Log in

Relevant bibliographies by topics / Picture fuzzy / Journal articles

To see the other types of publications on this topic, follow the link: Picture fuzzy.

Journal articles on the topic 'Picture fuzzy'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Picture fuzzy.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Cong, Cuong Bui, Roan Thi Ngan, and Le Ba Long. "Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic." Journal of Computer Science and Cybernetics 33, no. 2 (2018): 143–64. http://dx.doi.org/10.15625/1813-9663/33/2/10706.

Full text

Abstract:

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators.

APA, Harvard, Vancouver, ISO, and other styles

2

Hasan, Mohammad Kamrul, Abeda Sultana, and Nirmal Kanti Mitra. "Picture Fuzzy Relations over Picture Fuzzy Sets." American Journal of Computational Mathematics 13, no. 01 (2023): 161–84. http://dx.doi.org/10.4236/ajcm.2023.131008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Soujanya, Gundeti, and B. Surender Reddy. "N-Cubic Picture Fuzzy Linear Spaces." Indian Journal Of Science And Technology 17, no. 31 (2024): 3228–43. http://dx.doi.org/10.17485/ijst/v17i31.1793.

Full text

Abstract:

Objectives: The major objective of the present work is to apply the concept of N-cubic structure to N-Picture Fuzzy Linear Spaces. It also examines the fundamental operations such as P-union, P-intersection, R-union and R- intersection of N-Cubic Picture Fuzzy Linear Spaces, ENCPFLS and INCPFLS, and discusses in detail both of them with examples. Methods: We define P(R)-union and P(R)- intersection of N- Cubic Picture Fuzzy Linear Spaces and its properties by giving few examples with the motivation of the notion of Cubic Picture Fuzzy Linear Space (CPFLS). Findings: The notion of external and

APA, Harvard, Vancouver, ISO, and other styles

4

V.S.Subha and P.Dhanalakshmi. "Characterization of near-ring by interval valued Picture fuzzy ideals." Asia Mathematika 5, no. 3 (2021): 14——21. https://doi.org/10.5281/zenodo.5809160.

Full text

Abstract:

The aim of this paper is to introduce a concept of interval valued picture fuzzy ideals in near rings. Also we investigate the union and intersection of two interval valued picture fuzzy ideals.Moreover the union and intersection of interval valued picture fuzzy ideals is also an interval valued picture fuzzy ideal. We illustrate direct product of two interval valued picture fuzzy ideals. Furthermore we prove the image and pre-image of an interval valued picture fuzzy ideal is also an interval valued picture fuzzy ideal.  

APA, Harvard, Vancouver, ISO, and other styles

5

DOGRA, SHOVAN, and MADHUMANGAL PAL. "Picture Fuzzy Subgroup." Kragujevac Journal of Mathematics 47, no. 6 (2023): 911. http://dx.doi.org/10.46793/kgjmat2306.911d.

Full text

Abstract:

Picture fuzzy subgroup of a crisp group is established here and some properties connected to it are investigated. Also, normalized restricted picture fuzzy set, conjugate picture fuzzy subgroup, picture fuzzy coset, picture fuzzy normal subgroup and the order of picture fuzzy subgroup are deﬁned. The order of picture fuzzy subgroup is deﬁned using the cardinality of a special type of crisp subgroup. Some corresponding properties are established in this regard. Signiﬁcant Statement. Subgroup is an important algebraic structure in the ﬁeld of Pure Mathematics. Study of diﬀerent properties of sub

APA, Harvard, Vancouver, ISO, and other styles

6

Dogra, Shovan, Madhumangal Pal, and Qin Xin. "Picture fuzzy sub-hyperspace of a hyper vector space and its application in decision making problem." AIMS Mathematics 7, no. 7 (2022): 13361–82. http://dx.doi.org/10.3934/math.2022738.

Full text

Abstract:

<abstract><p>In this paper, the notion of picture fuzzy sub-hyperspace of a hyper vector space is introduced and some related results are investigated on the basis of some basic operations (intersection, union, Cartesian product etc.) on picture fuzzy sets. The concept of picture fuzzy linear transformation with respect to some picture fuzzy sub-hyperspace is initiated here and some important results are studied in this regard. It is shown that with respect to some pre-assumed picture fuzzy sub-hyperspace, linear combination of two picture fuzzy linear transformations is a picture

APA, Harvard, Vancouver, ISO, and other styles

7

Zuo, Cen, Anita Pal, and Arindam Dey. "New Concepts of Picture Fuzzy Graphs with Application." Mathematics 7, no. 5 (2019): 470. http://dx.doi.org/10.3390/math7050470.

