

Olgun, Murat; Ünver, Mehmet; Yardımcı, Şeyhmus

doi:10.1007/s00500-020-05522-2

Cited by 15 publications

(9 citation statements)

References 30 publications

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“…After that, Peng et al (2017) presented the axiomatic definitions of distance measure, similarity measure and entropy measure for PFSs. Further studies on MCDM with fuzzy sets and aggregation operators can be found in Beliakov et al (2007), Biswas and Sarkar (2018), Garg (2016), Garg and Arora (2021), Grabisch et al (2009), Kahraman (2008), Olgun et al (2019), Olgun et al (2021a), Yeni and Özçelik (2019), Ünver et al (2022a), Ünver et al (2022b), Ye et al (2022), Yolcu et al (2021), Zhang and Xu (2014), Zeng et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making

Bozyigit,

Olgun,

Ünver

2023

Informatica

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In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the non-membership degree and whose centre consists of non-negative real numbers μ and ν with the condition ${\mu ^{2}}+{\nu ^{2}}\leqslant 1$. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain centre and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general triangular norms and triangular conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a C-PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making

Bozyigit,

Olgun,

Ünver

2023

Informatica

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“…It meets the constraint that the value of the square sum of its grades is below or equal to one.i.e.0 ≤ ϑ 2 + κ 2 ≤ 1. Olgun introduced PyF points [22], Peng presented PyFS results [23], Einstein operations [24] and norms were explored [25], and an extended TOPSIS method was proposed [26]. The study also covered TODIM [27], similarity measures [28], [29], and Biswas' work on TOPSIS with entropy [30].…”

Section: Introductionmentioning

confidence: 99%

Circular Spherical Fuzzy Sugeno Weber Aggregation Operators: A Novel Uncertain Approach for Adaption a Programming Language for Social Media Platform

Ashraf,

Iqbal,

Ahmad

et al. 2023

IEEE Access

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This study's major purpose is to highlight circular spherical fuzzy sets, that happens to be a prolongation of spherical fuzzy sets. The primary purpose of this research is to demonstrate the basic operations and theorems of circular spherical fuzzy structures (C-SFS), which give an effective way for dealing with data ambiguity. Aggregation operators (AOs) play a significant role in decision-making, particularly in situations where conflicting interests need to be taken into account. The Sugeno-Weber (SW) t-conorm and t-norm are employed in the C-SFS operating rules. The study describes in detail the fundamental operating criteria for C-SFS utilizing SW t-norms and t-conorms, as well as their crucial features. Furthermore, this research presents and fully investigates two novel operators, C-SFS Sugeno Weber weighted averaging (C-SFSWWA) and C-SFS Sugeno-Weber weighted geometric (C-SFSWWG), as well as their distinct applications and desired properties. A novel approach based on the C-SFSWWA and C-SFSWWG operators is suggested to address multiple attribute decision-making (MADM) problems utilizing C-SF information. A numerical example shows how this approach may be used to adapt a programming language for social media platform analytics, followed by a comparison study to highlight its advantages. The advised approach is successful, according to an investigation of authenticity and a comparison study. In reality, the recommended aggregation operators and decision-making approach are quite useful for decision analysis.

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“…Finally, q-rung orthopair picture fuzzy sets (q-ROPFSs) [13] combine the ideas of q-rung orthopair fuzzy sets and picture fuzzy sets. These various extensions and variations of fuzzy set theory have found numerous applications in the fields such as decision-making, image processing, and pattern recognition [14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

q‐Rung Orthopair Picture Fuzzy Topological Spaces and Parameter‐Dependent Continuity: Control System Applications

Ünver,

Olgun

2023

Mathematical Problems in Engineering

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This paper presents novel concepts in fuzzy topologies, namely q -rung orthopair picture fuzzy ( q -ROPF) topology and q -rung orthopair picture fuzzy point ( q -ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called q ε -ROPF continuity, which allows for a flexible analysis of functions between q -ROPF topological spaces by incorporating an error bound ε . We define the q -neighborhood system for a q -ROPF point in a q -ROPF topological space and investigate the convergence of sequences of such points. Our results shed light on the behavior of functions and sequences in these spaces, as well as the conditions for uniqueness of limits within the realm of supports. This research has practical implications in control systems, providing valuable insights into the stability and robustness of the control strategies in the presence of small changes represented by the epsilon value.

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Pythagorean fuzzy points and applications in pattern recognition and Pythagorean fuzzy topologies

Cited by 15 publications

References 30 publications

Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making

Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making

Circular Spherical Fuzzy Sugeno Weber Aggregation Operators: A Novel Uncertain Approach for Adaption a Programming Language for Social Media Platform

q‐Rung Orthopair Picture Fuzzy Topological Spaces and Parameter‐Dependent Continuity: Control System Applications

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