Full text

Abstract:

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, comple

APA, Harvard, Vancouver, ISO, and other styles

8

Tamilselvan, K., V. Visalakshi, and Prasanalakshmi Balaji. "Applications of picture fuzzy filters: performance evaluation of an employee using clustering algorithm." AIMS Mathematics 8, no. 9 (2023): 21069–88. http://dx.doi.org/10.3934/math.20231073.

Full text

Abstract:

<abstract><p>This article defines the concepts of picture fuzzy filter, picture fuzzy grill, picture fuzzy section, picture fuzzy base, picture fuzzy subbase, picture fuzzy ultrafilter, as well as their fundamental features. Characteristics of the aforementioned concepts are addressed, and equivalence between the picture fuzzy filter and picture fuzzy grills is established. Real-world examples are offered to demonstrate the advantages of picture fuzzy filters in the classification of sets using a clustering technique. Illustration is provided to show the advantages of picture fuzzy

APA, Harvard, Vancouver, ISO, and other styles

9

Oktaviani, Dinni Rahma. "KAJIAN PICTURE FUZZY SUBGRUP." Jurnal Riset dan Aplikasi Matematika (JRAM) 7, no. 1 (2023): 66–79. http://dx.doi.org/10.26740/jram.v7n1.p66-79.

Full text

Abstract:

Zadeh pada tahun 1965. Himpunan fuzzy membahas mengenai ketidakpastian dari keanggotaan himpunan. Ketidakpastian dari keanggotaan himpunan ini dapat dilihat dari derajat keanggotaan himpunan fuzzy berada pada interval [0,1]. Banyak penelitian yang telah dilakukan untuk mengembangkan konsep himpunan fuzzy tersebut, salah satunya himpunan fuzzy gambar/ picture fuzzy set (PFS). PFS pertama kali diperkenalkan oleh Cuong & Kreinovich pada tahun 2013. Penelitian PFS juga telah banyak dilakukan baik dalam penerapannya maupun teorinya. Salah satu penelitian teori mengenai PFS adalah picture fuzzy

APA, Harvard, Vancouver, ISO, and other styles

10

Tamilselvan, K., and V. Visalakshi. "Identifying the Severity of Criminal Activity in Society Using Picture Fuzzy Baire Space." International Journal of Analysis and Applications 22 (April 8, 2024): 67. http://dx.doi.org/10.28924/2291-8639-22-2024-67.

Full text

Abstract:

In this paper, the idea of picture fuzzy Baire space is explored and its properties are examined. The features of picture fuzzy semi-closed and semi-open sets, picture fuzzy nowhere dense sets, picture fuzzy first and second category sets, picture fuzzy residual sets, picture fuzzy submaximal spaces, picture fuzzy strongly irresolvable spaces, picture fuzzy Gδ set, picture fuzzy Fσ set, and picture fuzzy regular closed sets are analyzed. To understand the concepts, some examples are provided. An algorithm using picture fuzzy Baire space is developed to address real-world scenarios. This method

APA, Harvard, Vancouver, ISO, and other styles

11

Das, Sankar, Ganesh Ghorai, and Madhumangal Pal. "Picture fuzzy tolerance graphs with application." Complex & Intelligent Systems 8, no. 1 (2021): 541–54. http://dx.doi.org/10.1007/s40747-021-00540-5.

Full text

Abstract:

AbstractIn this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy $$\phi $$ ϕ -tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking $$\phi $$ ϕ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy $$\phi $$ ϕ -tolerance chaingraphs which is the picture fuzzy $$\phi $$ ϕ -tolerance grap

APA, Harvard, Vancouver, ISO, and other styles

12

Razaq, Abdul, Ibtisam Masmali, Harish Garg, and Umer Shuaib. "Picture fuzzy topological spaces and associated continuous functions." AIMS Mathematics 7, no. 8 (2022): 14840–61. http://dx.doi.org/10.3934/math.2022814.

Full text

Abstract:

<abstract> <p>This paper describes a study of picture fuzzy topological spaces. We prove some basic results related to picture fuzzy sets together with the introduction of new notions such as the rank, picture fuzzy base and picture fuzzy sub-base of picture fuzzy topological spaces. With the help of these notions, we present a method to design picture fuzzy topological spaces. Furthermore, we introduce the concept of continuity to picture fuzzy topological spaces and find a necessary and sufficient condition for a picture fuzzy continuous function between two picture fuzzy topolog

APA, Harvard, Vancouver, ISO, and other styles

13

Chitra, V., and B. Maheswari. "Picture Logic Operators and Implications on Fermatean Picture Fuzzy Sets." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 193–207. https://doi.org/10.56557/ajomcor/2025/v32i29215.

Full text

Abstract:

Fermatean Picture Fuzzy sets (FPFS) represent an advanced extension of Picture Fuzzy sets and Pythagorean Picture Fuzzy sets, aimed at enhancing uncertainty modeling through the principles of Fermatean geometry. FPFS deliver heightened precision and adaptability rendering them highly applicable to complex decision-making, voting analysis and computational intelligence tasks. This work details the mathematical formulation of FPFS which explores their fundamental operations and demonstrates their practical relevance via numerical examples. The results highlight the efficacy of FPFS as a dynamic

APA, Harvard, Vancouver, ISO, and other styles

14

Cuong, Bui Cong. "Pythagorean Picture Fuzzy Sets, Part 1- basic notions." Journal of Computer Science and Cybernetics 35, no. 4 (2019): 293–304. http://dx.doi.org/10.15625/1813-9663/35/4/13898.

Full text

Abstract:

Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the pa

APA, Harvard, Vancouver, ISO, and other styles

15

Luo, Minxia, and Huifeng Long. "Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application." Symmetry 13, no. 1 (2021): 119. http://dx.doi.org/10.3390/sym13010119.

Full text

Abstract:

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted g

APA, Harvard, Vancouver, ISO, and other styles

16

Jin, Jiulin, Fuyang Zhu, and Taijie You. "Picture fuzzy tensor and its application in multi-attribute decision making." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 11995–2009. http://dx.doi.org/10.3233/jifs-210093.

Full text

Abstract:

In this paper, picture fuzzy tensor is proposed, and some related properties are studied. In the meantime, the decomposition theorem of picture fuzzy tensors is established by using picture fuzzy cutting tensors and picture fuzzy t-norm. Moreover, we propose the generalized picture fuzzy weighted interaction aggregation (GPFWIA) operator and the generalized picture fuzzy weighted interaction geometric (GPFWIG) operator. Finally, an application of picture fuzzy tensor in multi-attribute decision making (MADM) problems is presented, that is, a method is suggested to solve picture fuzzy MADM prob

APA, Harvard, Vancouver, ISO, and other styles

17

Khan, Waheed Ahmad, Babir Ali, and Abdelghani Taouti. "Bipolar Picture Fuzzy Graphs with Application." Symmetry 13, no. 8 (2021): 1427. http://dx.doi.org/10.3390/sym13081427.

Full text

Abstract:

In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different types of operations to bipolar picture fuzzy graphs and then we introduce various products of bipolar picture fuzzy graphs. Several other terms such as order and size, path, neighbourhood degrees, busy values of vertices and edges of bipolar picture fuzzy graphs are also discussed. These terminologies also

APA, Harvard, Vancouver, ISO, and other styles

18

Qiyas, Muhammad, Muhammad Ali Khan, Saifullah Khan, and Saleem Abdullah. "Concept of Yager operators with the picture fuzzy set environment and its application to emergency program selection." International Journal of Intelligent Computing and Cybernetics 13, no. 4 (2020): 455–83. http://dx.doi.org/10.1108/ijicc-06-2020-0064.

Full text

Abstract:

PurposeThe aim of this study as to find out an approach for emergency program selection.Design/methodology/approachThe authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.FindingsFirst of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fu

APA, Harvard, Vancouver, ISO, and other styles

19

Lu, Hanchuan, Ahmed Mostafa Khalil, W. Alharbi, and M. A. El-Gayar. "A new type of generalized picture fuzzy soft set and its application in decision making." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 12459–75. http://dx.doi.org/10.3233/jifs-201706.

Full text

Abstract:

In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

APA, Harvard, Vancouver, ISO, and other styles

20

Shi, Dali, M. N. Abu_Shugair, S. E. Abbas, and Ismail Ibedou. "Picture Fuzzy Modal Ideal Multifunctions." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5956. https://doi.org/10.29020/nybg.ejpam.v18i2.5956.

Full text

Abstract:

This paper introduces the notion of a picture fuzzy modal topological structures (PFMTSs) via ideal. These structures are grounded on novel picture fuzzy topological operators for closure and interior types, utilizing the two standard picture fuzzy modal operators $\square $ and $\Diamond $. The paper discusses several fundamental properties of picture fuzzy multifunctions PFMs via ideals. The results indicate that some properties considered satisfactory in the intuitionistic fuzzy modal topological structures, as defined by Atanassov in 2022, are not fulfilled. Also, we introduce many types o

APA, Harvard, Vancouver, ISO, and other styles

21

Khamrot, Pannawit, and Thiti Gaketem. "On picture fuzzy almost ideals of semigroups." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 6 (2024): 1817–30. http://dx.doi.org/10.47974/jdmsc-1820.

Full text

Abstract:

In this paper, we give the concept of picture fuzzy almost ideals, minimal picture fuzzy almost ideals, and prime (semiprime, strongly prime) picture fuzzy almost ideals in semigroups. We prove the basic properties of picture fuzzy almost ideals in semigroups. Moreover, we investigate the connection between almost ideals and picture fuzzy almost ideals in semigroups.

APA, Harvard, Vancouver, ISO, and other styles

22

Khan, Muhammad, Poom Kumam, Shahzaib Ashraf, and Wiyada Kumam. "Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems." Symmetry 11, no. 3 (2019): 415. http://dx.doi.org/10.3390/sym11030415.

Full text

Abstract:

In this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersection, restricted union, restricted intersection and also prove the De Morgan’s laws for picture fuzzy soft information. We investigate upper and lower substitution for both picture fuzzy sets and generalized picture fuzzy soft sets. Meanwhile, the related proofs are given in detail. Finally, we propose an algorithm to deal with generalized picture f

APA, Harvard, Vancouver, ISO, and other styles

23

Ali, Zeeshan, Tahir Mahmood, and Miin-Shen Yang. "Aczel–Alsina Power Aggregation Operators for Complex Picture Fuzzy (CPF) Sets with Application in CPF Multi-Attribute Decision Making." Symmetry 15, no. 3 (2023): 651. http://dx.doi.org/10.3390/sym15030651.

Full text

Abstract:

Complex picture fuzzy sets are the updated version of the complex intuitionistic fuzzy sets. A complex picture fuzzy set covers three major grades such as membership, abstinence, and falsity with a prominent characteristic in which the sum of the triplet will be contained in the unit interval. In this scenario, we derive the power aggregation operators based on the Aczel–Alsina operational laws for managing the complex picture of fuzzy values. These complex picture fuzzy power aggregation operators are complex picture fuzzy Aczel–Alsina power averaging, complex picture fuzzy Aczel–Alsina weigh

APA, Harvard, Vancouver, ISO, and other styles

24

Ali, Zeeshan, Tahir Mahmood, and Kifayat Ullah. "Picture Hesitant Fuzzy Clustering Based on Generalized Picture Hesitant Fuzzy Distance Measures." Knowledge 1, no. 1 (2021): 40–51. http://dx.doi.org/10.3390/knowledge1010005.

Full text

Abstract:

Certain scholars have generalized the theory of fuzzy set, but the theory of picture hesitant fuzzy set (PHFS) has received massive attention from distinguished scholars. PHFS is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with awkward and complicated information in real-life issues. The well-known characteristic of PHFS is that the sum of the maximum of the membership, abstinence, and non-membership degree is limited to the unit interval. This manuscript aims to develop some generalized picture hesitant distance measures (GPHDMs) as a generalization of gene

APA, Harvard, Vancouver, ISO, and other styles

25

V. Chitra. "Fermatean Picture Fuzzy Sets." Advances in Nonlinear Variational Inequalities 28, no. 1s (2024): 390–99. https://doi.org/10.52783/anvi.v28.2441.

Full text

Abstract:

This paper introduces the concept of the Fermatean Picture Fuzzy Set (FPFS). We define several operations on these set. Additionally, we establish the concepts of images and preimages within the context of FPFS. Finally, we extend our discussion to the Fermatean Picture fuzzy topological space and define the properties using the theorems.

APA, Harvard, Vancouver, ISO, and other styles

26

Son, Le Hoang. "DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets." Expert Systems with Applications 42, no. 1 (2015): 51–66. http://dx.doi.org/10.1016/j.eswa.2014.07.026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Son, Le Hoang, Pham Van Viet, and Pham Van Hai. "Picture inference system: a new fuzzy inference system on picture fuzzy set." Applied Intelligence 46, no. 3 (2016): 652–69. http://dx.doi.org/10.1007/s10489-016-0856-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Muhiuddin, Ghulam, Nabilah Abughazalah, Afaf Aljuhani, and Manivannan Balamurugan. "Tripolar Picture Fuzzy Ideals of BCK-Algebras." Symmetry 14, no. 8 (2022): 1562. http://dx.doi.org/10.3390/sym14081562.

Full text

Abstract:

In this paper, we acquaint new kinds of ideals of BCK-algebras built on tripolar picture fuzzy structures. In fact, the notions of tripolar picture fuzzy ideal, tripolar picture fuzzy implicative ideal (commutative ideal) of BCK-algebra are introduced, and related properties are studied. Also, a relation among tripolar picture fuzzy ideal, and tripolar picture fuzzy implicative ideal is well-known. Furthermore, it is shown that a tripolar picture fuzzy implicative ideal of BCK-algebra may be a tripolar picture fuzzy ideal, but the converse is not correct in common. Further, it is obtained that

APA, Harvard, Vancouver, ISO, and other styles

29

Gundeti, Soujanya, and Surender Reddy B. "N-Cubic Picture Fuzzy Linear Spaces." Indian Journal of Science and Technology 17, no. 31 (2024): 3228–43. https://doi.org/10.17485/IJST/v17i31.1793.

Full text

Abstract:

Abstract <strong>Objectives:</strong> The major objective of the present work is to apply the concept of N-cubic structure to N-Picture Fuzzy Linear Spaces. It also examines the fundamental operations such as P-union, P-intersection, R-union and R- intersection of N-Cubic Picture Fuzzy Linear Spaces, ENCPFLS and INCPFLS, and discusses in detail both of them with examples.<strong> Methods:</strong> We define P(R)-union and P(R)- intersection of N- Cubic Picture Fuzzy Linear Spaces and its properties by giving few examples with the motivation of the notion of Cubic Picture Fuzzy L

APA, Harvard, Vancouver, ISO, and other styles

30

DOGRA, SHOVAN, and MADHUMANGAL PAL. "Picture Fuzzy Subspace of a Crisp Vector Space." Kragujevac Journal of Mathematics 47, no. 4 (2003): 577–97. http://dx.doi.org/10.46793/kgjmat2304.577d.

Full text

Abstract:

In this paper, the notion of picture fuzzy subspace of a crisp vector space is established and some related properties are explored on the basis of some basic operations (intersection, Cartesian product, union, (θ, ϕ, ψ)-cut etc.) on picture fuzzy sets. Direct sum of two picture fuzzy subspaces is initiated here over the direct sum of two crisp vector spaces. Also, the concepts of picture fuzzy linear transformation and picture fuzzy linearly independent set of vectors are introduced and some corresponding results are presented. Isomorphism between two picture fuzzy subspaces is developed here

APA, Harvard, Vancouver, ISO, and other styles

31

Tekin, Özlem. "A Picture Fuzzy Based Approach Using Proximal Relator Spaces." Turkish Journal of Mathematics and Computer Science 17, no. 1 (2025): 232–42. https://doi.org/10.47000/tjmcs.1579906.

Full text

Abstract:

Picture fuzzy sets are extensions of the fuzzy sets and the intuitonistic fuzzy sets which consist of membership, a neutral membership and a non-membership degrees. In this paper, we define the picture fuzzy proximity relations which are extension of picture fuzzy sets and fuzzy proximity relations, and give some examples. Also, we give the definition of picture fuzzy spatial and descriptive Lodato proximity space.

APA, Harvard, Vancouver, ISO, and other styles

32

Luqman, Anam, Muhammad Akram, and Ali N. A. Koam. "Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment." Mathematics 7, no. 6 (2019): 496. http://dx.doi.org/10.3390/math7060496.

Full text

Abstract:

In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different lev

APA, Harvard, Vancouver, ISO, and other styles

33

Cuong, Bui Cong. "PYTHAGOREAN PICTURE FUZZY SETS(PPFS), PART 2- SOME MAIN PICTURE LOGIC OPERATORS ON PPFS AND SOME PICTURE INFERENCE PROCESSES IN PPF SYSTEMS." Journal of Computer Science and Cybernetics 38, no. 1 (2022): 1–14. http://dx.doi.org/10.15625/1813-9663/38/1/15992.

Full text

Abstract:

Pythagorean picture fuzzy set (PPFS) - is a combination of Picture fuzzy set with the Yager’s Pythagorean fuzzy set [12-14]. In the first part of the paper [17] we considered basic notions on PPFS as set operators of PPFS. Unfortunately, we have not papers [18,19, 20] about spherical fuzzy sets with the same definition with some operators and applications to multi attribute group decision making problems. Now in the second part, we will present some main operators in picture fuzzy logic on PPFS: picture negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.

APA, Harvard, Vancouver, ISO, and other styles

34

WEI, Guiwu. "PICTURE FUZZY CROSS-ENTROPY FOR MULTIPLE ATTRIBUTE DECISION MAKING PROBLEMS." Journal of Business Economics and Management 17, no. 4 (2016): 491–502. http://dx.doi.org/10.3846/16111699.2016.1197147.

Full text

Abstract:

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. The advantage of picture fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the picture fuzzy sets are suitable for capturing imprecise, uncertain, and inconsistent information in the multiple attribute decision making analysis. Thus, the cross entropy of picture fuzzy sets, called picture fuzzy cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multiple attribute decision making method based on the proposed picture f

APA, Harvard, Vancouver, ISO, and other styles

35

Chen, Zhihua, Waheed Ahmad Khan, and Aysha Khan. "Concepts of Picture Fuzzy Line Graphs and Their Applications in Data Analysis." Symmetry 15, no. 5 (2023): 1018. http://dx.doi.org/10.3390/sym15051018.

Full text

Abstract:

The process of bundling and clustering hasno clear boundaries; hence, their analysis contains uncertainities. Thus, it is more suitable to deal withbundling and clusteringby usingfuzzy graphs. Since picture fuzzy sets (PFSs) are more accurate, compatible, and flexible compared to the other generalizations of fuzzy sets (FSs),hence, it would be more effective to present edge bundling and clustering usingpicture fuzzy line graphs (PFLGs). The aim of our study is to introduce the notions of picture fuzzy intersection graphs (PFIGs) and picture fuzzy line graphs (PFLGs). These concepts are the gen

APA, Harvard, Vancouver, ISO, and other styles

36

Khoshaim, Ahmad Bakr, Muhammad Qiyas, Saleem Abdullah, Muhammad Naeem, and Muneeza. "An approach for supplier selection problem based on picture cubic fuzzy aggregation operators." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 10145–62. http://dx.doi.org/10.3233/jifs-200194.

Full text

Abstract:

This article is an advanced approach to picture fuzzy set through the application of cubic set theory. For instance, we establish the idea of the picture cubic fuzzy sets (PCFSs) theory and define several operations for PCFS. Also, presented some weighted aggregation operators under picture cubic fuzzy information, so called picture cubic fuzzy weighted averaging (PCFWA) operator, picture cubic fuzzy order weighted averaging (PCFOWA) operator, picture cubic fuzzy weighted geometric (PCFWG) operator, and picture cubic fuzzy order weighted geometric (PCFOWG) operator. Further, we study their fun

APA, Harvard, Vancouver, ISO, and other styles

37

Naeem, Khalid, Samet Memiş, and Sumbul Azeem. "Picture Fuzzy Topological Spaces with Picture Fuzzy Prevalence Effect Method for Group Decision-Making." Turkish Journal of Mathematics and Computer Science 17, no. 1 (2025): 212–31. https://doi.org/10.47000/tjmcs.1615488.

Full text

Abstract:

The concept of picture fuzzy sets (pf-sets) expands intuitionistic fuzzy sets to model uncertain information, mainly when handling the feedbacks ``Yes'', ``No'', and ``Abstain''. Recently, the definitions of pf-sets and their elemental operations have been revised to address some inconsistencies in Cuong’s original definitions. Building on these two studies, our first objective is to redefine the concept of picture fuzzy topology and investigate its properties, such as limit points and compactness. We then propose a group decision-making technique called the Picture Fuzzy Prevalence Effect Met

APA, Harvard, Vancouver, ISO, and other styles

38

Wang, Rui, Jie Wang, Hui Gao, and Guiwu Wei. "Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk." Symmetry 11, no. 1 (2018): 6. http://dx.doi.org/10.3390/sym11010006.

Full text

Abstract:

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the P

APA, Harvard, Vancouver, ISO, and other styles

39

Zhang, Hongran, Runtong Zhang, Huiqun Huang, and Jun Wang. "Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making." Symmetry 10, no. 11 (2018): 593. http://dx.doi.org/10.3390/sym10110593.

Full text

Abstract:

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and wides

APA, Harvard, Vancouver, ISO, and other styles

40

Zhao, Ruirui, Minxia Luo, and Shenggang Li. "A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application." Symmetry 13, no. 3 (2021): 436. http://dx.doi.org/10.3390/sym13030436.

Full text

Abstract:

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, w

APA, Harvard, Vancouver, ISO, and other styles

41

Dhivya, J., K. Meena, and M. N. Saroja. "A New Technique for solving Picture Fuzzy Differential Equation." Journal of Physics: Conference Series 2070, no. 1 (2021): 012021. http://dx.doi.org/10.1088/1742-6596/2070/1/012021.

Full text

Abstract:

Abstract Picture Fuzzy set (PFS) is an extension of fuzzy set (FS) and intuitionistic fuzzy set (IFS) that can model the uncertainty by integrating the concept of positive, negative and neutral membership degree of an element. In this paper, the solution of Picture Fuzzy ordinary differential equation of first order by means of picture fuzzy number is exemplified and intend to define the picture fuzzy number for (∝, δ, β)-cut. Finally, we illustrate the numerical example for drug distribution in human body for different drug levels is discussed for determining its effectiveness and practicalit

APA, Harvard, Vancouver, ISO, and other styles

42

Khan, Saifullah, Saleem Abdullah, Lazim Abdullah, and Shahzaib Ashraf. "Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems." Mathematics 7, no. 7 (2019): 608. http://dx.doi.org/10.3390/math7070608.

Full text

Abstract:

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted ave

APA, Harvard, Vancouver, ISO, and other styles

43

Ahmad, Nur Azlida, and Mohammad Izat Emir Zulkifly. "Generation of Picture Fuzzy B-Spline Curve Interpolation with Open Uniform Knot Vector." Semarak International Journal of Applied Sciences and Engineering Technology 3, no. 1 (2024): 18–28. http://dx.doi.org/10.37934/sijaset.3.1.1828.

Full text

Abstract:

An open uniform knot vector ensures that the resulting B-spline curve starts at the first control point and ends at the last control points, providing a more intuitive and predictable shape at the boundaries. When dealing uncertainty in data, open uniform knot vector B-spline are particularly useful because they offer several advantages. In this paper, the picture fuzzy set approach was used to introduce the picture fuzzy B-spline curve interpolation model with open uniform knot vector. Firstly, picture fuzzy control point relation is introduced by using basic concepts of picture fuzzy set whi

APA, Harvard, Vancouver, ISO, and other styles

44

Ahmad, Nur Azlida, and Mohammad Izat Emir Zulkifly. "Generation of Picture Fuzzy B-Spline Curve Interpolation with Open Uniform Knot Vector." Semarak International Journal of Applied Sciences and Engineering Technology 3, no. 1 (2025): 18–28. https://doi.org/10.37934/sijaset.3.1.1828a.

Full text

Abstract:

An open uniform knot vector ensures that the resulting B-spline curve starts at the first control point and ends at the last control points, providing a more intuitive and predictable shape at the boundaries. When dealing uncertainty in data, open uniform knot vector B-spline are particularly useful because they offer several advantages. In this paper, the picture fuzzy set approach was used to introduce the picture fuzzy B-spline curve interpolation model with open uniform knot vector. Firstly, picture fuzzy control point relation is introduced by using basic concepts of picture fuzzy set whi

APA, Harvard, Vancouver, ISO, and other styles

45

Mathew, Bibin, Sunil Jacob John, and José Carlos R. Alcantud. "Multi-Granulation Picture Hesitant Fuzzy Rough Sets." Symmetry 12, no. 3 (2020): 362. http://dx.doi.org/10.3390/sym12030362.

Full text

Abstract:

We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimist

APA, Harvard, Vancouver, ISO, and other styles

46

Hasan, Mohammad Kamrul, Abeda Sultana, and Nirmal Kanti Mitra. "Compositions of Picture Fuzzy Relations with Application in Decision Making." European Journal of Mathematics and Statistics 4, no. 2 (2023): 19–28. http://dx.doi.org/10.24018/ejmath.2202.4.2.188.

Full text

Abstract:

Picture fuzzy relation is an important and powerful concept which is suitable for describing correspondences between objects. It represents the strength of association of the elements of picture fuzzy sets. In this paper we have defined min-max composition for picture fuzzy relations and some properties are explored based on this definition. Also we have discussed some properties of max-min composition for picture fuzzy relations. Finally, an application is discussed as illustration to show how the picture fuzzy relation are applied in decision making.

APA, Harvard, Vancouver, ISO, and other styles

47

He, Jiahuan, Xindi Wang, Runtong Zhang, and Li Li. "Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment." Mathematics 7, no. 5 (2019): 468. http://dx.doi.org/10.3390/math7050468.

Full text

Abstract:

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules

APA, Harvard, Vancouver, ISO, and other styles

48

Sulaiman, Raden, Yuliani Puji Astuti, Dwi Nur Yunianti, and N. Azzah Awang. "On the Picture Fuzzy-TOPSIS Method." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1727–36. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5225.

Full text

Abstract:

Research related to the Technique for Order Preference by Similarity to Ideal Solotion (TOPSIS) method have been developed using fuzzy or intuitionistic fuzzy sets. In this article, we provide the development of the topsis method based on the generalization of fuzzy sets. We present a new method of topsis based on picture fuzzy sets. In this article, we propose steps of TOPSIS picture fuzzy sets method. Finally, we presented the illustrative example of this method.

APA, Harvard, Vancouver, ISO, and other styles

49

Panpho, Phakakorn, and Pairote Yiarayong. "On picture fuzzy ideals on commutative rings." Bulletin of Electrical Engineering and Informatics 11, no. 5 (2022): 2783–88. http://dx.doi.org/10.11591/eei.v11i5.3482.

Full text

Abstract:

In this paper, we focus on combining the theories of picture fuzzy sets on rings and establishing a new framework for picture fuzzy sets on commutative rings. The aim of this manuscript is to apply picture fuzzy set for dealing with several kinds of theories in commutative rings. Moreover, we introduce the notions of picture fuzzy ideals on commutative rings and some properties of them are obtained. Finally, we give suitable definitions of the operations of picture fuzzy ideals over a commutative ring, as composition, product and intersection.

APA, Harvard, Vancouver, ISO, and other styles

50

Meliya, Kiky, Admi Nazra, and Nova Noliza Bakar. "Classification of Tutoring Teachers Uses the Concept of The Correlation Coefficient." International Journal of Progressive Sciences and Technologies 40, no. 2 (2023): 139. http://dx.doi.org/10.52155/ijpsat.v40.2.5614.

Full text

Abstract:

Picture Fuzzy Set is a development of the intuitionistic fuzzy set concept. Picture Fuzzy Set is modeled in a situation when facing human opinion which involves more answers: yes, abstention or neutral, no and rejection. Therefore, to deal with situations like this, the concept of the proposed correlation coefficient is used to calculate the degree of correlation between picture fuzzy set that aim to group different objects. The correlation concept used in picture fuzzy set uses two formulas. And in deciding on a problem, we use the grouping method for picture fuzzy sets introduced by Xu et al

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!